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Strain‐gradient viscoplasticity in one‐dimensional structural dynamics

Based on the static theory of strain‐gradient viscoplasticity proposed by [1], 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‐ and microscopic‐force balances 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. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)