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Active macro‐zone approach for incremental elastoplastic‐contact analysis
Author(s) -
Cucco F.,
Terravecchia S.,
Zito L.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4558
Subject(s) - mathematics , linear complementarity problem , boundary element method , macro , finite element method , nonlinear system , stress field , boundary value problem , mathematical analysis , linear elasticity , plasticity , matrix (chemical analysis) , contact mechanics , unilateral contact , elasticity (physics) , computer science , physics , structural engineering , engineering , materials science , quantum mechanics , composite material , thermodynamics , programming language
SUMMARY 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. Copyright © 2013 John Wiley & Sons, Ltd.