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Volumetric locking-free mixed Virtual Element Methods for contact problems
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DOI：10.1016/j.cma.2026.119006.png)
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Abstract
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We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed displacement/pressure ( u/p) variational formulation, where pressure is introduced as an independent unknown. We present the VEM discretization and develop a general error analysis, keeping explicit track of the constants involved in the error estimates, thus allowing to consider meshes with small edges. As examples, we consider two possible VEM schemes: a first-order scheme and a second-order scheme. The numerical results confirm the theoretical predictions, specifically both schemes show: (1) robustness with respect to the volumetric parameter λ, thus preventing the occurrence of the volumetric locking phenomenon; (2) good behavior even in the presence of small edges; (3) achievement of the expected theoretical convergence rates.
Keywords:
Virtual Element Methods
Contact problem
Volumetric locking
Mixed variational formulations
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