On account of viscous properties of materials in the theory of large elastoplastic strains

S. V. Belykh ; A. A. Burenin ; L. V. Kovtanyuk ; A. N. Prokudin

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 108-130

Résumé

A geometrically and thermodynamically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. It is believed that at the stage of a strain, which precedes the plastic flow and during unloading, the viscous material properties provide the creep process and thus a slow growth of irreversible strains. While rapid growth of irreversible strains under plastic flow conditions, viscous properties act as a mechanism that retards the flow. The accumulation of irreversible strains, therefore, occurs successively: initially, in the creep process, then under plastic flow and, finally, again due to creep of the material (during unloading). On the elastoplastic boundaries advancing along the deformable material, there is a change in the growth mechanism of irreversible strains from creep to plasticity and vice versa. Such a change is possible only under conditions of continuity of irreversible strains and their change rates, which imposes the requirement of consistency in the definitions of irreversible stress distribution rates, i.e., the laws of creep and plasticity. Changing the production mechanisms of irreversible strains means various setting up of the source in the differential equation of the change (transfer) of these strains, hence irreversible strains are not divided into plastic strains and creep strains. To maximize the visibility of the model's correlations, the hypothesis on the independence of thermodynamic potentials (internal energy, free energy) on irreversible strains is accepted. As a consequence of the hypothesis, an analog of the Murnaghan formula is obtained, the classical position of the elastoplasticity is that the stresses in the material are completely determined by the level and distribution of reversible strains. The main provisions of the proposed model are illustrated by the solution in its framework of the boundary value problem of the elastoviscoplastic material motion in a pipe due to a varying pressure drop.

Détail

Keywords: large deformations, elasticity, viscoelasticity, plasticity, unloading.