Table of Contents
Overview
Definition and Scope
Computational mechanics is the discipline that employs computational methods to study phenomena governed by the principles of mechanics. This field emerged as a significant area of research in the 1970s and 1980s, focusing on the reconstruction of attractor geometry from measurement time series to understand weak fluid turbulence.[1.1] Over the years, computational mechanics has evolved to encompass a wide range of theoretical and practical applications, including the closed-form analysis of both finite- and infinite-state Markov and non-Markov stochastic processes, which can be either ergodic or nonergodic.[2.1] The International Association of Computational Mechanics (IACM) was established to promote advancements in this discipline, fostering collaboration among scholars and practitioners globally. Since its inception in 1984, IACM has been affiliated with the International Union of Theoretical and Applied Mechanics (IUTAM), further enhancing its role in the field.[3.1] The impact of computational mechanics on science and technology has been profound, effectively transforming classical Newtonian theory into practical tools for prediction and simulation, thereby bridging the gap between theoretical concepts and real-world applications.[31.1]Key Principles and Concepts
Computational mechanics is fundamentally rooted in the integration of traditional engineering disciplines, such as civil engineering, structures, geomechanics, hydraulics, and construction. This integration unifies various subject matters related to the analysis, simulation, and modeling of physical engineering problems through computational methods.[19.1] The field has evolved significantly since its inception in the 1970s and 1980s, focusing initially on identifying strange attractors as mechanisms driving weak fluid turbulence and estimating equations of motion from complex time series.[11.1] A key principle in computational mechanics is the application of numerical methods and algorithms, which allow engineers to transform complex problems into manageable simulations. This capability is essential for modeling intricate mechanical systems with remarkable accuracy, paving the way for innovative solutions.[21.1] The emergence of machine learning techniques, particularly Physics-Inspired Neural Networks (PINNs), has further enhanced traditional engineering methods by providing faster and more efficient computational solutions.[20.1] The role of artificial intelligence (AI) and machine learning (ML) in computational mechanics is increasingly prominent. These technologies are revolutionizing traditional design, manufacturing, and maintenance processes by enabling engineers to generate optimized designs more rapidly and efficiently, leading to improved product performance and reduced development cycles.[8.1] The breadth of AI applications in mechanical engineering includes predictive maintenance, design optimization, and quality control, underscoring the transformative influence of these technologies on the field.[6.1] The study of nonlinear dynamics and strange attractors is crucial for understanding complex systems. Strange attractors, first discovered by Lorenz, are fundamental to the comprehension of complexity, illustrating how complex systems navigate through phase space in shapes reminiscent of butterfly wings.[15.1] These attractors are pivotal in enhancing our ability to model and predict behaviors in complex systems, particularly within the realm of computational mechanics.[25.1] The Journal of Computational and Nonlinear Dynamics serves as an important medium for the rapid dissemination of original research results in both theoretical and applied aspects of computational and nonlinear dynamics, thereby contributing to advancements in this scientific and technological area.[25.1]History
Evolution of Computational Methods
The evolution of computational methods in computational mechanics began in the 1970s and early 1980s, a period characterized by significant advancements in understanding complex systems. Researchers during this era focused on identifying strange attractors as mechanisms driving weak fluid turbulence, employing methods to reconstruct attractor geometry from measurement time series.[49.1] This foundational work established the basis for computational mechanics, which seeks to define patterns and structures to detect and quantify the organization of complex systems.[1.1] As the field progressed, computational mechanics broadened its scope to encompass a wide range of theoretical and practical applications. It has notably enabled closed-form analyses of both finite- and infinite-state Markov and non-Markov stochastic processes, crucial for understanding ergodic and nonergodic systems.[2.1] The formation of the International Association of Computational Mechanics (IACM) in 1984 further advanced the field by fostering collaboration among scholars and practitioners.[3.1] Advanced computational methods, especially in simulating physical phenomena, have become essential in structural engineering and mechanics. Techniques such as finite element analysis (FEM) have emerged as vital tools for engineering design analysis and scientific modeling across various domains, including material mechanics, fluid flow, and heat conduction.[44.1] The year 2021 marked the eightieth anniversary of FEM, highlighting its importance in addressing complex engineering challenges.[44.1] Recent advancements in nonlinear mathematics and stochastic processes have significantly influenced the development of computational methods in stochastic mechanics. A comprehensive assessment of these computational procedures reveals both theoretical developments and practical applications, structured into four sections.[40.1] A detailed review of techniques for simulating Gaussian and non-Gaussian stochastic processes is essential, as these methods are crucial for addressing uncertainties in various applications.[41.1] Furthermore, advanced computational methods have been applied to the nonlinear mechanics of solids and fluids, encompassing large deformations, nonlinear dynamics, and coupled problems, which are vital for accurately modeling complex real-world scenarios such as earthquake analysis and fluid dynamics.[42.1] This evolution in computational methods aims to identify necessary modeling, methodological, and computational advancements to tackle emerging research challenges, thereby expanding the theoretical and practical interest in nonlinear dynamics.[43.1]In this section:
Applications
Engineering Applications
