Nonlocal damage modelling using the element-free Galerkin method in the frame of finite strains

Prediction of size effects has been a challenging problem since some experiments found the size effect in material damage. Both material model and numerical algorithm have to be improved to consider the complex damage process. In the present paper we implement element-free Galerkin (EFG) method for a strain-gradient based nonlocal damage model and use it to analyze ductile material damage process. The EFG algorithm overcomes some drawbacks of the FEM in convergence of numerical iteration due to large deformations as well as evaluation of the higher-order gradients of the plastic strain. The numerical benchmarks show that the EFG method for the nonlocal damage model provides more stable numerical results. The size effect in notched specimens can be predicted in the computations. Both ductile fracture in tensile specimens as well as their size effects are investigated and the computational results agree very well with experiments.