Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish. (English) Zbl 1397.35306
In this article the author considers the evolution of two visco-elastic bodies connected by a viscous adhesive. The evolution is governed by the classical equations of linear elasticity and a nonlinear equation describing the behaviour of the adhesive at the interface. The author proves the existence of a solution of those equations using a discretisation in time. Moreover, in case of a simple potential describing the energy stored by the adhesive, the author studies the limit of the solutions of the problem when time is rescaled by \(t/\varepsilon\) and \(\varepsilon\) tends to 0. It is shown that this limit still satisfies a balance of momentum and of energy. Finally, in the one-dimensional case, the author is able to show that the limit of the solutions satisfies a certain partial differential equation itself.
Reviewer: Sascha Trostorff (Dresden)
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35L04 | Initial-boundary value problems for first-order hyperbolic equations |
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74R99 | Fracture and damage |
| 74B10 | Linear elasticity with initial stresses |
| 74B20 | Nonlinear elasticity |
Keywords:
visco-elasticity; delamination; contact mechanics; vanishing viscosity; hyperbolic PDEs systemsReferences:
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