Genesis of the multiscale approach for materials with microstructure

被引:36
作者
Trovalusci, Patrizia [1 ]
Capecchi, Danilo [1 ]
Ruta, Giuseppe [1 ]
机构
[1] Univ Roma La Sapienza, Dipartimento Ingn Strutturale & Geotecn, Rome, Italy
关键词
Molecular theory of elasticity; Multiscale modeling; Constitutive models; Lattice mechanics; HOMOGENIZATION; ELASTICITY; ELEMENT; MODEL; DERIVATION; CONTINUA; FRACTURE; STRESS; SIZE;
D O I
10.1007/s00419-008-0269-7
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This paper presents an overview of the origin of multiscale approaches in mechanics. While the pioneer molecular models of linear elastic bodies by Navier, Cauchy and Poisson were contradicted by experiments, the phenomenological energetic approach by Green still seems suitable for simple materials only. Voigt's molecular model, here reinterpreted in the light of contemporary mechanics, reconciled the two approaches providing a conceptual guideline for developing constitutive models based on a direct link between continuum and discrete solid mechanics. Such a theoretical background proves to be especially suitable for new complex materials. An example referred to masonry-like materials is given.
引用
收藏
页码:981 / 997
页数:17
相关论文
共 98 条
[1]  
ALICANDRO R, 2007, INTEGRAL REPRESENTAT
[2]  
[Anonymous], 2012, Microcontinuum field theories: I. Foundations and solidsM
[3]  
[Anonymous], 2006, Milieux continus generalises et materiaux heterogenes
[4]  
[Anonymous], CISM COURSES LECT
[5]  
[Anonymous], 1987, LECT NOTES PHYS
[6]  
[Anonymous], 1910, LEHRBUCH KRISTALLPHY
[7]  
Askar A., 1985, Lattice Dynamical Foundations of Continuum Theories
[8]   DERIVATION OF HIGHER-ORDER GRADIENT CONTINUUM-THEORIES IN 2,3-D NONLINEAR ELASTICITY FROM PERIODIC LATTICE MODELS [J].
BARDENHAGEN, S ;
TRIANTAFYLLIDIS, N .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1994, 42 (01) :111-139
[9]   From molecular models to continuum mechanics [J].
Blanc, X ;
Le Bris, C ;
Lions, PL .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (04) :341-381
[10]   Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case [J].
Braides, A ;
Dal Maso, G ;
Garroni, A .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1999, 146 (01) :23-58