A statistical approach to modeling heterogeneous material behavior is necessary to capture local behavior, which profoundly affects such macroscale behaviors as brittle fracture and wave propagation. The study of mesoscale Statistical Volume Elements (SVE) is complicated by the fact that, by definition, SVE material behavior is non-unique and depends on the boundary conditions applied. The choice of the scale of material evaluation is a significant modeling choice. The benefits of a mesoscale material representation are evident: continuum fields are well-suited to stochastic simulation, and the scale of representation can be controlled, allowing for adaptive changes in mesh density, which is useful for example in fracture modeling. In this work, a method for statistical characterization of mesoscale material property behavior will be presented. This method relies on the use of the reduced finite element stiffness matrix for each SVE, which reduces the computational cost. Results demonstrate the accuracy of this technique compared to other methods, particularly a method that uses a Voronoi geometry to avoid SVE boundary intersection with inclusions. In addition to increasing efficiency, the current method does not require SVE geometry to depend on the morphology of the microstructure, making it more generally applicable to any random material morphology.

需要采用统计方法对异质材料行为进行建模，以捕获局部行为，这会深刻影响脆性断裂和波传播等宏观行为。介观尺度统计体积元 (SVE) 的研究变得复杂，因为根据定义，SVE 材料行为是非唯一的，并且取决于所应用的边界条件。材料评估尺度的选择是一个重要的建模选择。介观尺度材料表示的好处是显而易见的：连续介质场非常适合随机模拟，并且可以控制表示的尺度，允许网格密度的自适应变化，这在断裂建模等中非常有用。在这项工作中，将提出一种介观材料性能行为的统计表征方法。该方法依赖于对每个 SVE 使用简化的有限元刚度矩阵，从而降低了计算成本。结果证明了与其他方法相比，该技术的准确性，特别是使用 Voronoi 几何来避免 SVE 边界与夹杂物相交的方法。除了提高效率之外，当前方法不需要 SVE 几何形状依赖于微结构的形态，使其更普遍地适用于任何随机材料形态。