Computational mechanics has become a pivotal tool in various engineering disciplines, particularly in enhancing our understanding of the mechanical behavior of biological tissues under diverse physiological and pathological conditions. By encompassing the entire kinematic space, refined constitutive models have been developed to provide deeper insights into tissue mechanics, which are essential for characterizing the three-dimensional mechanical behavior of soft tissues.[77.1] These investigations have demonstrated that viscoelasticity plays a crucial role in regulating spatiotemporal tissue organization, influencing tissue growth dynamics and leading to phenomena such as symmetry-breaking instabilities like buckling.[78.1] Furthermore, advanced prediction methods have been verified to effectively forecast the mechanical responses of soft tissues, thereby aiding in the prevention of potential tissue damage during surgical operations.[79.1] In the realm of cardiac surgery, computational modeling has emerged as a valuable tool for evaluating the effects of clinical devices and surgical procedures. This application demonstrates the capabilities of computational mechanics in optimizing surgical outcomes and improving patient care.[80.1] Furthermore, in neurosurgery, computer-integrated systems that utilize computational mechanics have been shown to enhance surgical accuracy and efficiency, ultimately leading to better clinical outcomes.[81.1] The field of Computational Fluid Dynamics (CFD), a subset of computational mechanics, plays a critical role in simulating fluid behavior under various conditions. This capability is essential for optimizing performance and ensuring safety in engineering applications.[82.1] The continuous evolution of computational mechanics, driven by advancements in computational power and algorithms, has enabled increasingly detailed and accurate simulations, thereby revolutionizing the modeling of intricate mechanical systems.[83.1] The integration of machine learning techniques with computational mechanics is increasingly recognized for its potential to enhance predictive capabilities in engineering applications. Recent advances in machine learning and deep learning are being applied to computational mechanics, focusing on the development and understanding of coupled machine learning and physical modeling for complex physical systems.[85.1] This trend has been significantly supported by the extraordinary progress of digital computers over the last few decades, which has had a profound impact on information science and technology, including computational mechanics.[86.1] As a result, the combination of data-driven approaches with traditional physical modeling is paving the way for innovative solutions across various industrial domains.Scientific Applications
The mechanical properties of biological soft tissues are crucial in various scientific applications, particularly in biomechanics and tissue engineering. One significant challenge in this field is the experimental mechanical characterization and constitutive modeling of these tissues, which necessitates a thorough understanding of the material properties and their appropriate applications.[100.1] Additionally, the personalization of constitutive parameters through non-invasive and non-destructive bedside testing methods presents another layer of complexity.[101.1] To accurately model the mechanical behavior of soft tissues, researchers employ a variety of testing techniques at different scales. These techniques are essential for developing accurate tissue simulants and numerical models, which are vital for advancing protective measures against human injury.[102.1] The response of soft tissues to mechanical cues, as well as extracellular and intracellular signals, is influenced by biological events ranging from embryonic development to aging and disease.[103.1] This response is typically characterized by nonlinear, viscoelastic, and anisotropic behavior, which emerges from the hierarchical structure of the tissues.[103.1] Various modeling approaches have been developed to capture the mechanical behavior of soft tissues. These models often incorporate factors such as cell density fields and cytokine concentrations, which influence tissue composition, mechanical properties, and active stress.[104.1] However, these models may oversimplify the underlying biological processes, indicating a need for further refinement. Recent advancements in three-dimensional (3D) bioprinting techniques have significantly enhanced tissue engineering capabilities. These methods facilitate the creation of biological constructs that closely resemble native tissues, allowing for better integration with the host tissue's extracellular matrix.[105.1] This integration is crucial for the successful application of engineered tissues in medical and therapeutic contexts, highlighting the importance of computational mechanics in advancing scientific applications in this field.In this section:
Recent Advancements
Integration with Machine Learning and AI
The integration of machine learning (ML) and artificial intelligence (AI) into computational mechanics has revolutionized traditional methodologies, providing innovative solutions to complex mechanical challenges. A key benefit of this integration is the development of efficient surrogate or reduced-order models, which significantly enhance computational efficiency when traditional methods become impractical.[128.1] Moreover, ML techniques have been instrumental in improving accuracy in scenarios where conventional methods fall short, particularly through the assimilation of additional data.[128.1] Numerous applications underscore the potential of ML in computational mechanics. For example, deep neural networks (DNNs) have been utilized to solve boundary value problems (BVPs), showcasing the capability of deep learning tools to address significant mechanical issues.[126.1] Additionally, various ML techniques, such as artificial neural networks and ensemble methods, have been applied across different branches of computational mechanics, including solids, structures, and fluids.[127.1] Notable examples include the use of physics-informed neural networks for reliability assessments in structural dynamics and the application of graph neural networks for predicting structural responses.[127.1] In the aerospace sector, AI integration has led to advancements in predictive maintenance, quality control, and manufacturing efficiency.[132.1] Companies like GE Aerospace and Boeing have harnessed AI technologies to enhance operational processes, including real-time monitoring of aircraft engines and automation of manufacturing tasks.