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Quadratic finite elements with non-matching grids for the unilateral boundary contact

S. Auliac;  Z. Belhachmi;  F. Ben Belgacem;  F. Hecht — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...

Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

Z. Belhachmi;  J.-M. Sac-Epée;  S. Tahir — 2009

Mathematical Modelling of Natural Phenomena

We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity....

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