A one-dimensional dynamic analysis of strain-gradient viscoplasticity

Based on the static theory of strain-gradient viscoplasticity proposed by Anand et al. (2005), a one-dimensional dynamic analysis is derived for finite element computation of isotropic hardening materials. The kinetic energy is assumed to be composed of the conventional and internal kinetic energy. The internal energy is described phenomenologically in terms of the equivalent plastic strain in order to capture the heterogeneity of plastic flow. Herein the microscopic density is assumed to be related to the macroscopic one through a microscopic-inertia parameter. The macroscopic-force balance and microscopic-force balance including inertia effects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a one-dimensional dynamic problem. A parameter study to find the microscopic-inertia parameter is carried out. At last, suitable microscopic boundary conditions and dynamic effects are discussed through comparison with the conventional plasticity.