[132.1] The rapid advancement of aerospace technology, coupled with the exponential growth of available data, has further accelerated AI adoption across the industry.[135.1] However, integrating ML and AI into existing computational mechanics workflows presents significant challenges. Engineers must balance traditional computational methods with new data-driven approaches, necessitating collaborative solutions to address architectural challenges.[141.1] As industries increasingly adopt neural networks, the engineering challenges related to model optimization and deployment infrastructure will require innovative strategies.[141.1] Furthermore, the evolving landscape of data engineering introduces hurdles that must be carefully considered when incorporating generative AI into workflows.[142.1] Despite these challenges, deep learning has shown a strong ability to integrate across disciplines, enabling engineers and researchers to effectively address various issues in complex natural environments, such as geological disaster prediction and engineering design.[143.1]Advances in Computational Power and Algorithms
Recent advancements in computational mechanics have been significantly influenced by improvements in computational power and the development of sophisticated algorithms. This field, situated at the intersection of mechanics, applied mathematics, and computer science, has evolved into a dominant area of study within the Engineering Mechanics Institute (EMI).[118.1] This evolution is driven by the enhanced capabilities of modern computing systems, which have dramatically improved the ability to perform analyses that inform engineering design decisions.[124.1] The transformation of engineering design processes through advancements in computational power and algorithms is evident in the increased use of computational modeling. Over the past fifty years, the ability to conduct analysis as a precursor to decision-making in engineering design has grown significantly, with modern computing systems and advanced numerical methods establishing computational modeling as a vital tool for producing optimized designs.[124.1] In the aerospace industry, computational fluid dynamics (CFD) has become crucial for the design and analysis of both new and derivative aircraft, underscoring its essential role in industry practices.[125.1] Additionally, the integration of machine learning and deep learning into computational mechanics has focused on understanding and applying coupled machine learning and physical modeling for complex systems.[122.1] This integration highlights the ongoing evolution of engineering applications, emphasizing the critical role of mathematical modeling in enhancing the accuracy and efficiency of simulations across various industrial domains.[129.1] Significant developments in mathematical modeling have emerged from recent advancements in computational mechanics, leading to novel numerical models that effectively address solid and fluid problems, including solid-fluid interactions.[136.1] These advancements enhance our understanding of complex physical phenomena and have been applied across a broad range of fields, including civil, offshore, aerospace, automotive, naval, and nuclear structures.[131.1] The importance of these developments is underscored by events such as the 7th International Congress on Computational Mechanics and Simulation, which showcases research on the application of modern computing methods to analyze these diverse applications.[119.1] Furthermore, the ongoing evolution of mathematical methods continues to address various challenges in applied mechanics and mechanical engineering, as highlighted by conferences like the '1st International Conference on Mathematical Modeling in Mechanics and Engineering'.[137.1]Challenges And Considerations
Limitations of Current Methods
Computational mechanics, while a powerful tool in engineering, faces several limitations that impact its effectiveness and applicability. One of the primary challenges is the computational complexity of simulations, which often require significant processing power and time, particularly for high-fidelity models that are resource-intensive and may necessitate the use of high-performance computing (HPC) resources.[193.1] This complexity can hinder the ability to conduct timely analyses, especially in scenarios where rapid decision-making is crucial. Moreover, the accuracy of computational models is another critical consideration. The reliability of simulations heavily depends on the quality of input data and the assumptions made within the models. Inaccurate material properties or boundary conditions can lead to erroneous results, which may compromise the integrity of engineering designs.[193.1] This trade-off between model accuracy and computational efficiency is a persistent issue, as achieving better accuracy often requires additional computational effort, which can be at odds with the need for timely results.[158.1] Additionally, the unpredictable nature of environmental factors poses significant challenges. Natural stimuli, such as variations in temperature, humidity, and other environmental conditions, can introduce randomness that deterministic models may fail to capture. This unpredictability complicates the modeling of physical systems, as it requires the integration of stochastic methods, such as the stochastic finite element method (SFEM), to better account for these uncertainties.[186.1] However, the implementation of such advanced techniques can further exacerbate computational demands.Future Directions in Research
The future of computational mechanics is set to be revolutionized by the strategic integration of machine learning (ML) and advancements in high-performance computing (HPC). ML techniques are increasingly being applied to enhance predictive accuracy and reduce computational costs across various domains, such as Structural/Solid Mechanics, Fluid Mechanics, and Fluid-Structure Interaction. These techniques offer the potential to solve complex systems of equations with precision comparable to traditional methods, while also improving the efficiency of navigating intricate design spaces through iterative learning processes [174.1][175.1]. HPC advancements are equally pivotal, enabling the execution of large-scale simulations that were once beyond reach. This has particularly transformed computational fluid dynamics (CFD), allowing for more precise simulations of turbulence and its effects on momentum, heat, and mass transfer [165.1]. The evolution of HPC systems has been driven by the need to meet the demands of increasingly complex scientific computing tasks, leading to innovations in architectural design and computational techniques, such as distributed and shared memory parallelism [167.1][166.1]. A promising area of future research lies in the synergy between ML and traditional computational methods, particularly for applications involving complex geometries in geological and civil engineering. Surrogate modeling approaches, which leverage synthetic data from advanced simulations, are expected to significantly advance the modeling, simulation, and optimization of complex systems across various industrial domains [159.1][162.1]. This integration not only enhances design processes but also opens new avenues for innovation in computational mechanics.In this section:
