Semi-Implicit Numerical Strategy for Implementing a Nonlocal Finite-Deformation Gurson Model for Glassy Polymer Using Finite Element Analysis

Post-peak strain softening for some thermoplastic resins often leads to localized deformation with plastic flow instability, spurious energy dissipation, and numerical solutions with mesh dependency using finite element analysis (FEA) due to the lack of a length scale. This paper introduces the nonlocal integral theory with a length scale into the Gurson model to capture objective void evolution and shear bands for glassy polymer under quasi-static loading. Nonlocal numerical technique using the finite-deformation Gurson model is developed, where the nonlocal implicit stress return algorithm and the nonlocal consistent tangent stiffness are presented in the corotational configuration by performing nonlocal averaging on the void volume fraction in a semi-implicit way. The numerical strategy is implemented by combining the finite element software ABAQUS-UMAT, USDFLD, and UEXTERNALDB subroutines. For plane tension problem, the developed nonlocal numerical technique circumvents mesh dependency well by studying the void growth, the evolution of shear bands, and the load responses.