Various multiscale methods are reviewed in the context of modelling mechanical and thermo-mechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown

Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.

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The ability to compute accurately the strain field in Nb 3 Sn filaments is a crucial point in cable design, due to the significant strain sensitivity of niobium-tin wires. Due to its heterogeneity, a straightforward numerical simulation of a cable, taking into account all the details of the microstructure, would result in an enormous number of unknowns. As an alternative, multiscale approaches can be used to deal with this kind of problem, to understand the behaviour across the various scales. In this framework, a simple and efficient approach to obtain the homogenized properties of a heterogeneous strand is proposed here. This approach is developed for the non-linear, thermo-mechanical field. It consists of the solutions to some boundary value problems formulated on a suitably chosen statistically representative volume element of the wire. Two bronze-route strands and one internal-tin strand are considered and the equivalent parameters are obtained. Finally, the cool down and the subsequent application of a tensile axial load are simulated taking into account the homogenized wires. Computed results are shown to be in excellent agreement with measured stress-strain curves.

This paper presents a development of the usual generalized self-consistent method for homogenization of composite materials. The classical self-consistent scheme is appropriate for phases that are “disordered”, i.e. what is called “random texture”. In the case of both linear and non linear components, the self-consistent homogenization can be used to identify expressions for bounds of effective mechanical characteristics. In this paper we formulate a coupled thermo-mechanical problem for non linear composites having properties depending on temperature. The solution is found in a non-classical way, as we use the Finite Element Method to solve the elastic-plastic problem at hand. In this sense we propose a “problem oriented” technique of solution. The method is finally applied to the real case of superconducting strands used for the coils of the future ITER experimental reactor