Analysis of two quasistatic history-dependent contact models

DOI10.3934/dcdsb.2014.19.2425zbMath1310.74035OpenAlexW2331692642MaRDI QIDQ478727

Anna Ochal, Mircea Sofonea, Stanislaw Migórski, Xiao-liang Cheng

Publication date: 4 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.2425

zbMATH Keywords

weak solutionfrictional contactviscoelastic materialClarke subdifferentialviscoplastic materialmemory termnormal compliancehistory-dependent hemivariational inequality

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) (74C10) Friction in solid mechanics (74M10) Contact in solid mechanics (74M15) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30) PDEs in connection with mechanics of deformable solids (35Q74) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

Related Items (9)

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics ⋮ A class of evolution variational inequalities with memory and its application to viscoelastic frictional contact problems ⋮ Numerical analysis of a dynamic viscoplastic contact problem ⋮ A unilateral constraint contact problem for viscoelastic materials with wear ⋮ Error estimate for quasistatic history-dependent contact model ⋮ Numerical analysis of a thermal frictional contact problem with long memory ⋮ Numerical analysis of a viscoplastic contact problem with normal compliance, unilateral constraint, memory term and friction ⋮ Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems ⋮ Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Cites Work

• Nonlinear inclusions and hemivariational inequalities. Models and analysis of contact problems
• Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator
• History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics
• Models and computational methods for dynamic friction phenomena
• Frictional contact problems with normal compliance
• Models and analysis of quasistatic contact. Variational methods
• A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient
• A unified approach to dynamic contact problems in viscoelasticity
• Mathematical Models in Contact Mechanics
• Optimization and nonsmooth analysis
• Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws
• Analysis of a history-dependent frictionless contact problem
• Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction
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