Constitutive equations and the corresponding material properties used in structural analyses are in most cases obtained from experimental studies performed on specimens which are large enough to represent the effective, i.e. overall, material behaviour. In the case of multi-phase materials, this effective response typically is determined by the topology and geometry as well as the thermo-mechanical material and interfacial behaviour at lower length scales, i.e. meso-, micro- and submicro-scales.

The present contribution gives some examples of how finite element methods can be used for studying problems related to the thermo-mechanical behaviour of two groups of inhomogeneous materials: metallic materials that can be treated as ductile matrix composites and highly porous metals. As representatives of the former group high speed tool steels, which consist of a martensitic steel matrix that contains carbidic particles, are studied by different finite element based approaches and fibre reinforced metal matrix composites are discussed. With regard to highly porous metals the uniaxial compressive and tensile behaviour of a syntactic foam as well as the fracture behaviour of an open cell metallic foam are modelled.

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