Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization

被引:54
作者
Goury, Olivier [1 ,2 ,3 ]
Amsallem, David [4 ]
Bordas, Stephane Pierre Alain [1 ,5 ]
Liu, Wing Kam [6 ]
Kerfriden, Pierre [1 ]
机构
[1] Cardiff Univ, Sch Engn, Queens Bldg, Cardiff CF24 3AA, S Glam, Wales
[2] Inria Lille Nord Europe, DEFROST Team, 40 Ave Halley, F-59000 Lille, France
[3] Univ Paris 06, UMR S 1159, INSERM, F-75005 Paris, France
[4] Stanford Univ, Dept Aeronaut & Astronaut, Mail Code 4035, Stanford, CA 94305 USA
[5] Univ Luxembourg, Campus Kirchberg G 007, Luxembourg, Luxembourg
[6] Northwestern Univ, Dept Mech Engn, 2145 Sheridan Rd, Evanston, IL 60208 USA
基金
英国工程与自然科学研究理事会; 欧洲研究理事会;
关键词
Model order reduction; Computational homogenisation; Reduced basis; Hyperreduction; Damage mechanics; Multiscale; PROPER ORTHOGONAL DECOMPOSITION; TRANSFORMATION FIELD ANALYSIS; PARTIAL-DIFFERENTIAL-EQUATIONS; EMPIRICAL INTERPOLATION; HETEROGENEOUS MATERIALS; COMPOSITE-MATERIALS; HOMOGENIZATION; REDUCTION; FRACTURE; PROJECTION;
D O I
10.1007/s00466-016-1290-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by any load path applied onto the representative volume element. We take special care of the challenge of selecting an exhaustive snapshot set. This is treated by first using a random sampling of energy dissipating load paths and then in a more advanced way using Bayesian optimization associated with an interlocked division of the parameter space. Results show that we can insure the selection of an exhaustive snapshot set from which a reliable reduced-order model can be built.
引用
收藏
页码:213 / 234
页数:22
相关论文
共 57 条
[11]   Discrete Empirical Interpolation for Nonlinear Model Reduction [J].
Chaturantabut, Saifon ;
Sorensen, Danny C. .
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, :4316-4321
[12]   NONLINEAR MODEL REDUCTION VIA DISCRETE EMPIRICAL INTERPOLATION [J].
Chaturantabut, Saifon ;
Sorensen, Danny C. .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (05) :2737-2764
[13]   RESIDUAL MINIMIZING MODEL INTERPOLATION FOR PARAMETERIZED NONLINEAR DYNAMICAL SYSTEMS [J].
Constantine, Paul G. ;
Wang, Qiqi .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (04) :A2118-A2144
[14]   The ROMES Method for Statistical Modeling of Reduced-Order-Model Error [J].
Drohmann, Martin ;
Carlberg, Kevin .
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2015, 3 (01) :116-145
[15]   TRANSFORMATION FIELD ANALYSIS OF INELASTIC COMPOSITE-MATERIALS [J].
DVORAK, GJ .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 437 (1900) :311-327
[16]   KARHUNEN-LOEVE PROCEDURE FOR GAPPY DATA [J].
EVERSON, R ;
SIROVICH, L .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1995, 12 (08) :1657-1664
[17]   Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency [J].
Farhat, Charbel ;
Avery, Philip ;
Chapman, Todd ;
Cortial, Julien .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2014, 98 (09) :625-662
[18]   FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials [J].
Feyel, F ;
Chaboche, JL .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 183 (3-4) :309-330
[19]   Computational plasticity for composite structures based on mathematical homogenization: Theory and practice [J].
Fish, J ;
Shek, K ;
Pandheeradi, M ;
Shephard, MS .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1997, 148 (1-2) :53-73
[20]   Higher-order homogenization of initial/boundary-value problem [J].
Fish, J ;
Chen, W .
JOURNAL OF ENGINEERING MECHANICS-ASCE, 2001, 127 (12) :1223-1230