Component assembling model and its application to quasi-brittle damage S.C. Deng * , J.X. Liu, J. Zhang, N.G. Liang State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences (CAS), Graduate School of CAS, Beijing 100080, China Available online 25 October 2006 Abstract Potential energy can be approximated by ‘‘pair-functional’’ potentials which is composed of pair potentials and embed- ding energy. Pair potentials are grouped according to discrete directions of atomic bonds such that each group is repre- sented by an orientational component. Meanwhile, another kind of component, the volumetric one is derived from embedding energy. Damage and fracture are the changing and breaking of atomic bonds at the most fundamental level and have been reflected by the changing of these components’ properties. Therefore, material is treated as a component assembly, and its constitutive equations are formed by means of assembling these two kinds of components’ response func- tions. This material model is referred to as the component assembling model. Theoretical analysis and numerical comput- ing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of physical explicitness and intrinsic induced anisotropy, etc. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Damage; Fracture; Anisotropy; Constitutive equation; Pair-functional potentials; Pair potentials; Embedding energy; Orientational/volumetric component; Component assembling model 1. Introduction Material made up of a large number of atoms is regarded as a many-body system. The binding forces among atoms determine the material structures and its intrinsic mechanical and electromagnetic properties [1–3]. The exact treatment of this many-body problem by formulation and solution of Schrodinger wave equa- tions [1,4] is not tractable because of the large number of atoms involved. By using the adiabatic Born–Oppen- heimer approximation [1,5], the interatomic potentials that express directly the interactions among atoms have been proposed. The difficulties in solving many-body system have been reduced greatly. Pair-functional is a representative model of interatomic potentials. It considers the interaction among the atoms and electrons [1,3,6–8]. However, the space and time scales in molecular dynamics simulation [9–11] based on interatomic potentials have been confined for the limited computational power. 0167-8442/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2006.09.002 * Corresponding author. Tel.: +86 10 6254 5533 3182; fax: +86 10 6257 9511. E-mail address: dengsc@lnm.imech.ac.cn (S.C. Deng). Theoretical and Applied Fracture Mechanics 46 (2006) 232–242 www.elsevier.com/locate/tafmec