Rate-independent systems
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 …
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 …
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
This chapter reviews mathematical approaches to inelastic processes on the surfaces of
elastic bodies. We mostly consider a quasistatic and rateindependent evolution at small …
elastic bodies. We mostly consider a quasistatic and rateindependent evolution at small …
Modeling solutions with jumps for rate-independent systems on metric spaces
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 …
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
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 …
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 …
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 …
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 …
Voigt rheology at small strains is scrutinized. The flow rule for debonding the adhesive is …
Quasistatic delamination problem
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 …
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 …
crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we …