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On a lack of stability of parametrized BV solutions to rate‐independent systems with nonconvex energies and discontinuous loads
Merlin Andreia and Christian Meyer ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 104(7) (2024) https://doi.org/10.1002/zamm.202300654
On the Viscoplastic Approximation of a Rate-Independent Coupled Elastoplastic Damage Model
Vito Crismale, Giuliano Lazzaroni and Riccarda Rossi SIAM Journal on Mathematical Analysis 56(6) 7940 (2024) https://doi.org/10.1137/23M1620429
Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs
Ryan Hynd Contemporary Mathematics, Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs 781 49 (2023) https://doi.org/10.1090/conm/781/15709
The notions of inertial balanced viscosity and inertial virtual viscosity solution for rate-independent systems
Fully discrete approximation schemes for rate-independent crack evolution
Dorothee Knees, Andreas Schröder and Viktor Shcherbakov Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380(2236) (2022) https://doi.org/10.1098/rsta.2021.0361
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Roland Herzog, Dorothee Knees, Christian Meyer, et al. International Series of Numerical Mathematics, Non-Smooth and Complementarity-Based Distributed Parameter Systems 172 121 (2022) https://doi.org/10.1007/978-3-030-79393-7_6
Jump processes as generalized gradient flows
Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré and Oliver Tse Calculus of Variations and Partial Differential Equations 61(1) (2022) https://doi.org/10.1007/s00526-021-02130-2
Non-standard Discretisation Methods in Solid Mechanics
Sören Bartels, Marijo Milicevic, Marita Thomas, Sven Tornquist and Nico Weber Lecture Notes in Applied and Computational Mechanics, Non-standard Discretisation Methods in Solid Mechanics 98 505 (2022) https://doi.org/10.1007/978-3-030-92672-4_17
Elasto-plastic evolution of single crystals driven by dislocation flow
Vanishing‐viscosity solutions to a rate‐independent two‐field gradient damage model
Livia Betz ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 101(11) (2021) https://doi.org/10.1002/zamm.201900226
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
Two-Speed Solutions to Non-convex Rate-Independent Systems
Filip Rindler, Sebastian Schwarzacher and Juan J. L. Velázquez Archive for Rational Mechanics and Analysis 239(3) 1667 (2021) https://doi.org/10.1007/s00205-020-01599-z
Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia
Giuliano Lazzaroni, Riccarda Rossi, Marita Thomas and Rodica Toader Journal of Dynamics and Differential Equations 30(3) 1311 (2018) https://doi.org/10.1007/s10884-018-9666-y
Viscous Corrections of the Time Incremental Minimization Scheme and Visco-Energetic Solutions to Rate-Independent Evolution Problems
Linearly constrained evolutions of critical points and an application to cohesive fractures
Marco Artina, Filippo Cagnetti, Massimo Fornasier and Francesco Solombrino Mathematical Models and Methods in Applied Sciences 27(02) 231 (2017) https://doi.org/10.1142/S0218202517500014
Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement
Maria Giovanna Mora, Mark A. Peletier and Lucia Scardia SIAM Journal on Mathematical Analysis 49(5) 4149 (2017) https://doi.org/10.1137/16M1096098
From adhesive to brittle delamination in visco-elastodynamics
Regularity and approximation of strong solutions to rate-independent systems
Filip Rindler, Sebastian Schwarzacher and Endre Süli Mathematical Models and Methods in Applied Sciences 27(13) 2511 (2017) https://doi.org/10.1142/S0218202517500518
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
Riccarda Rossi and Giuseppe Savaré Springer INdAM Series, Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs 22 489 (2017) https://doi.org/10.1007/978-3-319-64489-9_19
Globally stable quasistatic evolution for strain gradient plasticity coupled with damage
Optimal control of a rate-independent evolution equation via viscous regularization
Ulisse Stefanelli, Daniel Wachsmuth and Gerd Wachsmuth Discrete & Continuous Dynamical Systems - S 10(6) 1467 (2017) https://doi.org/10.3934/dcdss.2017076
Visco-Energetic solutions to one-dimensional rate-independent problems
Quasi-static damage evolution and homogenization: A case study of non-commutability
Andrea Braides, Biagio Cassano, Adriana Garroni and David Sarrocco Annales de l'Institut Henri Poincaré C, Analyse non linéaire 33(2) 309 (2016) https://doi.org/10.1016/j.anihpc.2014.10.003
Energetic formulation for rate-independent processes: remarks on discontinuous evolutions with a simple example
Analysis and Computation of Microstructure in Finite Plasticity
Alexander Mielke Lecture Notes in Applied and Computational Mechanics, Analysis and Computation of Microstructure in Finite Plasticity 78 125 (2015) https://doi.org/10.1007/978-3-319-18242-1_5
Regularity of weak solutions to rate‐independent systems in one‐dimension
Nonsmooth analysis of doubly nonlinear evolution equations
Alexander Mielke, Riccarda Rossi and Giuseppe Savaré Calculus of Variations and Partial Differential Equations 46(1-2) 253 (2013) https://doi.org/10.1007/s00526-011-0482-z
Quasistatic adhesive contact of visco‐elastic bodies and its numerical treatment for very small viscosity
T. Roubíček, C.G. Panagiotopoulos and V. Mantič ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93(10-11) 823 (2013) https://doi.org/10.1002/zamm.201200239
Adhesive Contact of Visco-elastic Bodies and Defect Measures Arising by Vanishing Viscosity
Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution
Gianni Dal Maso, Antonio DeSimone and Francesco Solombrino Calculus of Variations and Partial Differential Equations 44(3-4) 495 (2012) https://doi.org/10.1007/s00526-011-0443-6
Second order approximations of quasistatic evolution problems in finite dimension