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Lattice-cell approach to quasibrittle fracture modeling

The present paper deals with a lattice-cell approach to fracture modeling. The struts in the lattice form triangular cells, which resist volume change and thus introduce a coupling of the constitutive responses of the struts. With this approach, the full range of Poisson's ratio ofan elastic solid can be modeled. Poisson's ratio is controlled by the ratio of the material stiffness of the struts and the cells. The relationship of the parameters of the lattice-cell model to the parameters of the Hooke's law of the elastic solid in plane strain is derived using as an example an equilateral triangle. The validity of these derivations is supported by numerical simulation of an elastic solid in uniaxial tension. Furthermore, the constitutive respo~e of the strut is extended to take into account the evolution of damage, which allows the simulation of fracture. The fracture process of a solid in plane strain subjected to' uniaxial tension is studied. Both the positions of the vertices and the material strengths of the struts are assumed to be random. The results show that the lattice-cell model is able to describe the full range of Poisson's ratio of an elastic solid and still remains suitable for modeling fracture. So far, the model,is limited to plane strain and tensile fracture.