A MLS-Based lattice spring model for simulating elasticity of materials

GAO-FENG ZHAO

A MLS-based lattice spring model is presented for numerical modeling of elasticity ofmaterials. In the model, shear springs between particles are introduced in addition tonormal springs. However, the unknowns contain only particle displacements but no particle rotations. The novelty of the model lies in that the deformations of shear springs arecomputed by using the local strain obtained by the moving least squares (MLS) approximation rather than using the particle displacements directly. By doing so, the proposedlattice spring model can represent the diversity of Poisson’s ratio without violating therequirement of rotational invariance. Relationships between micro spring parameters andmacro material constants are derived from the Cauchy-born rules and the hyperelastictheory. Numerical examples show that the proposed model is able to reproduce elasticsolutions obtained by finite element methods for problems without fractures. Therefore,it is capable of simulating solid materials which are initially continuous, but eventuallyfracture when critical stress and/or displacement levels are reached. A demonstratingexample is presented