Calculus of Variations and Geometric Measure Theory

E. Davoli - T. Roubicek - U. Stefanelli

Dynamic perfect plasticity and damage in viscoelastic solids

created by davoli on 15 Jun 2018
modified on 04 Sep 2020


Published Paper

Inserted: 15 jun 2018
Last Updated: 4 sep 2020

Journal: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik
Year: 2019

ArXiv: 1904.02083 PDF


In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting. The interplay between the viscoelastic rheology with inertia, elasto-plasticity, and unidirectional rate-dependent incomplete damage affecting both the elastic and viscous response, as well as the plastic yield stress, is rigorously characterized by showing existence of weak solutions to the constitutive and balance equations of the model. The analysis relies on the notions of plastic-strain measures and bounded-deformation displacements, on sophisticated time-regularity estimates to establish a duality between acceleration and velocity of the elastic displacement, on the theory of rate-independent processes for the energy conservation in the dynamical-plastic part, and on the proof of the strong convergence of the elastic strains. Existence of a suitably defined weak solutions is proved rather constructively by using a staggered two-step time discretization scheme.