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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
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
Balanced-Viscosity Solutions to Infinite-Dimensional Multi-Rate Systems
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-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
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
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
A penalized version of the local minimization scheme for rate-independent systems
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
Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model
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
Quasistatic evolution in non-associative plasticity revisited
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
Finite Plasticity in $P^\top\!P$. Part II: Quasi-Static Evolution and Linearization
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
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
Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening
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
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
Quasistatic crack growth based on viscous approximation: a model with branching and kinking
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
Balanced-Viscosity solutions for multi-rate systems
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
Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes
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
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 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