Hybrid Computational Modelling of Heterogeneous Materials

This paper presents a numerically efficient and accurate finite element for heterogeneous materials that fully captures the microscopic mechanical fields without the need for the finite element mesh to explicitly resolve the microscopic geometry. This represents a novel upscaling strategy that is achieved through rigorous treatment of the material's microstructure yet realized in a computationally tractable manner. Fine-scale fluctuations of the mechanical fields are accurately calculated from analytical formulae derived from classical micromechanics theory for ellipsoidal inclusions and incorporated into Hybrid-Trefftz stress finite elements. An important feature of this technique is that the element stiffness matrix can be conveniently expressed as a boundary integral of continuous functions. Although this method is applied in this paper to elastic composites comprising inclusions embedded in a matrix, it has been designed to be extended to fracturing, heterogenous, quasi-brittle materials.