Finite element procedure for solving contact thermoelastoplastic problems at large strains, normal and high pressures

Abstract

The paper presents a finite element (FE) procedure for solving contact thermoelastoplastic problems at large strains. A rigorous derivation of the constitutive relations used and the structure of a tangent stiffness matrix and load vector at arbitrary thermomecanical loading are given. The deformation model [1,2] is used which is based on the multiplicative decomposition of the total deformation gradient to an elastic, temperature and plastic parts and the generalization of Prandtl-Reuss equations to the case of large strains, high pressures and temperatures. A method is proposed for the generalization of the elastic law at small strains to the case of high pressures which is based on the use of the existence of an elastic potential (hyperelastic material) at large elastic strains. The algorithms for solving thermoelastoplastic problems at large strains and contact elastic problems at small strains are considered individually and in combination for solving contact thermoelastoplastic problems at large strains. An algorithm for solving thermoelastoplastic problems at large strains is based on a modified method of initial stresses allowing the use of both the constant and the variable tangent stiffness matrices. An algorithm allowing for contact conditions (which are described using a friction surface, in the particular case, the Coulomb's law of friction is considered) involves the simultaneous consideration of an arbitrary number of deformable bodies in contact. The pairs of nodes with the same coordinates are introduced along the interface. Owing to transformation of the set of FEM equations, the contact conditions reduce to the usual boundary conditions in terms of stresses or displacement with iterative redetermination of their types (adhesion, slip, no contact) in each pair of nodes. Optimum variants of combinations of the iterative procedures allowing for plastic flow and contact interaction are studied. Particular problems are solved. An attractive feature of the present approach is the simplicity of allowing for the contact conditions for an arbitrary number of deformable bodies in contact and insignificant modifications of computer program which are necessary for the change from small strains to large ones.