Implementation of a high order lattice spring model for elasticity

In a lattice spring model (LSM), the material is discretised into particles linked by springs. However, LSMs always adopt linear springs, which results in a stiff approximation of the corresponding elastic solution. In this work, a high order LSM is proposed to overcome this limitation by introducing additional degrees of freedoms (DOFs) to the particles. Based on the energy minimisation principle and the local strain technique, equations for the stiffness matrices of high order LSM are derived. Relationships between micro spring parameters and macro material constants are derived from the Cauchy-born rules and the hyperelastic theory. Numerical examples show that the high order LSM can provide a better solution than that of the linear LSM and that the LSM is more suitable for modelling singularity and fracture problems.