An improved complex variable element-free Galerkin method for two-dimensional large deformation elastoplasticity problems

• ICVEFG method for 2D large deformation problems of elastoplasticity is presented.
• The ICVEFG method is a novel EFG method based on the ICVMLS approximation.
• The ICVEFG method is more precision and efficient than EFG and CVEFG methods.

This paper presents the formulation and numerical implementation of the improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional large deformation problems of elastoplasticity in total Lagrangian description. The ICVEFG method is a novel element free Galerkin (EFG) method based on the improved complex variable moving least-squares (ICVMLS) approximation. The ICVMLS approximation has all the advantages inherited from the complex variable moving least-squares (CVMLS) approximation. The function J in the ICVMLS approximation has an explicit physical meaning, compared with the former. The Galerkin weak form is employed to obtain the equations system and the penalty method is used to apply essential boundary conditions. Several numerical examples presented show that the ICVEFG method has greater precision and efficiency compared to the EFG and CVEFG methods.