Journal ArticleDOI
Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish
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Roubicek et al. as discussed by the authors introduced a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive and proved the existence of solutions of the corresponding system of PDEs and then studied the behavior of such solutions when the data of the problem vary slowly.Abstract:
We introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.read more
Citations
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Journal ArticleDOI
Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia
TL;DR: In this article, a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects is presented, where the heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way.
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Rate-independent damage in thermo-viscoelastic materials with inertia
TL;DR: In this paper, a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects is presented, where the heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way.
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A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations
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Balanced-Viscosity solutions for multi-rate systems
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References
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Viorel Barbu,Theodor Precupanu +1 more
TL;DR: In this article, the authors propose a method to solve the problem of convex control problems in Banach spaces. But this method is not suitable for functional analysis.Convex Functions and Convex Programming