Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based on Laplacians of Stress and Strain. Part III: Numerical Simulations

A two-dimensional formulation of the 3-PG Model of implicit gradient elasticity has been developed in Part I. The predicted near-tip fields for Mode-I and Mode-II crack problems have been derived in Part II. It has been found that both the classical Cauchy stress and the nonclassical double stress are singular with the order of singularity r−12. In the present chapter, the two-dimensional model formulation is implemented in a finite element code. For verification of the resulting finite element model, a square section with a circular hole subjected to displacement-controlled tension loading is considered and discussed. The main concerns of the chapter are, on the one hand, to validate the analytical solutions of Part II. On the other hand, the chapter aims to investigate the effect of nonclassical material parameters on the stress intensity factors