Rate-independent systems

A Mielke, T Roubíček - Applied Mathematical Sciences, 2015 - Springer
Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

A vanishing viscosity approach to a rate-independent damage model

D Knees, R Rossi, C Zanini - Mathematical Models and Methods in …, 2013 - World Scientific
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 …

Delamination and adhesive contact models and their mathematical analysis and numerical treatment

T Roubíček, M Kružík, J Zeman - Mathematical methods and models …, 2014 - World Scientific
This chapter reviews mathematical approaches to inelastic processes on the surfaces of
elastic bodies. We mostly consider a quasistatic and rateindependent evolution at small …

Modeling solutions with jumps for rate-independent systems on metric spaces

A Mielke, R Rossi, G Savaré - arxiv preprint arxiv:0807.0744, 2008 - arxiv.org
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 …

Differential, energetic, and metric formulations for rate-independent processes

S Bianchini, EA Carlen, A Mielke, C Villani… - Nonlinear PDE's and …, 2011 - Springer
In these notes we want to give an overview of the recently developed theory for rate-
independent systems. Such systems are used to model hysteresis, dry friction …

Shape derivatives of energy and regularity of minimizers for shallow elastic shells with cohesive cracks

V Shcherbakov - Nonlinear Analysis: Real World Applications, 2022 - Elsevier
The paper addresses the analysis of a model for a thin shallow linear elastic shell with a
smooth vertical through crack that is based on the Kirchhoff–Love shell theory and accounts …

Fully discrete approximation schemes for rate-independent crack evolution

D Knees, A Schröder… - … Transactions of the …, 2022 - royalsocietypublishing.org
Over the past two decades, several distinct solution concepts for rate-independent
evolutionary systems driven by non-convex energies have been suggested in an attempt to …

Adhesive contact of visco-elastic bodies and defect measures arising by vanishing viscosity

T Roubicek - SIAM Journal on Mathematical Analysis, 2013 - SIAM
An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin--
Voigt rheology at small strains is scrutinized. The flow rule for debonding the adhesive is …

Quasistatic delamination problem

T Roubíček, L Scardia, C Zanini - Continuum Mechanics and …, 2009 - Springer
We study delamination of two elastic bodies glued together by an adhesive that can undergo
a unidirectional inelastic rate-independent process. The quasistatic delamination process is …

Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening

S Almi - ESAIM: Control, Optimisation and Calculus of …, 2017 - numdam.org
In the setting of planar linearized elasticity, we study a fracture model depending on the
crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we …