A vanishing viscosity approach to a rate-independent damage model
Please always quote using this URN:urn:nbn:de:0296-matheon-8769
- We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arc-length reparameterization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps.
Author: | Dorothee Knees, Riccarda Rossi, Chiara Zanini |
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URN: | urn:nbn:de:0296-matheon-8769 |
Referee: | Dietmar Hömberg |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/07/27 |
Release Date: | 2011/07/27 |
Tag: | arc-length reparameterization; rate-independent damage evolution; time-discretization; vanishing viscosity method |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS |
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] | |
74-XX MECHANICS OF DEFORMABLE SOLIDS | |
Preprint Number: | 810 |