Random Field Generation of the Material Properties in the Truss-Like Discrete Element Method

Abstract

In the truss-like Discrete Element Method (DEM), masses are considered lumped at nodal points and linked by means of uni-dimensional elements characterized by arbitrary constitutive relations. When regular arrays are employed for determining the response of bodies made of homogeneous materials, the mechanical properties of the elements depend only on the material properties and on the length of the element. In case on non-homogeneous materials, its mechanical properties must be characterized as 3D random fields and the resulting mechanical properties of the elements vary with their location within the field. Thus, the numerical simulation of 3D scalar random fields becomes one important step in the analysis. When the size L of the elements is larger than the cor relation length of the random field, the properties of adjacent elements may be assumed un correlated. In such case all the random properties, ssuch as the elements stiffness, may be assumed independent and the numerical simulation is straight-forward. Similarly, if the 3D random field is Gaussian, recourse may be made to available numerical procedures. In this paper a scheme is suggested to simulate 3D random fields characterized by arbitrary probability distributions. This is important because when a dense mesh is required in discrete models of non-homogeneous materials, the properties of neighboring elements may be highly correlated. The specific fracture energy is defined as a scalar 3D random field with Weibull Probability Distribution and given correlation lengths. The proposed approach is illustrated with two examples that show that mesh objectivity is achieved when localization is induced in the rupture process (for instance in the case of a concrete plate subjected to simple shear). On the other hand, in the second example, when a uniaxial tensile stress field is applied, computed results do not show mesh objectivity. In both cases the correlation length of the random field is maintained constant when the discretization changes.