Mielke, Alexander; Roubíček, Tomáš Rate-independent elastoplasticity at finite strains and its numerical approximation. (English) Zbl 1349.35371 Math. Models Methods Appl. Sci. 26, No. 12, 2203-2236 (2016). MSC: 35Q74 35K85 49S05 65M60 74A30 74C15 74M15 74S05 74B05 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{T. Roubíček}, Math. Models Methods Appl. Sci. 26, No. 12, 2203--2236 (2016; Zbl 1349.35371) Full Text: DOI OpenURL
Mielke, Alexander Variational approaches and methods for dissipative material models with multiple scales. (English) Zbl 1365.74087 Conti, Sergio (ed.) et al., Analysis and computation of microstructure in finite plasticity. Cham: Springer (ISBN 978-3-319-18241-4/hbk; 978-3-319-18242-1/ebook). Lecture Notes in Applied and Computational Mechanics 78, 125-155 (2015). MSC: 74G65 74C15 PDF BibTeX XML Cite \textit{A. Mielke}, Lect. Notes Appl. Comput. Mech. 78, 125--155 (2015; Zbl 1365.74087) Full Text: DOI OpenURL
Mielke, Alexander; Roubíček, Tomáš Rate-independent systems. Theory and application. (English) Zbl 1339.35006 Applied Mathematical Sciences 193. New York, NY: Springer (ISBN 978-1-4939-2705-0/hbk; 978-1-4939-2706-7/ebook). xxii, 660 p. (2015). Reviewer: Alain Brillard (Riedisheim) MSC: 35-02 35K85 35Q74 47J35 49J40 49J45 49S05 74-02 74C15 35B27 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{T. Roubíček}, Rate-independent systems. Theory and application. New York, NY: Springer (2015; Zbl 1339.35006) Full Text: DOI OpenURL
Mielke, Alexander; Stefanelli, Ulisse Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity. (English) Zbl 1334.74021 J. Eur. Math. Soc. (JEMS) 15, No. 3, 923-948 (2013). MSC: 74C05 49J45 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{U. Stefanelli}, J. Eur. Math. Soc. (JEMS) 15, No. 3, 923--948 (2013; Zbl 1334.74021) Full Text: DOI arXiv OpenURL
Hackl, K.; Heinz, S.; Mielke, A. A model for the evolution of laminates in finite-strain elastoplasticity. (English) Zbl 1348.74060 ZAMM, Z. Angew. Math. Mech. 92, No. 11-12, 888-909 (2012). MSC: 74C05 74A05 74H20 35Q74 PDF BibTeX XML Cite \textit{K. Hackl} et al., ZAMM, Z. Angew. Math. Mech. 92, No. 11--12, 888--909 (2012; Zbl 1348.74060) Full Text: DOI OpenURL
Mielke, Alexander; Truskinovsky, Lev From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results. (English) Zbl 1286.74024 Arch. Ration. Mech. Anal. 203, No. 2, 577-619 (2012). MSC: 74C05 74A25 74D99 35Q74 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{L. Truskinovsky}, Arch. Ration. Mech. Anal. 203, No. 2, 577--619 (2012; Zbl 1286.74024) Full Text: DOI OpenURL
Bartels, Sören; Mielke, Alexander; Roubíçek, Tomáş Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. (English) Zbl 1248.35105 SIAM J. Numer. Anal. 50, No. 2, 951-976 (2012). MSC: 35K65 35K85 49S05 65M60 74C05 PDF BibTeX XML Cite \textit{S. Bartels} et al., SIAM J. Numer. Anal. 50, No. 2, 951--976 (2012; Zbl 1248.35105) Full Text: DOI OpenURL
Mielke, Alexander On thermodynamically consistent models and gradient structures for thermoplasticity. (English) Zbl 1279.74008 GAMM-Mitt. 34, No. 1, 51-58 (2011). MSC: 74C99 74A15 35Q74 PDF BibTeX XML Cite \textit{A. Mielke}, GAMM-Mitt. 34, No. 1, 51--58 (2011; Zbl 1279.74008) Full Text: DOI OpenURL
