Effective relaxation for microstructure simulations: algorithms and applications

[1]  Carsten Carstensen,et al.  An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads , 2004, Numerische Mathematik.

[2]  Andreas Prohl,et al.  Multiscale resolution in the computation of crystalline microstructure , 2004, Numerische Mathematik.

[3]  Carsten Carstensen,et al.  Adaptive Finite Element Methods for Microstructures? Numerical Experiments for a 2-Well Benchmark , 2003, Computing.

[4]  Carsten Carstensen,et al.  All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable , 2003, Math. Comput..

[5]  Sylvie Aubry,et al.  A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials , 2003 .

[6]  Carsten Carstensen,et al.  A Posteriori Finite Element Error Control for the P-Laplace Problem , 2003, SIAM J. Sci. Comput..

[7]  M. Lambrecht,et al.  Energy relaxation of non-convex incremental stress potentials in a strain-softening elastic–plastic bar , 2003 .

[8]  M. Lambrecht,et al.  A two-scale finite element relaxation analysis of shear bands in non-convex inelastic solids: small-strain theory for standard dissipative materials , 2003 .

[9]  Carsten Carstensen,et al.  Non–convex potentials and microstructures in finite–strain plasticity , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  Carsten Carstensen,et al.  Local Stress Regularity in Scalar Nonconvex Variational Problems , 2002, SIAM J. Math. Anal..

[11]  Carsten Carstensen,et al.  Numerical analysis of a relaxed variational model of hysteresis in two-phase solids , 2001 .

[12]  John M. Ball,et al.  Regularity of quasiconvex envelopes , 2000 .

[13]  Carsten Carstensen,et al.  Numerical Analysis of Compatible Phase Transitions in Elastic Solids , 2000, SIAM J. Numer. Anal..

[14]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[15]  Georg Dolzmann,et al.  Numerical Computation of Rank-One Convex Envelopes , 1999 .

[16]  Michael Ortiz,et al.  Nonconvex energy minimization and dislocation structures in ductile single crystals , 1999 .

[17]  Peter Spellucci,et al.  An SQP method for general nonlinear programs using only equality constrained subproblems , 1998, Math. Program..

[18]  Carsten Carstensen,et al.  Numerical solution of the scalar double-well problem allowing microstructure , 1997, Math. Comput..

[19]  ROY A. NICOLAIDES,et al.  Numerical Methods for a Nonconvex Optimization Problem Modeling Martensitic Microstructure , 1997, SIAM J. Sci. Comput..

[20]  Tomáš Roubíček,et al.  Relaxation in Optimization Theory and Variational Calculus , 1997 .

[21]  Klaus Hackl,et al.  Generalized standard media and variational principles in classical and finite strain elastoplasticity , 1997 .

[22]  Mitchell Luskin,et al.  On the computation of crystalline microstructure , 1996, Acta Numerica.

[23]  János D. Pintér,et al.  Global optimization in action , 1995 .

[24]  Luc Tartar,et al.  Beyond young measures , 1995 .

[25]  R. A. Nicolaides,et al.  Strong convergence of numerical solutions to degenerate variational problems , 1995 .

[26]  Robert V. Kohn,et al.  The relaxation of a double-well energy , 1991 .

[27]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[28]  R. Kohn,et al.  Numerical study of a relaxed variational problem from optimal design , 1986 .

[29]  John M. Ball,et al.  Strict convexity, strong ellipticity, and regularity in the calculus of variations , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[30]  J. Ball Convexity conditions and existence theorems in nonlinear elasticity , 1976 .

[31]  Charles B. Morrey,et al.  QUASI-CONVEXITY AND THE LOWER SEMICONTINUITY OF MULTIPLE INTEGRALS , 1952 .

[32]  O. Bolza A Fifth Necessary Conditions for a Strong Extremum of the Integral: x 1 x 0 F(x, y, y )dx , 1906 .

[33]  Oskar Bolza,et al.  A Fifth Necessary Condition for a Strong Extremum of the Integral , 1906 .

[34]  Sören Bartels,et al.  Reliable and Efficient Approximation of Polyconvex Envelopes , 2005, SIAM J. Numer. Anal..

[35]  S. B ARTELS,et al.  Convergence for stabilisation of degenerately convex minimisation problems , 2004 .

[36]  Klaus Hackl,et al.  On the Calculation of Microstructures for Inelastic Materials using Relaxed Energies , 2003 .

[37]  Marc Oliver Rieger,et al.  Young Measure Solutions for Nonconvex Elastodynamics , 2003, SIAM J. Math. Anal..

[38]  Alexander Mielke,et al.  Evolution of Rate{Independent Inelasticity with Microstructure using Relaxation and Young Measures , 2003 .

[39]  Christian Miehe,et al.  IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains , 2003 .

[40]  A. Mielke Finite Elastoplasticity Lie Groups and Geodesics on SL(d) , 2002 .

[41]  C. Carstensen,et al.  On microstructures occuring in a model of finite‐strain elastoplasticity involving a single slip—system , 2000 .

[42]  S. Müller Variational models for microstructure and phase transitions , 1999 .

[43]  P. Pedregal Parametrized measures and variational principles , 1997 .

[44]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[45]  Pablo Pedregal,et al.  Weak convergence of integrands and the young measure representation , 1992 .

[46]  V. Sverák,et al.  Rank-one convexity does not imply quasiconvexity , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[47]  G. Gladwell,et al.  Solid mechanics and its applications , 1990 .

[48]  J. Ball A version of the fundamental theorem for young measures , 1989 .

[49]  Quoc Son Nguyen,et al.  Sur les matériaux standard généralisés , 1975 .

[50]  Carsten Carstensen,et al.  Esaim: Mathematical Modelling and Numerical Analysis Young-measure Approximations for Elastodynamics with Non-monotone Stress-strain Relations , 2022 .

[51]  Michel Chipot,et al.  F Ur Mathematik in Den Naturwissenschaften Leipzig Sharp Energy Estimates for Nite Element Approximations of Non-convex Problems Sharp Energy Estimates for Finite Element Approximations of Non-convex Problems , 2022 .