Modeling solutions with jumps for rate-independent systems on metric spaces
By Alexander Mielke, Riccarda Rossi, Giuseppe Savar'e. 2008
118 citations recorded by the source corpus.
Rate-independent systems allow for solutions with jumps that need additional modeling. Here we suggest a formulation that arises as limit of viscous regularization of the solutions in the extended state space. Hence, our parametrized metric solutions of a rate-independent system are absolutely continuous mappings from a parameter interval into the extended state space. Jumps appear as generalized gradient flows during which the time is constant. The closely related notion of BV solutions is developed afterwards. Our approach is based on the abstract theory of generalized gradient flows in metric spaces, and comparison with other notions of solutions is given.
Subfields: Control and Systems Engineering, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ebd2ec6a830b280869fc16717ad00261231e0653
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In Control and Systems Engineering
In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling (2011, methodology): “This idea has already been used in [8, 17, 18] for rate independent dissipative problems in finite”