Liero, Matthias; Mielke, Alexander An evolutionary elastoplastic plate model derived via \(\Gamma\)-convergence. (English) Zbl 1232.35165 Math. Models Methods Appl. Sci. 21, No. 9, 1961-1986 (2011). MSC: 35Q74 49J45 74C05 74K20 PDF BibTeX XML Cite \textit{M. Liero} and \textit{A. Mielke}, Math. Models Methods Appl. Sci. 21, No. 9, 1961--1986 (2011; Zbl 1232.35165) Full Text: DOI OpenURL
Mielke, Alexander Complete-damage evolution based on energies and stresses. (English) Zbl 1209.74010 Discrete Contin. Dyn. Syst., Ser. S 4, No. 2, 423-439 (2011). Reviewer: Alain Brillard (Riedisheim) MSC: 74C05 35K65 35K85 49S05 74R05 PDF BibTeX XML Cite \textit{A. Mielke}, Discrete Contin. Dyn. Syst., Ser. S 4, No. 2, 423--439 (2011; Zbl 1209.74010) Full Text: DOI OpenURL
Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse Error estimates for space-time discretizations of a rate-independent variational inequality. (English) Zbl 1219.65059 SIAM J. Numer. Anal. 48, No. 5, 1625-1646 (2010). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 65K15 49J40 74C05 74N30 PDF BibTeX XML Cite \textit{A. Mielke} et al., SIAM J. Numer. Anal. 48, No. 5, 1625--1646 (2010; Zbl 1219.65059) Full Text: DOI Link OpenURL
Mielke, Alexander (ed.); Ortiz, Michael (ed.) Microstructures in solids: from quantum models to continua. Abstracts from the workshop held March 14th – March 20th, 2010. (English) Zbl 1209.00066 Oberwolfach Rep. 7, No. 1, 733-798 (2010). MSC: 00B05 82-06 74-06 35-06 35Q74 82Dxx 49J45 74A60 74Cxx 74N15 PDF BibTeX XML Cite \textit{A. Mielke} (ed.) and \textit{M. Ortiz} (ed.), Oberwolfach Rep. 7, No. 1, 733--798 (2010; Zbl 1209.00066) Full Text: DOI Link OpenURL
Thomas, M.; Mielke, A. Damage of nonlinearly elastic materials at small strain – existence and regularity results. (English) Zbl 1191.35159 ZAMM, Z. Angew. Math. Mech. 90, No. 2, 88-112 (2010). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35K85 74C15 74R20 PDF BibTeX XML Cite \textit{M. Thomas} and \textit{A. Mielke}, ZAMM, Z. Angew. Math. Mech. 90, No. 2, 88--112 (2010; Zbl 1191.35159) Full Text: DOI OpenURL
Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. (English) Zbl 1201.49011 SIAM J. Math. Anal. 41, No. 4, 1388-1414 (2009). MSC: 49J40 74C05 74F05 74M05 74N30 49M25 49N60 PDF BibTeX XML Cite \textit{A. Mielke} et al., SIAM J. Math. Anal. 41, No. 4, 1388--1414 (2009; Zbl 1201.49011) Full Text: DOI HAL OpenURL
Bouchitté, Guy; Mielke, Alexander; Roubíček, Tomáš A complete-damage problem at small strains. (English) Zbl 1238.74005 Z. Angew. Math. Phys. 60, No. 2, 205-236 (2009). MSC: 74A45 74R20 74C05 74G65 35Q74 PDF BibTeX XML Cite \textit{G. Bouchitté} et al., Z. Angew. Math. Phys. 60, No. 2, 205--236 (2009; Zbl 1238.74005) Full Text: DOI OpenURL
Mainik, Andreas; Mielke, Alexander Global existence for rate-independent gradient plasticity at finite strain. (English) Zbl 1173.49013 J. Nonlinear Sci. 19, No. 3, 221-248 (2009). MSC: 49J40 49S05 74C15 PDF BibTeX XML Cite \textit{A. Mainik} and \textit{A. Mielke}, J. Nonlinear Sci. 19, No. 3, 221--248 (2009; Zbl 1173.49013) Full Text: DOI Link OpenURL
Mielke, Alexander; Roubíček, Tomáš Numerical approaches to rate-independent processes and applications in inelasticity. (English) Zbl 1166.74010 ESAIM, Math. Model. Numer. Anal. 43, No. 3, 399-428 (2009). MSC: 74H15 74C05 65M12 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{T. Roubíček}, ESAIM, Math. Model. Numer. Anal. 43, No. 3, 399--428 (2009; Zbl 1166.74010) Full Text: DOI EuDML OpenURL
