A one-dimensional dynamic analysis of strain-gradient viscoplasticity

an Danh Nguyen (1) , Marcus Stoel (1) , Dieter Weichert (1)

1 Institute of General Mechanics

Based on the static theory of strain-gradient viscoplasticity proposed by Anand et al. (2005), a one-dimensional dynamic analysis is derived for _nite 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 ow. 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 eects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a onedimensional dynamic problem. A parameter study to nd the microscopic-inertia parameter is carried out. At last, suitable microscopic boundary conditions and dynamic eects are discussed through comparison with the conventional plasticity.

Mots clés: Physical Sciences

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

an Danh Nguyen, Marcus Stoel, Dieter Weichert. A one-dimensional dynamic analysis of strain-gradient viscoplasticity. European Journal of Mechanics - A/Solids, 2010, 29 (6), pp.1042. ⟨10.1016/j.euromechsol.2010.07.004⟩. ⟨hal-00687355⟩