Continuous constitutive model for bimodulus materials with meshless approach

One of the difficulties in dealing with bimodular materials including composites, rock and asphalt-mixture material is the discontinuity of Young's modulus when the principal stress changes sign, i.e. from a tensile stress state to a compressive stress state. According to the general elastic theory proposed by Ambartsumyan, there are two kinds of domains in which the coefficients of elasticity are constant. The discontinuity of Young's modulus causes divergence in the computational procedure. In order to overcome this difficulty, two continuous modes for bimodular materials are proposed in this paper. The non-linear equilibrium equations have been formulated with a continuous constitute equation of stress and strain. The meshless finite block method is successful in solving the nonlinear problems for bimodular materials. The numerical solutions of the meshless finite block method in a strong form are obtained using an iterative technique. The degree of accuracy and convergence of the proposed technique is demonstrated by directly comparing the achieved results with the finite element method and analytical solutions.