Mielke, Alexander; Rindler, Filip Reverse approximation of energetic solutions to rate-independent processes. (English) Zbl 1163.49030 NoDEA, Nonlinear Differ. Equ. Appl. 16, No. 1, 17-40 (2009). MSC: 49M25 49J45 49S05 65J15 74C05 74H15 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{F. Rindler}, NoDEA, Nonlinear Differ. Equ. Appl. 16, No. 1, 17--40 (2009; Zbl 1163.49030) Full Text: DOI OpenURL
Mielke, Alexander Numerical approximation techniques for rate-independent inelasticity. (English) Zbl 1209.74011 Daya Reddy, B. (ed.), IUTAM symposium on theoretical, computational and modelling aspects of inelastic media. Proceedings of the IUTAM symposium held at Cape Town, South Africa, January 14–18, 2008. Dordrecht: Springer (ISBN 978-1-4020-9089-9/hbk; 978-1-4020-9090-5/ebook). IUTAM Bookseries 11, 53-63 (2008). MSC: 74C05 74G65 PDF BibTeX XML Cite \textit{A. Mielke}, IUTAM Bookser. 11, 53--63 (2008; Zbl 1209.74011) Full Text: DOI OpenURL
Mielke, Alexander; Petrov, Adrien; Martins, João A. C. Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit. (English) Zbl 1147.49004 J. Math. Anal. Appl. 348, No. 2, 1012-1020 (2008). MSC: 49J20 74H55 74C05 74K10 PDF BibTeX XML Cite \textit{A. Mielke} et al., J. Math. Anal. Appl. 348, No. 2, 1012--1020 (2008; Zbl 1147.49004) Full Text: DOI OpenURL
Auricchio, Ferdinando; Mielke, Alexander; Stefanelli, Ulisse A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. (English) Zbl 1151.74319 Math. Models Methods Appl. Sci. 18, No. 1, 125-164 (2008). MSC: 74C05 49J40 PDF BibTeX XML Cite \textit{F. Auricchio} et al., Math. Models Methods Appl. Sci. 18, No. 1, 125--164 (2008; Zbl 1151.74319) Full Text: DOI arXiv OpenURL
Dal Maso, Gianni (ed.); Francfort, Gilles (ed.); Mielke, Alexander (ed.); Roubíček, Tomáš (ed.) Analysis and numerics for rate-independent processes. Abstracts from the workshop held February 25 – March 3, 2007. (English) Zbl 1177.74016 Oberwolfach Rep. 4, No. 1, 591-666 (2007). MSC: 74-06 74Cxx 00B05 49J40 49S05 74Nxx PDF BibTeX XML Cite \textit{G. Dal Maso} (ed.) et al., Oberwolfach Rep. 4, No. 1, 591--666 (2007; Zbl 1177.74016) Full Text: DOI Link OpenURL
Mielke, Alexander; Timofte, Aida M. Two-scale homogenization for evolutionary variational inequalities via the energetic formulation. (English) Zbl 1185.35282 SIAM J. Math. Anal. 39, No. 2, 642-668 (2007). MSC: 35Q74 49J40 74C05 74Q05 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{A. M. Timofte}, SIAM J. Math. Anal. 39, No. 2, 642--668 (2007; Zbl 1185.35282) Full Text: DOI Link OpenURL
Mielke, Alexander; Petrov, Adrien Thermally driven phase transformation in shape-memory alloys. (English) Zbl 1138.49014 Adv. Math. Sci. Appl. 17, No. 2, 667-685 (2007). MSC: 49J40 74C05 74F05 74M05 74N30 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{A. Petrov}, Adv. Math. Sci. Appl. 17, No. 2, 667--685 (2007; Zbl 1138.49014) OpenURL
Gürses, Ercan; Mainik, Andreas; Miehe, Christian; Mielke, Alexander Analytical and numerical methods for finite-strain elastoplasticity. (English) Zbl 1298.74040 Helmig, Rainer (ed.) et al., Multifield problems in solid and fluid mechanics. Berlin: Springer (ISBN 3-540-34959-6/hbk). Lecture Notes in Applied and Computational Mechanics 28, 491-529 (2006). MSC: 74C15 74H20 74S99 35Q74 PDF BibTeX XML Cite \textit{E. Gürses} et al., Lect. Notes Appl. Comput. Mech. 28, 491--529 (2006; Zbl 1298.74040) Full Text: DOI OpenURL
