Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation

Abstract

Modern lightweight materials are often decomposed into several distinct materials, e.g. a matrix material and some reinforcements. A manufacturing process for these materials often induces eigenstrains, both reversible and non reversible. This could lead to an initial damage of a composite material, and eventually result into fracture of the structure. This contribution deals with non-local integral-type damage of composites subjected to eigenstrains. It is well known that local damage models lead to mesh sensitive simulation results. To avoid this effect, non-local integral-type regularization of equivalent strains and damage variables are exploited. Effective macroscopic properties are obtained using mean-field homogenization methods. A regularization in each material phase within the framework of an iterative Newton–Raphson procedure leads to the update of a non-local tangent stiffness matrix at each equilibrium iteration. To reduce the computational time parallel non-local assembly and averaging procedures are introduced. In this regard, the performance of different representations of dynamic sparse matrices and the scalability of the parallel implementation are investigated. Various microstructural morphologies are distinguished in representative examples to show the capability of the proposed work. Furthermore, the transition from damage to fracture is performed by aid of an element deletion method. To achieve the best compromise between memory consumption and speed over a range of non-zero entries, an array of flatmaps should be used. It is shown that the introduced parallel algorithms enable a drastic reduction of computational time. Moreover, it is illustrated that for various volume fractions of an inclusion a mesh sensitivity is clearly reduced.