Multiscale Mechanics Overview

Principles

Definition

Multiscale mechanics is a research field and methodological approach that investigates the mechanical behavior and properties of materials and systems by analyzing the interplay and emergence of phenomena occurring across multiple interacting length and/or time scales. It seeks to bridge understanding from fundamental microscopic interactions to macroscopic observable responses, often employing computational modeling and experimental techniques to link these different scales.

Ontological type

Core Methods

Scale Bridging Strategies

Applications

Key developments

Key Figures

Nonlocal Length-Scale Mechanics era

Zdeněk P. Bažant [1] is associated with Northwestern University [3] and Sorbonne Université [4] during this era, and his key contributions include Nonlocal Damage Theory [7] (1987), Continuum Theory for Strain-Softening [8] (1984), and Microplane Model for Progressive Fracture of Concrete and Rock [9] (1985). These works introduced Nonlocal Damage Theory [7] (1987), Continuum Theory for Strain-Softening [8] (1984), and Microplane Model for Progressive Fracture of Concrete and Rock [9] (1985), stabilizing localization and enabling size-dependent predictions. Paul K. Hansma [2] has affiliations with University of California, Santa Barbara [5] and California Institute of Technology [6] during this era. His 1993 paper A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy [10] provided a practical nondestructive approach enabling accurate AFM calibration and nanoscale-mechanics studies.

Gradient and Micromorphic Mechanics era

Martina Hofacker [1], associated with the University of Stuttgart [3] in this era, embodies the focus on gradient and micromorphic mechanics. Hofacker [1]'s 2010 paper Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations [5] advances thermodynamically consistent phase-field formulations and multi-field FE approaches, enabling robust modeling of fracture in gradient-enhanced continua and bridging nanoscale constraints to macroscopic behavior. L.J. Sluys [2] from Delft University of Technology [4] is a central figure in this gradient and micromorphic era. Sluys [2]'s 2001 paper A new method for modelling cohesive cracks using finite elements [6] introduced cohesive cracking modeling with finite elements, advancing fracture mechanics and enabling size-aware analyses.

Data-Driven Nonlocal Mechanics era

Abdelouahed Tounsi [1] is a scholar whose work in multiscale, data-driven nonlocal mechanics spans Yonsei University [3] and King Abdulaziz University [4] in this era. His key contributions include the nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation [7], a refined nonlocal shear deformation theory for functionally graded nanoscale beams [8], and thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory [9], all of which advanced accurate predictions of size-dependent dynamic and thermal responses central to multiscale mechanics. Ivan Giorgio [2] has shaped multiscale mechanics through Sapienza University of Rome [5] and the University of L'Aquila [6], with works like Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium [10] and Nonlinear dynamics of uniformly loaded <i>Elastica</i>: Experimental and numerical evidence of motion around curled stable equilibrium configurations [11]. These contributions exemplify how nonlocal mechanics and multiscale homogenization can be paired with data-driven surrogates to accelerate predictions of stability and dynamic responses in metamaterial-inspired systems.