Mielke, Alexander; Müller, Stefan Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. (English) Zbl 1102.74006 ZAMM, Z. Angew. Math. Mech. 86, No. 3, 233-250 (2006). Reviewer: Jan Lovíšek (Bratislava) MSC: 74C15 74G65 49S05 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{S. Müller}, ZAMM, Z. Angew. Math. Mech. 86, No. 3, 233--250 (2006; Zbl 1102.74006) Full Text: DOI Link OpenURL
Mielke, Alexander; Roubíček, Tomáš Rate-independent damage processes in nonlinear elasticity. (English) Zbl 1094.35068 Math. Models Methods Appl. Sci. 16, No. 2, 177-209 (2006). MSC: 35K85 49S05 74C15 74R20 PDF BibTeX XML Cite \textit{A. Mielke} and \textit{T. Roubíček}, Math. Models Methods Appl. Sci. 16, No. 2, 177--209 (2006; Zbl 1094.35068) Full Text: DOI OpenURL
Mielke, Alexander Necessary and sufficient conditions for polyconvexity of isotropic functions. (English) Zbl 1098.49013 J. Convex Anal. 12, No. 2, 291-314 (2005). MSC: 49J45 49K10 74B20 74C05 PDF BibTeX XML Cite \textit{A. Mielke}, J. Convex Anal. 12, No. 2, 291--314 (2005; Zbl 1098.49013) OpenURL
Mielke, Alexander Evolution of rate-independent systems. (English) Zbl 1120.47062 Dafermos, C.M.(ed.) et al., Evolutionary equations. Vol. II. Amsterdam: Elsevier/North-Holland (ISBN 0-444-52048-1/hbk). Handbook of Differential Equations, 461-559 (2005). Reviewer: Evgeniy Panov (Novgorod) MSC: 47N20 47J40 47J20 74C15 74N30 35Q72 34G25 35-00 35B35 35K85 74H99 PDF BibTeX XML Cite \textit{A. Mielke}, in: Handbook of differential equations: Evolutionary equations. Vol. II. Amsterdam: Elsevier/North-Holland. 461--559 (2005; Zbl 1120.47062) OpenURL
Mainik, Andreas; Mielke, Alexander Existence results for energetic models for rate-independent systems. (English) Zbl 1161.74387 Calc. Var. Partial Differ. Equ. 22, No. 1, 73-99 (2005). MSC: 74H20 49J10 74A45 74C15 74G65 74R10 PDF BibTeX XML Cite \textit{A. Mainik} and \textit{A. Mielke}, Calc. Var. Partial Differ. Equ. 22, No. 1, 73--99 (2005; Zbl 1161.74387) Full Text: DOI OpenURL
Mielke, Alexander Modeling and analysis of rate-independent processes in continuum mechanics. (English) Zbl 1079.74010 Wang, Yongqi (ed.) et al., Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22–28, 2004. Aachen: Shaker (ISBN 3-8322-3600-7/pbk). Berichte aus der Mathematik, 299-309 (2005). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 74C05 74N30 74-02 PDF BibTeX XML Cite \textit{A. Mielke}, in: Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22--28, 2004. Aachen: Shaker Verlag. 299--309 (2005; Zbl 1079.74010) OpenURL
Mielke, Alexander A new approach to elasto-plasticity using energy and dissipation functionals. (English) Zbl 1135.74009 Hill, James M. (ed.) et al., Applied mathematics entering the 21st century. Papers from the 5th international congress on industrial and applied mathematics (ICIAM 2003), Sydney, Australia, July 7–11, 2003. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-89871-559-0/hbk). Proceedings in Applied Mathematics 116, 315-335 (2004). MSC: 74C15 74H20 35Q72 22E70 PDF BibTeX XML Cite \textit{A. Mielke}, Proc. Appl. Math. 116, 315--335 (2004; Zbl 1135.74009) OpenURL
Mielke, Alexander Deriving new evolution equations for microstructures via relaxation of variational incremental problems. (English) Zbl 1112.74332 Comput. Methods Appl. Mech. Eng. 193, No. 48-51, 5095-5127 (2004). MSC: 74C15 74A60 PDF BibTeX XML Cite \textit{A. Mielke}, Comput. Methods Appl. Mech. Eng. 193, No. 48--51, 5095--5127 (2004; Zbl 1112.74332) Full Text: DOI OpenURL
