Injective weak solutions in second-gradient nonlinear elasticity
ESAIM: COCV, 15 4 (2009) 863-871
Published online: 2008-07-19
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Nonlinear Relations of Viscous Stress and Strain Rate in Nonlinear Viscoelasticity
Lennart MachillJournal of Elasticity 157 (1) (2025)
https://doi.org/10.1007/s10659-025-10118-8
Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization
Antonín Češík and Sebastian SchwarzacherJournal of Differential Equations 415 434 (2025)
https://doi.org/10.1016/j.jde.2024.09.034
Inertial (self-)collisions of viscoelastic solids with Lipschitz boundaries
Antonín Češík, Giovanni Gravina and Malte KampschulteAdvances in Calculus of Variations 18 (2) 439 (2025)
https://doi.org/10.1515/acv-2024-0006
Viscoelasticity and accretive phase-change at finite strains
Andrea Chiesa and Ulisse StefanelliZeitschrift für angewandte Mathematik und Physik 76 (2) (2025)
https://doi.org/10.1007/s00033-025-02434-9
The weighted Inertia-Energy-Dissipation principle
Ulisse StefanelliMathematical Models and Methods in Applied Sciences 35 (02) 223 (2025)
https://doi.org/10.1142/S0218202525400019
Deformation of an elastic second gradient spherical body under equatorial line density of dead forces
F. dell’Isola, V.A. Eremeyev, V.A. Korolenko and Y.O. SolyaevEuropean Journal of Mechanics - A/Solids 103 105153 (2024)
https://doi.org/10.1016/j.euromechsol.2023.105153
Derivation of a von Kármán plate theory for thermoviscoelastic solids
Rufat Badal, Manuel Friedrich and Lennart MachillMathematical Models and Methods in Applied Sciences 34 (14) 2749 (2024)
https://doi.org/10.1142/S0218202524500581
Compressible fluids interacting with 3D visco-elastic bulk solids
Dominic Breit, Malte Kampschulte and Sebastian SchwarzacherMathematische Annalen 390 (4) 5495 (2024)
https://doi.org/10.1007/s00208-024-02886-w
Finite‐strain poro‐visco‐elasticity with degenerate mobility
Willem J. M. van Oosterhout and Matthias LieroZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 104 (5) (2024)
https://doi.org/10.1002/zamm.202300486
A new example for the Lavrentiev phenomenon in nonlinear elasticity
Stefano Almi, Stefan Krömer and Anastasia MolchanovaZeitschrift für angewandte Mathematik und Physik 75 (1) (2024)
https://doi.org/10.1007/s00033-023-02132-4
Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision
Antonín Češík, Giovanni Gravina and Malte KampschulteCalculus of Variations and Partial Differential Equations 63 (2) (2024)
https://doi.org/10.1007/s00526-023-02648-7
Second-grade elasticity of three-dimensional pantographic lattices: theory and numerical experiments
Ivan Giorgio, Francesco dell’Isola and David J. SteigmannContinuum Mechanics and Thermodynamics 36 (5) 1181 (2024)
https://doi.org/10.1007/s00161-023-01240-w
A variational approach to frame-indifferent quasistatic viscoelasticity of rate type
Yasemin ŞengülPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 382 (2277) (2024)
https://doi.org/10.1098/rsta.2023.0307
Nonlinear and Linearized Models in Thermoviscoelasticity
Rufat Badal, Manuel Friedrich and Martin KružíkArchive for Rational Mechanics and Analysis 247 (1) (2023)
https://doi.org/10.1007/s00205-022-01834-9
Gradient Flows for Coupling Order Parameters and Mechanics
Leonie Schmeller and Dirk PeschkaSIAM Journal on Applied Mathematics 83 (1) 225 (2023)
https://doi.org/10.1137/22M148478X
Surface penalization of self-interpenetration in linear and nonlinear elasticity
Stefan Krömer and Jan ValdmanApplied Mathematical Modelling 122 641 (2023)
https://doi.org/10.1016/j.apm.2023.06.018
On well‐posedness of the first boundary‐value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
Victor A. EremeyevZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103 (6) (2023)
https://doi.org/10.1002/zamm.202200474
Unrestricted deformations of thin elastic structures interacting with fluids
Malte Kampschulte, Sebastian Schwarzacher and Gianmarco SperoneJournal de Mathématiques Pures et Appliquées 173 96 (2023)
https://doi.org/10.1016/j.matpur.2023.02.007
Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
Stefano Almi, Elisa Davoli and Manuel FriedrichJournal de Mathématiques Pures et Appliquées 175 1 (2023)
https://doi.org/10.1016/j.matpur.2023.05.001
Variational methods for fluid–structure interaction and porous media
B. Benešová, M. Kampschulte and S. SchwarzacherNonlinear Analysis: Real World Applications 71 103819 (2023)
https://doi.org/10.1016/j.nonrwa.2022.103819
Energy Minimizing Configurations for Single-Director Cosserat Shells
Timothy J. Healey and Gokul G. NairJournal of Elasticity 154 (1-4) 569 (2023)
https://doi.org/10.1007/s10659-022-09975-4
On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
Victor A. Eremeyev and Francesco dell’IsolaMathematics and Mechanics of Solids 27 (3) 433 (2022)
