The Computation of Martensitic Microstructure with Piecewise Laminates

We present a numerical method for the approximation of microstructure in martensitic crystals by piecewise laminates, and we give computational results for several three-dimensional models of martensitic microstructure by using piecewise second-order laminates.

[1]  Zhiping Li.  Finite Order Rank-One Convex Envelopes and Computation of Microstructures with Laminates in Laminates , 2000 .

[2]  Mitchell Luskin,et al.  The computation of the austenitic-martensitic phase transition , 1989 .

[3]  D. Kinderlehrer,et al.  Numerical analysis of oscillations in multiple well problems , 1995 .

[4]  R. Kohn,et al.  Optimal design and relaxation of variational problems, III , 1986 .

[5]  M. Luskin,et al.  Stability of microstructure for tetragonal to monoclinic martensitic transformations , 2000 .

[6]  Pablo Pedregal,et al.  On the numerical analysis of non-convex variational problems , 1996 .

[7]  Mitchell Luskin,et al.  Analysis of the finite element approximation of microstructure in micromagnetics , 1992 .

[8]  Mitchell Luskin,et al.  The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic‐to‐Orthorhombic Phase Transformation , 1999 .

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

[10]  Martin Kruzík,et al.  Numerical Approach to Double Well Problems , 1998 .

[11]  A. Mielke,et al.  A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle , 2002 .

[12]  M. Luskin,et al.  On the numerical modeling of deformations of pressurized martensitic thin films , 2001 .

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

[14]  Andreas Prohl,et al.  Young measure approximation in micromagnetics , 2001, Numerische Mathematik.

[15]  Richard D. James,et al.  Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy , 1996 .

[16]  R. D. James,et al.  Proposed experimental tests of a theory of fine microstructure and the two-well problem , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

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

[18]  Charles Collins,et al.  Convergence of a Reduced Integration Method for Computing Microstructures , 1998 .

[19]  On the kinetics of an austenite → martensite phase transformation induced by impact in a CuAlNi shape-memory alloy , 1997 .

[20]  Mitchell Luskin,et al.  A computational model for the indentation and phase transformation of a martensitic thin film , 2002 .

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

[22]  M. Luskin,et al.  Stability of microstructures for some martensitic transformations , 2001 .

[23]  Tomáš Roubíček,et al.  Dissipative Evolution of Microstructure in Shape Memory Alloys , 2000 .

[24]  R. A. Nicolaides,et al.  Computation of Microstructure Utilizing Young Measure Representations , 1993 .

[25]  V. Lunin,et al.  Wavelet transform of signal for enhancement of SNR in wire rope inspection , 2002 .

[26]  Zhiping Li,et al.  Simultaneous numerical approximation of microstructures and relaxed minimizers , 1997 .

[27]  Klaus Schittkowski,et al.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[28]  Vladimir Sverak.  On the Problem of Two Wells , 1993 .

[29]  Mitchell Luskin,et al.  Computational modeling of microstructure , 2003, math/0305005.

[30]  Tomáš Roubíček,et al.  Evolution model for martensitic phase transformation in shape-memory alloys , 2002 .

[31]  Pablo Pedregal,et al.  Numerical approximation of parametrized measures , 1995 .

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

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

[34]  B. Li,et al.  Finite Element Analysis of Microstructure for the Cubic to Tetragonal Transformation , 1998 .

[35]  Andreas Prohl,et al.  A Discontinuous Finite Element Method for Solving a Multiwell Problem , 1999, SIAM J. Numer. Anal..

[36]  Mitchell Luskin,et al.  Approximation of a laminated microstructure for a rotationally invariant, double well energy density , 1996 .