Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

Abstract

A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture) of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA) method, which integrates the possibilities of particle-based discrete element method (DEM) and cellular automaton methods. Emergent advantages of the developed approach to formulation of manybody interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elasticplastic) and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

Modeling mechanical behaviors of composites with various ratios of matrix–inclusion properties using movable cellular automaton method

“…For this purpose Wilkins' algorithm [34] is adapted to the MCA method [27,40]. It is well known that Wilkins' radial return algorithm consists in the solution of elastic problem in the increments and subsequent "drop" of components of deviator stress tensor D ab ¼ s ab À 1=3s kk d ab to von Mises yield surface in the case that stress intensity exceeds it ( Fig.…”

“…Thus, the rheological properties of the material of the automaton i are determined by defining a unified hardening curve s i int ¼ Fðε i int Þ (here ε i int is the average intensity of strain tensor that can be computed, similar to s i ab [27,32]); this dependence is also named as automaton response function.…”

“…[27,32], the expression for the components of the average stress tensor in automaton i takes the form…”

“…shear ij ( Fig. 1(b)) calculated with taking into account the rotation of both automata [26,27]. Note that, although the last expression of Eq.…”

“…Many-body formulation of inter-element forces is adopted from the WienereRosenblueth model of cellular automaton interaction [23,24]. This hybrid technique is referred to as movable cellular automaton method (MCA) [21,22,25,27]. The proposed generalized expression for interelement forces is the ability to establish the relationship between vector parameters of the interaction and tensor parameters of the material constitutive law.…”