Microstructure-based failure surfaces of matrix-inclusion materials: The origin of J3 plasticity highlighted by limit analysis

Composites composed of two materials, exhibiting a matrix-particle morphology, can be described by three phases: the matrix phase, the particle phase, and the interface between the particle and the matrix. In order to relate macroscopic material properties to the matrix-particle behavior and the morphology (material microstructure), analytical and/or numerical schemes may be employed. As regards macroscopic strength properties, averaging schemes as e.g. used for upscaling of elastic and viscoelastic properties are not able to capture the localized mode of material failure. In this paper, the application of a discretized form of the upper-bound theorem of limit analysis to upscaling of strength properties is proposed. By varying the loading situation on the microstructural representation of the material, microstructure-based macroscopic failure criteria are derived for different material morphologies. The presented upscaling scheme illustrates the influence of the particle content, the particle strength, and the interface degradation on the macroscopic failure criterion.