Mielke, Alexander Existence of minimizers in incremental elasto-plasticity with finite strains. (English) Zbl 1076.74012 SIAM J. Math. Anal. 36, No. 2, 384-404 (2004). MSC: 74C15 74G65 74H20 PDF BibTeX XML Cite \textit{A. Mielke}, SIAM J. Math. Anal. 36, No. 2, 384--404 (2004; Zbl 1076.74012) Full Text: DOI OpenURL
Hackl, Klaus; Mielke, Alexander; Mittenhuber, Dirk Dissipation distances in multiplicative elastoplasticity. (English) Zbl 1095.74005 Wendland, Wolfgang (ed.) et al., Analysis and simulation of multifield problems. Selected papers of the international conference on multifield problems, Stuttgart, Germany, April 8–10, 2002. Berlin: Springer (ISBN 3-540-00696-6/hbk). Lect. Notes Appl. Comput. Mech. 12, 87-100 (2003). MSC: 74C15 PDF BibTeX XML Cite \textit{K. Hackl} et al., Lect. Notes Appl. Comput. Mech. 12, 87--100 (2003; Zbl 1095.74005) OpenURL
Mielke, A. Evolution of rate-independent inelasticity with microstructure using relaxation and Young measures. (English) Zbl 1040.74011 Miehe, Christian (ed.), IUTAM symposium on computational mechanics of solid materials at large strains. Proceedings of the IUTAM symposium, Stuttgart, Germany, August 20–24, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1170-9/hbk). Solid Mech. Appl. 108, 33-44 (2003). MSC: 74C15 74A60 74G65 PDF BibTeX XML Cite \textit{A. Mielke}, Solid Mech. Appl. 108, 33--44 (2003; Zbl 1040.74011) OpenURL
Mielke, A. Energetic formulation of multiplicative elasto-plasticity using dissipation distances. (English) Zbl 1068.74522 Contin. Mech. Thermodyn. 15, No. 4, 351-382 (2003). MSC: 74C15 74G65 PDF BibTeX XML Cite \textit{A. Mielke}, Contin. Mech. Thermodyn. 15, No. 4, 351--382 (2003; Zbl 1068.74522) Full Text: DOI OpenURL
Mielke, Alexander Finite elastoplasticity Lie groups and geodesics on \(\text{SL}(d)\). (English) Zbl 1146.74309 Newton, Paul (ed.) et al., Geometry, mechanics, and dynamics. Volume in honor of the 60th birthday of J. E. Marsden. New York, NY: Springer (ISBN 0-387-95518-6/hbk). 61-90 (2002). MSC: 74C15 53B40 22E40 53C22 PDF BibTeX XML Cite \textit{A. Mielke}, in: Geometry, mechanics, and dynamics. Volume in honor of the 60th birthday of J. E. Marsden. New York, NY: Springer. 61--90 (2002; Zbl 1146.74309) Full Text: DOI OpenURL
Mielke, Alexander Analysis of energetic models for rate-independent materials. (English) Zbl 1018.74007 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press. 817-828 (2002). Reviewer: N.Cristescu (Gainesville) MSC: 74C15 74G65 PDF BibTeX XML Cite \textit{A. Mielke}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 817--828 (2002; Zbl 1018.74007) Full Text: arXiv OpenURL
Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander Non-convex potentials and microstructures in finite-strain plasticity. (English) Zbl 1008.74016 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 299-317 (2002). MSC: 74C15 74G65 74A60 PDF BibTeX XML Cite \textit{C. Carstensen} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 299--317 (2002; Zbl 1008.74016) Full Text: DOI OpenURL
Kuczma, M. S.; Mielke, A. Influence of hardening and inhomogeneity on internal loops in pseudoelasticity. (English) Zbl 1031.74039 ZAMM, Z. Angew. Math. Mech. 80, No. 5, 291-306 (2000). Reviewer: I.A.Parinov (Rostov-na-Donu) MSC: 74N30 74N05 74C99 74A15 PDF BibTeX XML Cite \textit{M. S. Kuczma} and \textit{A. Mielke}, ZAMM, Z. Angew. Math. Mech. 80, No. 5, 291--306 (2000; Zbl 1031.74039) Full Text: DOI OpenURL