Active macro‐zone approach for incremental elastoplastic‐contact analysis

Abstract

The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem.A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The solution of the frictionless contact/detachment problem was performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment. the integral equations satisfying the boundary and domain conditions, the Signorini equations regarding the contact/detachment conditions rewritten as LCP, and the constitutive relations for rate-independent plasticity.

Boundary augmented Lagrangian method for contact problems in linear elasticity

“…In the case of contact problems, the key unknowns are displacement and stress on the contact boundary, which are considered primary variables in BEM and can be obtained directly [30,31]. Therefore, the BEM is more appropriate for contact problems [6][7][8][9][32][33][34][35][36]. However, little attention has been paid to the contact problem using the fixed point method and BEM up to now.…”

“…Presently there are two typical approaches for the numerical solution of the contact problem. One is to start with the discrete problem by the finite element method (FEM) [1][2][3][4][5] or the boundary element method (BEM) [6][7][8][9][10] and obtain a linear complementary problem, which generally results in an optimization problem in finite dimensional space. The second approach to solve the problem is to use the Lagrange multiplier.…”

Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

“…We note that there exist two types of approaches for the numerical solution of the contact problem. An option is to discrete the problem by the finite element method (FEM) [2][3][4][5] or the boundary element method (BEM) [6][7][8][9][10] and obtain a convex optimization problem in the finite dimensional space. Another option is to use the Lagrange multiplier which replaces the nonlinear problem with a sequence of linear problems in function spaces, and this idea has been introduced in [11][12][13][14][15][16][17][18].…”

“…For contact problems, the key unknowns are displacement and stress on the contact boundary, which are considered as primary variables and can be obtained directly in the BEM [28][29][30]. erefore, the BEM seems to be the natural way for these problems [6][7][8][9][10][31][32][33][34][35][36][37].…”