This paper deals with an existence theorem for a model describing an elasto-viscoplastic evolution of a 2D material with linear kinematic hardening and fracture where the Griffith fracture energy is regularized using a -Laplacian.
DOI : 10.1051/m2an/2015053
Mots clés : Fracture, plasticity, kinematic hardening
@article{M2AN_2016__50_2_455_0, author = {Jakab\v{c}in, Luk\'a\v{s}}, title = {Existence of solutions to an elasto-viscoplastic model with kinematic hardening and $r${-Laplacian} fracture approximation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {455--473}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/m2an/2015053}, mrnumber = {3482551}, zbl = {1338.74096}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2015053/} }
TY - JOUR AU - Jakabčin, Lukáš TI - Existence of solutions to an elasto-viscoplastic model with kinematic hardening and $r$-Laplacian fracture approximation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 455 EP - 473 VL - 50 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015053/ DO - 10.1051/m2an/2015053 LA - en ID - M2AN_2016__50_2_455_0 ER -
%0 Journal Article %A Jakabčin, Lukáš %T Existence of solutions to an elasto-viscoplastic model with kinematic hardening and $r$-Laplacian fracture approximation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 455-473 %V 50 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015053/ %R 10.1051/m2an/2015053 %G en %F M2AN_2016__50_2_455_0
Jakabčin, Lukáš. Existence of solutions to an elasto-viscoplastic model with kinematic hardening and $r$-Laplacian fracture approximation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 455-473. doi : 10.1051/m2an/2015053. http://archive.numdam.org/articles/10.1051/m2an/2015053/
Quasistatic evolution in non-associative plasticity – the cap model. SIAM J. Math. Anal. 44 (2012) 245–292. | DOI | MR | Zbl
, and ,Unilateral gradient flow of the Ambosio-Tortorelli functional by minimizing movements. Ann. Inst. Henri Poincaré (C) Anal. Non Lin. 31 (2014) 779–822. | DOI | Numdam | MR | Zbl
and ,Numerical simulation of a class of models that combine several mechanisms of dissipation: fracture, plasticity, viscous dissipation. J. Comput. Phys. 271 (2014) 397–414. | DOI | MR | Zbl
, , and ,B. Bourdin, Une formulation variationnelle en mécanique de la rupture, théorie et mise en oeuvre numérique. Ph.D. thesis, Université Paris Nord (1998).
Numerical implementation of the variational formulation of brittle fracture. Interfaces Free Bound. 9 (2007) 411–430. | DOI | MR | Zbl
,Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 (2000) 797–826. | DOI | MR | Zbl
, and ,The variational approach to fracture. J. Elasticity 91 (2008) 1–148. | DOI | MR | Zbl
, and ,V. Chrismale, Globally stable quasistatic evolution for a coupled elasto-plastic damage model. Preprint CVGMT (2015). | MR
Quasistatic crack growth in elasto-plastic materials: the two-dimensional case. Arch. Ration. Mech. Anal. 196 (2010) 867–906. | DOI | MR | Zbl
and ,Quasistatic evolution in perfect plasticity as limit of dynamic processes. J. Dyn. Differ. Equations 26 (2014) 915–954. | DOI | MR | Zbl
and ,A vanishing viscosity approach to quasistatic evolution in plasticity with softening. Arch. Ration. Mech. Anal. 189 (2008) 469–544. | DOI | MR | Zbl
, , and ,L.C. Evans, Partial Differential Equations. Grad. Stud. Math. AMS, Rhode Island (1998).
On the variational approximation of free discontinuity problems in the vectorial case. Math. Models Methods Appl. Sci. 11 (2001) 663–684. | DOI | MR | Zbl
,Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. | DOI | MR | Zbl
and ,Ambrosio−Tortorelli approximation of quasi-static evolution of brittle fracture. Calc. Var. Partial Differ. Equations 22 129–172. | DOI | MR | Zbl
,L. Jakabčin, Modélisation, analyse et simulation numérique de solides combinant plasticité, rupture et dissipation visqueuse. Ph.D. thesis, Université Grenoble-Alpes (2014).
A visco-elasto-plastic model with regularized fracture. ESAIM: COCV 22 (2016) 148–168. | Numdam | MR | Zbl
,Existence of solutions to a regularized model of dynamic fracture. Math. Models Methods Appl. Sci. 20 (2010) 1021–1048. | DOI | MR | Zbl
, and ,Existence results for energetic models for rate-independent systems. Calc. Var. Partial Differ. Equations 22 (2005) 73–99. | DOI | MR | Zbl
, ,Formation and evolution of strike-slip faults, rifts, and basins during the India-Asia collision: An experimental approach. J. Geophys. Res. 93 (1988) 15 085–15, 117.
and ,Sur les équations de la plasticité: existence et régularité des solutions. J. Mécanique 20 (1981) 3–39. | MR | Zbl
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