The cell model of materials

Abstract

The cell is regarded as the smallest material unit that contains reasonably sufficient information about crack growth in the material. A cell is either in a cohesive state or in a decohesive state, the latter implying instability at load control. It is characterized by its linear size and its cohesion-decohesion relation. The reference case of a uniaxially loaded, originally cubic, cell exhibits the cohesive strength and the elongations at which decohesion starts and ends. These quantities influence the size and shape of the process region at a crack edge and also the energy required for crack growth. A body can be modelled by an aggregate of cells, but such modelling is needed only in regions where cells are expected to reach the docohesive state. The cell model is a model of the material and is not necessarily connected to a particular computational method. However, the cells can be fitted into a finite element or finite difference formulation. For dynamic cases such as fast crack growth the cell model can be used to qualitatively reproduce experimental results which could hardly be obtained by means of continuum models.