https://doi.org/10.1177/10812865211025576
A theory of magneto-elastic nanorods obtained through rigorous dimension reduction
Jacopo Ciambella, Martin Kružík and Giuseppe TomassettiApplied Mathematical Modelling 106 426 (2022)
https://doi.org/10.1016/j.apm.2022.01.028
Existence of Weak Solutions for Non-Simple Elastic Surface Models
Timothy J. HealeyJournal of Elasticity 151 (1) 47 (2022)
https://doi.org/10.1007/s10659-021-09840-w
A finite-strain model for incomplete damage in elastoplastic materials
David Melching, Michael Neunteufel, Joachim Schöberl and Ulisse StefanelliComputer Methods in Applied Mechanics and Engineering 374 113571 (2021)
https://doi.org/10.1016/j.cma.2020.113571
A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains
Elisa Davoli, Tomáš Roubíček and Ulisse StefanelliMathematics and Mechanics of Solids 26 (10) 1483 (2021)
https://doi.org/10.1177/1081286521990418
Magnetoelastic thin films at large strains
Elisa Davoli, Martin Kružík, Paolo Piovano and Ulisse StefanelliContinuum Mechanics and Thermodynamics 33 (2) 327 (2021)
https://doi.org/10.1007/s00161-020-00904-1
Quasistatic Viscoelasticity with Self-Contact at Large Strains
Stefan Krömer and Tomáš RoubíčekJournal of Elasticity 142 (2) 433 (2020)
https://doi.org/10.1007/s10659-020-09801-9
Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains
Alexander Mielke and Tomáš RoubíčekArchive for Rational Mechanics and Analysis 238 (1) 1 (2020)
https://doi.org/10.1007/s00205-020-01537-z
Derivation of von Kármán Plate Theory in the Framework of Three-Dimensional Viscoelasticity
Manuel Friedrich and Martin KružíkArchive for Rational Mechanics and Analysis 238 (1) 489 (2020)
https://doi.org/10.1007/s00205-020-01547-x
Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
V. A. Eremeyev and F. dell’IsolaLobachevskii Journal of Mathematics 41 (10) 1992 (2020)
https://doi.org/10.1134/S1995080220100078
Variations of Deformations with Self-Contact on Lipschitz Domains
Aaron Zeff PalmerSet-Valued and Variational Analysis 27 (3) 807 (2019)
https://doi.org/10.1007/s11228-018-0485-4
Global injectivity in second-gradient nonlinear elasticity and its approximation with penalty terms
Stefan Krömer and Jan ValdmanMathematics and Mechanics of Solids 24 (11) 3644 (2019)
https://doi.org/10.1177/1081286519851554
Finite thermoelastoplasticity and creep under small elastic strains
Tomáš Roubíček and Ulisse StefanelliMathematics and Mechanics of Solids 24 (4) 1161 (2019)
https://doi.org/10.1177/1081286518774883
Generalized Models and Non-classical Approaches in Complex Materials 1
Victor A. Eremeyev and Francesco dell’IsolaAdvanced Structured Materials, Generalized Models and Non-classical Approaches in Complex Materials 1 89 301 (2018)
https://doi.org/10.1007/978-3-319-72440-9_15
Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling
Tomáš Roubíček and Ulisse StefanelliSIAM Journal on Applied Mathematics 78 (5) 2597 (2018)
https://doi.org/10.1137/17M1137656
A note on locking materials and gradient polyconvexity
Barbora Benešová, Martin Kružík and Anja SchlömerkemperMathematical Models and Methods in Applied Sciences 28 (12) 2367 (2018)
https://doi.org/10.1142/S0218202518500513
Global Existence Results for Viscoplasticity at Finite Strain
Alexander Mielke, Riccarda Rossi and Giuseppe SavaréArchive for Rational Mechanics and Analysis 227 (1) 423 (2018)
https://doi.org/10.1007/s00205-017-1164-6
Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Victor A. Eremeyev, Francesco dell’Isola, Claude Boutin and David SteigmannJournal of Elasticity 132 (2) 175 (2018)
https://doi.org/10.1007/s10659-017-9660-3
On the Passage from Nonlinear to Linearized Viscoelasticity
Manuel Friedrich and Martin KružíkSIAM Journal on Mathematical Analysis 50 (4) 4426 (2018)
https://doi.org/10.1137/17M1131428
A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis
Tomáš Roubíček and Giuseppe TomassettiZeitschrift für angewandte Mathematik und Physik 69 (3) (2018)
https://doi.org/10.1007/s00033-018-0932-y
Weak Lower Semicontinuity of Integral Functionals and Applications
Barbora Benešová and Martin KružíkSIAM Review 59 (4) 703 (2017)
https://doi.org/10.1137/16M1060947
Injectivity and self-contact in second-gradient nonlinear elasticity
Aaron Z. Palmer and Timothy J. HealeyCalculus of Variations and Partial Differential Equations 56 (4) (2017)
https://doi.org/10.1007/s00526-017-1212-y
Rate-independent elastoplasticity at finite strains and its numerical approximation
Alexander Mielke and Tomáš RoubíčekMathematical Models and Methods in Applied Sciences 26 (12) 2203 (2016)
https://doi.org/10.1142/S0218202516500512
Buckling modes in pantographic lattices
Ivan Giorgio, Alessandro Della Corte, Francesco dell'Isola and David J. SteigmannComptes Rendus. Mécanique 344 (7) 487 (2016)
https://doi.org/10.1016/j.crme.2016.02.009