Lattice spring model with angle spring and its application in fracture simulation of elastic brittle materials

Abstract

Lattice Spring Model with Angle Spring (LSMA) is a novel type of lattice model. Compared with the general lattice spring model, LSMA adds the rotational and tangential degrees of freedom, whose spring parameters are obtained by finite element parameter mapping. The traditional lattice spring model only consider the normal interaction between two points (the Poisson’s ratio is fixed), which limits the application of the lattice spring model in a wider range of materials. Some scholars proposed to add shear spring into the traditional model to solve the problem of fixed Poisson’s ratio, but the rotation invariance could not be maintained. The main reason is that the shear spring can not distinguish the difference of tangential velocity (or displacement) between the two particles due to the common rotation or shear. Therefore, the rotation of the whole rigid body may cause incorrect generation of additional strain energy inside the shear spring. LSMA model is able to maintain rotation invariance and reproduce different Poisson’s ratio because of the spring parameters with rotational degrees of freedom and the rotation effect of lattice points. In this paper, the finite element stiffness matrix with rotational freedom is derived by using LSMA as the basic mechanical model, and the parameter mapping theory of spring stiffness coefficient is introduced. By means of numerical simulation, the deflection and rotation Angle of cantilever beam, shear wave and compressional wave velocity of stress wave and the simulation of compact tensile test are checked and calculated respectively, and the correctness of the model is verified.