Lattice-based six-spring discrete element model for discretisation problems of 2D isotropic and anisotropic solids

Abstract

Development of the six-spring lattice-type dis-crete element (DE) model for planar classical continuum is considered. The discrete model is shaped by periodic HEXAGONAL lattice. A natural triangle finite element is employed for the development of the model, while discrete elasticity parameters are defined in terms of the natural stiffness matrix. The model operates using the stiffness of six springs for a general case of anisotropic material. For isotropic material the number of independent parameters is reduced to two.The developed six-spring discrete element (DE) model may be characterised as an alternative lattice model with central and angular interaction. The combination of axial and shear stiffness allows us to avoid singularity a wider range of Poisson’s ratio, including ν ≥ 0.33 for plane stress problem. The model validated by simulating the dy-namic behaviour of the plane stress problem for isotropic and orthotropic material.