Contact problems for nonlinearly elastic materials: weak solvability involving dual Lagrange multipliers

Authors

  • Andaluzia Matei
  • Raluca Ciurcea

DOI:

https://doi.org/10.21914/anziamj.v52i0.2212

Keywords:

contact models, nonlinearly elastic materials, dual Lagrange multipliers, weak solutions

Abstract

A class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions. doi:10.1017/S1446181111000629

Published

2011-09-03

Issue

Section

Articles for Printed Issues