Gao-Feng Zhao

A 3D distinct lattice spring model (DLSM) is proposed where matter is discretized into individual particleslinked by springs. The presented model is different from the conventional lattice spring models where ashear spring is introduced to model the multibody force by evaluating the spring deformation from the localstrain rather than the particle displacement. By doing this, the proposed model can represent the diversityof Poisson’s ratio without violating the rotational invariance. The local strain of the spring is calculatedthrough a least square method which makes the model possessing meshless properties. Because of thisand explicitly representing the microstructure, DLSM is able to model dynamic fracturing problems andcan be used to study the microstructure inflfluences. The material parameters inputted in the model is theconventional material parameters, e.g. the elastic modules and the Poisson’s ratio. Relationships betweenmicroscopic spring parameters and macroscopic material constants are derived based on the Cauchy–Bornrules and the hyperelastic theory. Numerical examples are presented to show the abilities and propertiesof DLSM in modeling elastic and dynamic failure problems. Copyright  2010 John Wiley & Sons, Ltd.Received 22 September 2009; Revised 15 March 2010; Accepted 19 March 2010KEY WORDS: 3D model; lattice spring model; microstructure; dynamic failure