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Metallic and polymer foams are widely used in modern industries, e.g., the aircraft and the automotive industries, but also with other application fields like biomechanics. The reason for this is some specific properties of these advanced materials. They are very light, but the specific strength is comparable with the classical structural materials. If they are applied as sandwiches, the specific properties can be even much better. In addition, they are able to absorb energy which allows the use of these materials as crash elements.

In general, technological parameters in foam production are adjusted such that a uniform effective foam density is achieved throughout the products. Some technologies, e.g., injecting foam in a cavity or filling a mold with foam by an expansion process, naturally result in non-uniform distributions of the effective density. These inhomogeneities of the effective foam density may be exploited in structural design, essentially treating the foam as a functionally graded material.

FGMs are composite materials where the composition or the microstructure is locally varied so that a certain variation of the local material properties is achieved. Modern FGMs are constructed for complex requirements, such as the heat shield of a rocket or implants for humans. In these cases the analysis of the material and
the structures made of FGMs cannot be only limited to the mechanical
behavior. FGMs can be modeled as a porous material with nonhomogeneous
distribution of porosity.

Engineering structures made of porous materials, especially metal
foams, have been used in different applications in the last decades.
A metal foam is a cellular structure consisting of a solid metal, for
example aluminium, steel, copper, etc., containing a large volume
fraction of gas-filled pores. There are two types of metal foams. One
is the closed-cell foam, while the second one is the open-cell foam.
The defining characteristics of metal foams are a very high porosity:
typically well over 80%, 90% and even 98% of the volume consists of
void spaces.

The basics of the analysis of structures made of foams is the continuum mechanics. Briefly were presented the foundations. In addition, the introduction in the theory of elasticity and plasticity was given. Special attention was paid to the yield criteria, to anisotropy and to the different behavior in tension and compression. Many structural elements made of foams can be presented by beam, plate or shell
models. As an example, a plate theory based on the direct approach
was presented. One of the basic elements of this theory is the effective
property concept. Such a theory is suitable for the global analysis of
plates (deflections, frequencies, etc.).



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