Dynamic frictionless contact in linear viscoelasticity. (English) Zbl 1155.74029

Ahn, Jeongho; Stewart, David E.

IMA J. Numer. Anal. 29, No. 1, 43-71 (2009).

Summary: We formulate a dynamic frictionless contact problem with linear viscoelasticity of Kelvin-Voigt type, based on the Signorini contact conditions. We show existence of solutions, and investigate the possibility for obtaining an energy balance. Employing time discretization and the finite element method, we compute numerical solutions. Our numerical scheme is implemented with non-smooth Newton’s method which solves the complementarity problem. The numerical results support the idea that the energy losses in the limit of the numerical solution are equal to the losses due to viscosity.

MSC:

74M15	Contact in solid mechanics
74D05	Linear constitutive equations for materials with memory
74H20	Existence of solutions of dynamical problems in solid mechanics
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

energy estimate; complementarity condition; Signorini conditions; existence; finite element method

Software:

DistMesh