Nonlocal Damage Modelling Using the Element-free Galerkin Method in the Frame of Finite Strains

Computational analysis of damage failure is of great importance in predicting assessment of structure integrity. Numerical modeling of ductile material damage using finite element methods often suffers from convergence problems of numerical iteration, especially, when working with a complex constitutive model as gradient plasticity and nonlocal damage models. Due to large strains in damaging elements the computation may result in non-convergence. For the higher order gradient plasticity the element formulation is often necessary, which causes additional difficulties in implementation and computations. In recent years meshless methods have been developed as an alternative for the finite element method (FEM) and can overcome some known shortcomings of the latter. One major advantage of the meshless methods is in continuous differentiation of the strain tensor for cases with finite strains. Complex constitutive models, such as gradient plasticity nonlocal damage models, are easy to be applied in meshless methods. In the present paper we have developed and implemented an algorithm of element-free Galerkin (EFG) methods for straingradient based nonlocal damage models and used it to simulate ductile material damage. The method provides a reliable and robust method for material failure with large damage zones. With the help of the meshless method material failure of specimens as well as the size effect are predicted accurately.

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