Consistent \(\overline {\boldsymbol {C}}\) Element-Free Galerkin Method for Finite Strain Analysis

We introduce both distinct quadrature and distinct polynomial degrees for the deviatoric and volumetric terms of the right Cauchy-Green tensor in the context of a Lagrangian-based element-free Galerkin (EFG) discretization. First and second derivatives of the mixed deformation gradient are made available. A finite element mesh is employed for quadrature purposes with the corresponding distribution of Gauss points. In terms of discretization, linear, quadratic, and cubic polynomials are combined, and support is determined from the number of pre-assigned nodes. Due to the adoption of a Lagrangian kernel, finite strain elastoplastic constitutive developments are based on the Mandel stress. These developments are found to be especially convenient from the implementation perspective, as EFG formulations for finite strain plasticity have been limited in terms of generality and amplitude of deformations in both compressible and quasi-incompressibility cases. Three benchmark tests are successfully solved, and it was found that a combination of cubic and quadratic bases provides superior results in the quasi-incompressible case. Besides absence of locking with selective interpolation, outstanding Newton convergence was observed regardless of strain levels.