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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
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
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
A minimizing-movements approach to GENERIC systems
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
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
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
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
Discrete approximation of dynamic phase-field fracture in visco-elastic materials
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
Balanced Viscosity Solutions to a Rate-Independent Coupled Elasto-plastic Damage System
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
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
Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening
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
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
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
From adhesive to brittle delamination in visco-elastodynamics
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
Finite Plasticity in $P^\top\!P$. Part II: Quasi-Static Evolution and Linearization
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
BV solutions constructed using the epsilon-neighborhood method
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
Local Minimization, Variational Evolution and Γ-Convergence
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
Quasi-Static Evolution for the Armstrong-Frederick Hardening-Plasticity Model
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
Variational Convergence of Gradient Flows and Rate-Independent Evolutions in Metric Spaces
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
Quasistatic Evolution of Sessile Drops and Contact Angle Hysteresis