Mechanical and Civil Engineering Seminar
A strategy often employed to predict the overall response of composite materials in terms of the local responses and the microstructure consists in identifying special classes of microgeometries that reproduce the essential geometrical features of the actual composite microstructure while at the same time allow the exact computation of the overall response via homogenization theory. Early works on linear composites showed that the set of solvable microgeometries could be enlarged by following iterative procedures whereby the constituent phases in a solvable microgeometry are themselves identified with solvable microgeometries at a lower length scale, thus producing hierarchical microgeometries of increasing complexity whose overall response can be determined via iterated homogenization. In this talk I will present recent advances on the use of such a strategy in the context of nonlinear composites. In particular, I will present a model for viscoplastic porous media based on sequentially laminated microgeometries. A distinctive feature of this model is that it is realizable, by construction, and therefore the resulting dissipation potential for the porous medium is guaranteed to satisfy all pertinent bounds and convexity requirements. Based on preliminary results, it will be argued that the new model should provide more reliable predictions for viscoplastic porous media than Gurson-type models.