Approximation in multiscale modelling of microstructure evolution in shape-memory alloys

被引：11
作者：
Roubicek, Tomas [1 ,2 ]
机构：
[1] Charles Univ Prague, Math Inst, Prague 18675 8, Czech Republic
[2] Inst Thermomech ASCR, Prague 18200 8, Czech Republic
来源：
CONTINUUM MECHANICS AND THERMODYNAMICS | 2011年 / 23卷 / 06期
关键词：
Smart materials; Rate-independent processes; Young measures; MARTENSITIC PHASE-TRANSFORMATIONS; NUMERICAL-SIMULATION; SINGLE-CRYSTALS; ENERGY; COMPUTATION; HYSTERESIS;
D O I：
10.1007/s00161-011-0190-0
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
Various models of microstructure in deformation gradient and its evolution arising in martensitic mechanically-induced isothermal phase transformation are surveyed and scrutinized, focusing on over-bridging of various scales of the problem and its numerical approximation. In particular, numerically efficient model of a relaxed problem is shown to be approximated by conventional but computationally less efficient model based on standard partial differential inequalities.
引用
收藏
页码：491 / 507
页数：17
相关论文
共 66 条
[1]  
[Anonymous], 1999, CALC VAR OPT CONTROL
[2]  
[Anonymous], 1997, Relaxation in Optimization Theory and Variational Calculus
[3]  
[Anonymous], 2003, Oxford Series on Materials Modelling
[4]   ON THE COMPUTATION OF THE RANK-ONE CONVEX HULL OF A FUNCTION [J].
Aranda, Ernesto ;
Pedregal, Pablo .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2001, 22 (05) :1772-1790
[5]   Martensitic transformation in NiMnGa single crystals:: Numerical simulation and experiments [J].
Arndt, M. ;
Griebel, M. ;
Novak, V. ;
Roubicek, T. ;
Sittner, P. .
INTERNATIONAL JOURNAL OF PLASTICITY, 2006, 22 (10) :1943-1961
[6]  
Arndt M, 2003, LN APP C M, V12, P59
[7]   A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials [J].
Aubry, S ;
Fago, M ;
Ortiz, M .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (26-27) :2823-2843
[8]   FINE PHASE MIXTURES AS MINIMIZERS OF ENERGY [J].
BALL, JM ;
JAMES, RD .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1987, 100 (01) :13-52
[9]   A micromechanical model for martensitic phase-transformations in shape-memory alloys based on energy-relaxation [J].
Bartel, Thorsten ;
Hackl, Klaus .
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2009, 89 (10) :792-809
[10]   Effective relaxation for microstructure simulation: algorithms and applications [J].
Bartels, S ;
Carstensen, C ;
Hackl, K ;
Hoppe, U .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (48-51) :5143-5175
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