Computational ComplexityComputational ModelsNatureEnvironmental FactorsFinite Element Method
Specializations Within Computational Mechanics
Computational Fluid Dynamics
Recent advancements in computational fluid dynamics (CFD) have significantly enhanced the accuracy and efficiency of simulations, particularly in the context of fluid-structure interaction (FSI) problems. One notable development is the improved smooth particle hydrodynamics-finite element method (SPH-FEM) coupling approach. This method addresses the challenges associated with the interaction of physical quantities at the fluid-structure interface by employing an interface particle coupling strategy, which utilizes two types of virtual interface particles to facilitate this interaction.[200.1] The Particle Finite Element Method (PFEM) is an innovative computational technique that integrates the strengths of particle-based methods with traditional finite element approaches.[201.1] This method represents a significant advancement in the field of computational fluid dynamics, particularly in enhancing the modeling capabilities for complex fluid behaviors. By leveraging the advantages of both methodologies, PFEM aims to improve the accuracy and efficiency of simulations, especially in applications related to fluid-structure interaction.[201.1] Moreover, advancements in finite element methods, such as adaptable hp-finite/infinite element approximations and Perfectly Matched Layer (PML) approximations, have further contributed to the refinement of simulations in computational acoustics and fluid-structure interaction. These techniques enhance the computational domain description, leading to improved simulation outcomes.[199.1] Together, these advancements represent a significant evolution in the field of computational fluid dynamics, enabling more precise and efficient analyses of fluid interactions with structures.Computational Solid Mechanics
Computational solid mechanics is a subdiscipline of mechanics that focuses on the development and solving of complex mathematical models representing physical phenomena through modern computing methods, including intensive computer simulations. This field has significant applications in areas such as renewable energy, biomechanics, sports engineering, defense, and manufacturing.[195.1] Computational mechanics is concerned with the use of computational methods to study phenomena governed by the principles of mechanics, and it has evolved as a distinct discipline alongside theoretical and experimental sciences.[196.1] The mathematical foundations of computational mechanics are closely related to partial differential equations, linear algebra, and numerical analysis, with Fortran being one of the most widely used programming languages in this domain.[196.1] One of the key advancements in computational solid mechanics is the application of finite element methods (FEM), which have been expanded to include a wide range of engineering disciplines such as structural engineering, aerospace engineering, and mechanics of materials.[214.1] These methods allow for the modeling of complex materials and geometries, enabling engineers to simulate real-world applications more accurately. Recent developments in FEM have enhanced the ability to model intricate behaviors, such as fracture mechanics and thermo-fluid interactions, which are critical in various engineering applications.[214.1] The integration of artificial intelligence (AI) and machine learning (ML) into computational solid mechanics is expected to significantly enhance traditional methodologies in the field. AI technologies have the potential to revolutionize design, manufacturing, and maintenance processes by enabling engineers to generate optimized designs more efficiently, which leads to improved product performance and shorter development cycles.[8.1] Furthermore, the application of AI in computational mechanics allows for the simulation of highly complex problems that exceed the capabilities of existing rigid computational methodologies.[9.1] Active research within this domain includes the development of new finite element methods, modeling of complex materials and biological tissues, and the exploration of physics-based learning models and reduced order models to simplify large-scale simulations.[194.1] This intersection of computational mechanics with AI and ML not only streamlines existing processes but also opens new avenues for research and application, particularly in areas such as tissue engineering and the mechanics of biological systems.[194.1] In addition to these technological advancements, interdisciplinary collaboration is a hallmark of modern computational solid mechanics. Research often involves a combination of concepts and methods from mechanics, mathematics, computer science, and other scientific disciplines, reflecting the complexity of the problems being addressed.[203.1] This collaborative approach enhances the ability to tackle real-world engineering challenges, as evidenced by ongoing projects that involve the modeling of biological systems, such as the mechanics of the ear and tissue engineering.[194.1]In this section:
References
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[20] How Machine Learning is Transforming Traditional Engineering and ... — The integration of machine learning, particularly through Physics-Inspired Neural Networks (PINNs), is transforming traditional engineering methods by providing faster, more efficient, and more
[21] Unlocking the Power of Computational Mechanics: How Simulation Solves ... — Computational mechanics plays a crucial role in today's engineering landscape. Its applications transform complex problems into manageable simulations, paving the way for innovative solutions. By harnessing the power of numerical methods and algorithms, engineers can model intricate Mechanical Systems with remarkable accuracy.
