Application of the BE subregion-by-subregion algorithm to evaluate stresses at general 3D solids and composites

Resumo

General solids and composites with any number of heterogeneous parts may be conveniently solved by the subregion-by-subregion (SBS) algorithm, proposed in previous works by the author. Particularly in this paper, options for calculating stresses at boundary (or interfacial) points of generic 3D solids, including composites, are incorporated into this algorithm. For that, the Hooke’s law along with global-to-local axis-rotation transformations is applied. In fact, for thin-walled domains, the Hooke’s law-based strategy is very relevant as nearly singular integrals are avoided. At inner points, regular boundary integration schemes are employed to evaluate stresses. Notice that the SBS-based algorithm applies to the stress analysis in any solid or composite, including the microstructural (grain-by-grain) modeling of materials. The independent assembly and algebraic manipulation of the BE matrices for the many substructures involved in the model, makes the formulation very suitable for dealing with large-order models, as typically happens in the 3D microstructural analysis of generic composites. For that, Krylov solvers are employed to construct the SBS algorithm. The performance of the technique is verified by solving complex 3D solids including representative volume elements (RVEs) of carbon-nanotube (CNT) composites with up to several tens of thousands of degrees of freedom.