Generalization of Lions' Nonoverlapping Domain Decomposition Method for Contact Problems

Domain Decomposition Methods for Problems of Unilateral Contact Between Elastic Bodies with Nonlinear Winkler Covers

“…The Young's moduli and Poisson's ratios of the bodies are the same: E 1 = E 2 = 2.1 · 10 5 MPa, ν 1 = ν 2 = 0.3. The distance between bodies is d 12…”

“…Many DDMs for contact problems without covers are obtained on discrete level [3,16]. Among DDMs, proposed on continuous level for contact problems without covers are methods presented in [1,9,12]. Domain decomposition methods for solution of problem of ideal contact between two bodies, connected through nonlinear Winkler layer are proposed in [2,8].…”

Penalty Robin-Robin Domain Decomposition Schemes for Contact Problems of Nonlinear Elasticity

“…Domain decomposition methods (DDMs), presented in [2,10,11,16] for unilateral two-body contact problems of linear elasticity, are obtained on continuous level. All of them require the solution of nonlinear one-sided contact problems for one or both of the bodies in each iteration.…”

Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity

“…Among the domain decomposition methods for unilateral two-body contact problems obtained on the continuous level, one should mention Dirichlet-Neumann [13,14,15], Neumann-Neumann [16,17] and optimization based [18] iterative algorithms. A generalization of Lions' Robin-Robin domain decomposition algorithm to a two-body contact problem was proposed in works [19,20,21]. All of these methods in each iteration require to solve a nonlinear one-sided contact problem with a rigid body (Signorini problem) for one of the bodies, and a linear elasticity problem with Neumann [13,14,15] or Dirichlet [16,17,18] boundary conditions on the possible contact area for the other body, or require to solve nonlinear Signorini problems for both of the bodies [19,20,21].…”

“…A generalization of Lions' Robin-Robin domain decomposition algorithm to a two-body contact problem was proposed in works [19,20,21]. All of these methods in each iteration require to solve a nonlinear one-sided contact problem with a rigid body (Signorini problem) for one of the bodies, and a linear elasticity problem with Neumann [13,14,15] or Dirichlet [16,17,18] boundary conditions on the possible contact area for the other body, or require to solve nonlinear Signorini problems for both of the bodies [19,20,21]. Moreover, to increase the convergence rate of Neumann-Neumann and Robin-Robin algorithms, it is recommended to perform an additional iteration, in which the linear elasticity problems with Neumann boundary conditions have to be solved for both of the bodies [16,20].…”