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[44] Eighty Years of the Finite Element Method: Birth, Evolution, and Future ... — The year 2021 marks the eightieth anniversary of the invention of the finite element method (FEM), which has become the computational workhorse for engineering design analysis and scientific modeling of a wide range of physical processes, including material and structural mechanics, fluid flow and heat conduction, various biological processes for medical diagnosis and surgery planning, electromagnetics and semi-conductor circuit and chip design and analysis, additive manufacturing, and in general every conceivable problem that can be described by partial differential equations (PDEs). J. Turner (1950–1956) at Boeing Company, who was later joined by R.W. Clough of UC Berkeley and H.C. Martin of Washington University, developed what we know today as the earliest form of the finite element method (1954), which was called the Matrix Stiffness Method at the time.
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[77] Structural constitutive models for soft biological tissues and ... — By encompassing the entire kinematic space, refined constitutive models can be defined to gain deeper insights into tissue mechanics across a spectrum of physiological and pathological conditions. Attempts to characterize 3D mechanical behavior of soft tissues have been made by conducting simple shear tests of cuboidal specimens in three
[78] Mechanobiological modeling of viscoelasticity in soft tissue growth and ... — These investigations are valuable for understanding the mechanical behavior of tissues under different physiological and pathological conditions. Studies using these techniques have revealed that viscoelasticity can regulate spatiotemporal tissue organization, driving tissue growth dynamics and symmetry-breaking instabilities like buckling
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[80] Applications of Computational Modeling in Cardiac Surgery — Despite its infancy in cardiac surgery, computational modeling has been useful in calculating the effects of clinical devices and surgical procedures. In this review, we present several examples that demonstrate the capabilities of computational cardiac modeling in cardiac surgery.
[81] Biomechanical modeling and computer simulation of the brain during ... — 1. Introduction By augmenting the surgeon's ability to perform operations, computer integrated surgery systems can increase surgical accuracy, improve the clinical outcomes and the efficiency of healthcare delivery. In this article we discuss the application of computational mechanics in computer-integrated neurosurgery systems.
[82] PDF — Computational Fluid Dynamics (CFD), a branch of computational mechanics, enables the simulation of fluid behavior under different conditions, providing insights that are acute for optimizing performance and ensuring safety. The field of computational mechanics is continually evolving, driven by advances in computational power and algorithms. The
[83] Unlocking the Power of Computational Mechanics: How Simulation Solves ... — Emerging technologies promise to revolutionize the field of computational mechanics. With advancements in hardware capabilities, simulations are becoming increasingly detailed and accurate. ... By harnessing the power of numerical methods and algorithms, engineers can model intricate Mechanical Systems with remarkable accuracy. This ability not
[85] Advances in Machine Learning and Computational Mechanics — Advanced Modeling and Simulation in Engineering Sciences is calling for submissions to our new Collection on "Advances in Machine Learning and Computational Mechanics". This Collection focuses on the latest advances in machine learning and deep learning for computational mechanics applications. The goal is to showcase recent advances in the development and understanding of coupled machine learning and physical modeling for complex physical systems, along with their applications across industrial domains. This Collection welcomes submission of Research Articles. During the submission process, under the section additional information, you will be asked whether you are submitting to a Collection/Thematic Series, please select "Advances in Machine Learning and Computational Mechanics" from the dropdown menu. The Correction to this article has been published in Advanced Modeling and Simulation in Engineering Sciences 2025 12:4
[86] Computational mechanics enhanced by deep learning — This trend in computational mechanics has been supported by the development of computers in the last decades. Extraordinary progress of digital computers has big impacts in information science and technology including computational mechanics. Machine learning is among them , .
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[101] A review of the characterizations of soft tissues used in human body ... — Two challenges that exist are experimental mechanical characterization and constitutive modeling of biological soft tissues and personalization of constitutive parameters using non-invasive, non-destructive bedside testing methods. ... Another challenge with the application of material properties is consideration of the experimental setup used
[102] Advances and Challenges in the Mechanics of Biological Soft Tissues ... — The mechanical properties of biological soft tissues play a critical role in the study of biomechanics and protective measures against human injury. Various testing techniques at different scales have been employed to characterize the mechanical behavior of soft tissues, which is essential for the development of accurate tissue simulants and numerical models.
[103] On modeling the multiscale mechanobiology of soft tissues: Challenges ... — Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues
[104] On modeling the multiscale mechanobiology of soft tissues: Challenges ... — There are a wide variety of approaches to model the mechanical behavior of soft tissue, ... The coupling from cell density fields and cytokine concentrations to changes in tissue composition, mechanical properties, and active stress are intuitive even though they leave out many of the details of the underlying biological processes
[105] Biological multiscale computational modeling: A promising tool for 3D ... — The progress of three-dimensional (3D) bioprinting techniques has driven several advances in tissue engineering (TE), which allow the obtention of biological constructs analogous to native tissues. These methods lead to the development of structures that can integrate with the extracellular matrix of the host tissue, promoting better
[118] Recent Advances in Computational Methods in Engineering Mechanics — _methods_engineering_mechanics). Computational mechanics lies at the intersection of mechanics, appliedmathematics,andcomputerscience.Inrecentyears,itgradu-ally became a dominantfield ofstudy in the Engineering Mechanics Institute (EMI); and we project that it will remain as the primary research focus of this community in the foreseeable future
[119] Recent Advances in Computational Mechanics and Simulations — This book presents selected papers from the 7th International Congress on Computational Mechanics and Simulation, held at IIT Mandi, India. The papers discuss the development of mathematical models representing physical phenomena and apply modern computing methods to analyze a broad range of applications including civil, offshore, aerospace, automotive, naval and nuclear structures.
