Three-dimensional J-integral evaluation for finite strain elastic–plastic solid using the quadratic tetrahedral finite element and automatic meshing methodology

In this paper, the three-dimensional J-integral for finite deformation problems is critically concerned when it is computed by the domain integral method for the quadratic tetrahedral finite element. When a cracked body undergoes a large elastic–plastic deformation, the domain independent property is not guaranteed. Evaluation procedures that guarantee the domain independent property by including the terms involving the spatial derivatives of the strain energy density, etc., are proposed. The proposed methodology includes a way to compute such derivatives by adopting the concept of superconvergent patch recovery method. Finally, numerical examples demonstrate that proposed procedures can guarantee the domain independent property.