Numerical Simulations Of Effective Mechanical Properties And Failure Process Of Heterogeneous Materials

Most materials are heterogeneous in nature due to the presence and interaction of the microstructures within. In conventional numerical analyses the macro non-linearity of the materials is simulated through assigning the nonlinear constitutive relation of homogeneous material to each element. Such deterministic model cannot reflect the randomness of the material properties. The statistical methods are needed to analyze and quantify the output of structural system in order to give reliable structural safety design. Based on the nature of meso-heterogeneity, the macro non-linearity of heterogeneous brittle material is numerically simulated by spatial-randomly distributed elements with linear constitutive relation of different material properties in this paper.The heterogeneous material specimen is discretized into lattice elements with the same size. The elastic modulus and failure strength of the lattice elements are randomly determined by corresponding discrete sequences produced by statistical distribution to represent the initial heterogeneity of material properties. In the failure simulation, the number of failed elements in each time step is well controlled by self-adaptive load-step size. The element with "air modulus" is introduced to replace the failed element so that the geometric continuity keeps unchanged for the damaged specimen and the 3-D failure process of the heterogeneous brittle material can be simulated through continual update of the structural stiffness matrix and iterative solution. By means of the self-adaptive load-step and "air modulus" element, the failure process of heterogeneous brittle material under quasi-static loading can be simulated more easily.The two-phase composites, such as granular reinforced composite, the laminated composite and the reinforced composite are modeled with the lattice approach to reflect the heterogeneous distribution of material component. The effects of heterogeneity on equivalent modulus and failure process are analyzed. The results obtained can provide useful instructions for the producing technique and manufacturing procedure of the composite materials.For the one-dimensional case of the heterogeneous brittle material, assumed that the distributions of the elastic modulus and the failure strength are random and independent, the one-dimensional analytical stress-strain relations with the heterogeneity parameters can be derived. These analytical expressions are helpful to understand the essential relations between macro non-linearity and the parameters of heterogeneous distribution, and to quickly calculate the statistical constants of the elastic field in the 1-D heterogeneous material structures.The Multi-sub-region Boundary Element Method is employed to analyze the structures consists of components with different material properties. The Reduplicate Sub-region Boundary Element Method is used to simulate the full failure process of heterogeneous brittle material since the lattice model with the same geometric size is used to discretize the specimen. The coefficient matrices are only generated just once, so the computational efficiency is increased significantly.