[122] Advances in Machine Learning and Computational Mechanics - SpringerOpen — Advanced Modeling and Simulation in Engineering Sciences is calling for submissions to our new Collection on "Advances in Machine Learning and Computational Mechanics". This Collection focuses on the latest advances in machine learning and deep learning for computational mechanics applications. The goal is to showcase recent advances in the development and understanding of coupled machine learning and physical modeling for complex physical systems, along with their applications across industrial domains. This Collection welcomes submission of Research Articles. During the submission process, under the section additional information, you will be asked whether you are submitting to a Collection/Thematic Series, please select "Advances in Machine Learning and Computational Mechanics" from the dropdown menu. The Correction to this article has been published in Advanced Modeling and Simulation in Engineering Sciences 2025 12:4
[124] Computational Approaches for Aerospace Design | Wiley Online Books — Over the last fifty years, the ability to carry out analysis as a precursor to decision making in engineering design has increased dramatically. In particular, the advent of modern computing systems and the development of advanced numerical methods have made computational modelling a vital tool for producing optimized designs. This text explores how computer-aided analysis has revolutionized
[125] A Perspective on the State of Aerospace Computational Fluid Dynamics ... — Over the past several decades, computational fluid dynamics has been increasingly used in the aerospace industry for the design and study of new and derivative aircraft. In this review we survey the CFD application process and note its place and importance within the everyday work of industry. Furthermore, the centrality of geometry and importance of turbulence models, higher-order numerical
[126] Computer Methods in Applied Mechanics and Engineering — An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications - ScienceDirect An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications The energy of a mechanical system seems to be the natural loss function for a machine learning method to approach a mechanical problem. Computational mechanics aims at solving mechanical problems using computer methods. Several very relevant examples from computational mechanics have been solved using DNNs to build the approximation space, which shows that it is possible to tackle the solution of very relevant BVPs using concepts and tools coming from deep learning.
[127] Machine Learning for Computational Mechanics - ScienceDirect — Models can be created using a wide range of techniques that include: artificial neural networks; decision tree learning; support-vector machines; regression analysis; Bayesian networks; ontology based systems; federated learning; ensemble methods; often integrated with or assisted by genetic algorithms and other heuristic methods. Authors using the above mentioned learning and model creation techniques or other machine learning techniques to solve new problems in the many branches of computational mechanics (solids, structures and fluids) are invited to submit papers to the special issue. select article Delamination identification in sandwich composite structures using machine learning techniques select article Ensemble technique to predict post-earthquake damage of buildings integrating tree-based models and tabular neural networks select article Machine learning prediction of structural dynamic responses using graph neural networks select article Physics-informed neural network for first-passage reliability assessment of structural dynamic systems
[128] Special issue of computational mechanics on machine learning theories ... — Specifically for mechanics and materials, there are a number of promising areas: (i) improving efficiency when traditional methods are computationally intractable by constructing efficient surrogate or reduced-order models; (ii) improving accuracy when traditional methods performs poorly, by assimilating additional data; (iii) solving “unsolvable” traditional models, when problem are ill-posed in presence of incomplete information; (iv) model discovery when the exact form of the physical model is unknown; (v) efficiently solving inverse problems, especially useful in processing or soft robotics; (vi) understanding and interpreting machine learning, by employing physics-informed strategies; and (vii) constructing digital twins combining intimately physics-based and data-driven models for representing a virtual replica of the physical systems, while guaranteeing fast and accurate responses, needed in diagnosis, control, prognosis and decision making.
[129] Mathematical modeling and simulations using software like MATLAB ... — This study explores the application of MATLAB, COMSOL, and Python in mathematical modeling and simulation within precision engineering. These tools are analyzed for their strengths in handling various engineering challenges, from control systems to multiphysics simulations and custom algorithm development. The study also investigates the role of artificial intelligence (AI), in supporting
[131] Recent Advances in Computational Mechanics and Simulations — This book presents selected papers from the 7th International Congress on Computational Mechanics and Simulation, held at IIT Mandi, India. The papers discuss the development of mathematical models representing physical phenomena and apply modern computing methods to analyze a broad range of applications including civil, offshore, aerospace, automotive, naval and nuclear structures.
