Calculation of J-Integral and Stress Intensity Factors using the Material Point Method

Abstract

The Material Point Method (MPM), which is a particle-based, meshless method that discretizes ma- terial bodies into a collection of material points (the par- ticles), is a new method for numerical analysis of dy- namic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers eval- uation of crack-tip parameters, such as J-integral and stress intensity factors, from MPM calculations involv- ing explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture parameters. The MPM results agree well with results ob- tained by other numerical methods and with analytical solutions. keyword: Material point method (MPM), dynamic fracture, J integral, stress intensity factor.