[132] The good, the bad, and the awful of AI in aerospace — The good, the bad, and the awful of AI in aerospace - Aerospace Manufacturing and Design The good, the bad, and the awful of AI in aerospace GE Aerospace is a leader in this area, with its digital twins AI technology enabling the company to monitor and analyze real-time data from aircraft engines. AI technology is also enhancing aerospace manufacturing through intelligent robotics and automation systems. Boeing uses AI-powered robotic systems for drilling, painting, and assembly operations, and reports experiencing enhanced production efficiency and reduced cycle times. Artificial intelligence (AI) facilitates predictive maintenance, improves quality control, and enhances manufacturing efficiency. AI technology also enhances the manufacturing process by automating quality control, detecting defects in components, and optimizing production lines for increased efficiency.
[135] A Review on Aerospace-AI, with Ethics and Implications - ResearchGate — The rapid advancement of aerospace technology, coupled with the exponential growth in available data, has catalyzed the integration of artificial intelligence (AI) across the aerospace sector.
[136] Advanced Techniques in Computational Mechanics - Wiley Online Library — Computational mechanics has su ered signi cant develop-ments in the last decades. Novel numerical models have been proposed to model solid and uid problems, as well as to deal with solid- uid interaction. Many of these methods are based in a spatial description of the model by points (such as in Meshless methods) or in enrichment strategies
[137] Special issue: Advanced mathematical modeling in mechanical engineering ... — With the advances in mathematical modeling, different mathematical methods and approaches are applied to solve a variety of problems in applied mechanics and mechanical engineering. Based on these premises, the '1st International Conference on Mathematical Modeling in Mechanics and Engineering-ICME2022′ was held in Belgrade, Serbia, 8-10
[141] A Deep Dive into the Engineering Challenges of Neural Networks — As industries increasingly integrate neural networks into their core operations, the engineering challenges we've discussed — from model optimization to deployment infrastructure — will require novel solutions. The future success of AI implementations will likely depend on: Collaborative approaches to solving complex architectural challenges
[142] The Impact of Generative AI on Data Engineering Workflows — Challenges in Implementing Generative AI in Data Workflows. As data engineering continuously evolves, the integration of generative AI poses several challenges that need careful consideration. Understanding these hurdles can be the first step in effectively incorporating this technology into your workflow.
[143] The Rise of Deep Learning: AI and Engineering ... - ScienceDirect — In rock mechanics and engineering, deep learning has also shown a strong cross-disciplinary integration ability, helping engineers and researchers effectively address many challenges in complex natural environments through applications such as geological disaster prediction, disaster mitigation monitoring, engineering design and construction
[158] Computational Considerations - SpringerLink — In this chapter, some computational considerations, related to the efficiency of the calculations and the accuracy of the results, are discussed. It has been noted that in general the efficiency and the accuracy are conflicting considerations, that is, better accuracy is often achieved at the expense of additional computational effort.
[159] Editorial UKACM 2022: advances in computational mechanics — The combination of machine learning techniques and traditional computational methods is particularly promising, in fact, for complex geometries in geological and civil engineering applications, as shown in the work of Makauskas et al. present a surrogate modelling approach for tunnel track design, where synthetic data are generated using a cut finite-element method-based multi-phase multi-physics simulation model. Makauskas P, Pal M, Kulkarni V, Kashyap AS, Tyagi H (2023) Comparative study of modelling flows in porous media for engineering applications using finite volume and artificial neural network methods. Makauskas P, Pal M, Kulkarni V, Kashyap AS, Tyagi H (2023) Comparative study of modelling flows in porous media for engineering applications using finite volume and artificial neural network methods.
[162] Advanced Computational Methods for Modeling, Prediction and ... — This paper provides a comprehensive review of recent advancements in computational methods for modeling, simulation, and optimization of complex systems in materials engineering, mechanical engineering, and energy systems. Since this paper reviews recent developments in artificial intelligence and computational methods focusing on the modeling, simulations, and optimization of complex systems in materials science, we should start by discussing emerging trends in AI, as now we can conduct virtual simulations that provide us with a depiction of the information landscape based on current knowledge. The modeling studies conducted in the works mentioned above, validated based on the experimental data sets, confirm the possibility of using practical artificial intelligence algorithms as advanced techniques for optimizing energy systems.
[165] High-Performance Computing in Computational Fluid Dynamics ... - JSTOR — Computational fluid dynamics (CFD) is by far the largest user of high-performance computing (HPC) in engineering. The main scientific challenge is the need to gain a greater understanding of turbulence and its consequences for the transfer of momen- tum, heat and mass in engineering applications, including aerodynamics, industrial flows and combustion systems. Availability of HPC has led to
[166] High-Performance Computing: Dos and Don'ts - IntechOpen — Computational fluid dynamics (CFD) is the main field of computational mechanics that has historically benefited from advances in high-performance computing. High-performance computing involves several techniques to make a simulation efficient and fast, such as distributed memory parallelism, shared memory parallelism, vectorization, memory access optimizations, etc. As an introduction, we
[167] Advances in Mathematical Methods and High Performance Computing - Springer — High-Performance Computing (HPC) systems have gone through many changes during the past two decades in their architectural design to satisfy the increasingly large-scale scientific computing demand. ... (> 50% are singleauthored) on applied mathematics, theoretical and computational mechanics, global optimization and operations research etc
[174] Machine Learning in Computational Mechanics - MDPI — Machine learning (ML) has emerged as a powerful tool in Computational Mechanics, impacting all of its areas, such as Structural/Solid Mechanics, Fluid Mechanics, Fluid-Structure Interaction, etc. Undoubtedly, pioneering work has demonstrated that ML may provide solutions to governing systems of equations with comparable accuracy to those
[175] Perspective: Machine learning in experimental solid mechanics — These are typically being explored in a self reinforcing structure, wherein ML algorithms are used to improve the efficiency of the platforms to navigate a complex design space, and the data collected on the platforms can be fed back into the ML models in order to improve their predictive capabilities. Physics-based computational simulations
[186] Research directions in computational mechanics - ScienceDirect — Research directions in computational mechanics - ScienceDirect Research directions in computational mechanics Computational mechanics: a core discipline in computational science and engineering Computational mechanics (CM) is that sub-discipline of TAM concerned with the use of computational methods and The natural stimuli that activate physical systems may be completely unpredictable by deterministic models: the randomness of a gust of wind, the characterization of forces in boundary and initial conditions on mechanical systems, random microstructural features of engineering materials, the random fluctuations in temperature, humidity, and other environmental factors, all make the A powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.
[193] Computational Methods in Mechanics of Machines — One of the primary challenges is the computational complexity of simulations, which can require significant processing power and time. High-fidelity simulations, in particular, can be resource-intensive and may necessitate the use of HPC resources. Model Accuracy. The accuracy of computational models is another critical consideration.
[194] Focus Areas - Mechanics and Computation — Active research topics within our Group include development of new finite element methods (e.g., discontinuous Galerkin method), computational acoustics and fluid-structure interaction, algorithms for dynamical and transient transport phenomena, adaptive solution schemes using configurational forces, modeling the behavior of complex materials and biological tissues. The group is playing an active part in this research effort at Stanford with current collaborative projects with the School of Medicine in areas such as the modeling of the mechanics of the ear and hearing, the eye and vision, growth and remodeling, simulation of proteins and mechanically gated ion channels, tissue engineering and stem cell differentiation. The Mechanics and Computation Group is pursuing several areas of research in ML that include: physics-based learning models, reduced order models to reduce the complexity of large-scale simulations, novel design strategies, autonomous driving, device and sensor monitoring, optimization, imaging and inverse problems, decision making, classification and regression.
[195] Computational Mechanics Specialisation | Curtin University — Overview Computational mechanics is a subdiscipline of mechanics focused on developing and solving complex mathematical models that represent physical phenomena through the use of modern computing methods, such as intensive computer simulations. These complex mathematical models arise in applications such as renewable energy, biomechanics, sports engineering, defence, manufacturing and
[196] Computational mechanics - Wikipedia — Computational mechanics - Wikipedia Computational mechanics Application of mechanics using computational methods Unsourced material may be challenged and removed.Find sources: "Computational mechanics" – news · newspapers · books · scholar · JSTOR (June 2017) (Learn how and when to remove this message)This article may require cleanup to meet Wikipedia's quality standards. Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. The areas of mathematics most related to computational mechanics are partial differential equations, linear algebra and numerical analysis. The most widely used programming language in the scientific community, including computational mechanics, is Fortran. Numerical Methods in Computational Mechanics. Computational mechanics
[199] PDF — Recent Advances in Finite Element Methods for Structural Acoustics Dr. Saikat Dey Code 7130, Naval Research Laboratory, Washington D.C. USA ... Adaptable hp-finite/infinite element approximations Acoustic finite and infinite elements Perfectly Matched Layer (PML) approximations ... Computational Domain Description
[200] An improved SPH-FEM coupling approach for modeling fluid-structure ... — An improved smooth particle hydrodynamics-finite element method (SPH-FEM) coupling approach was developed for investigating fluid-structure interaction (FSI) problems. To deal with the conjunction of physical quantities at the fluid-structure interfacial region, an interface particle coupling strategy was proposed, in which two kinds of virtual interface particles, i.e., interfacial
[201] Particle Finite Element Method in Fluid-Structure Interaction — The Particle Finite Element Method (PFEM) is an innovative computational technique that combines the advantages of particle-based methods with traditional finite element approaches.
[203] PDF — Not surprisingly, successful research in CM is usually interdisciplinary in nature, reflecting a combination of concepts, methods, and principles that often span sev- eral areas of mechanics, mathematics, computer sci- ences, and other scientific disciplines as well.
[214] Advanced Finite Element Method and Its Applications - MDPI — Since the first applications, many scientific contributions have aimed to broaden the applications of the finite element method to encompass structural engineering, aerospace engineering, mechanics of materials, fracture mechanics, thermo-fluid mechanics, chemical engineering, electro-magnetism, manufacturing processes, and more recently