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Definition of effective characteristics of heterogeneous materials

Lurie S.A., Shakhram Yu.

#### Abstract:

The problem of determination of effective stiffness characteristics of heterogeneous composite materials can be solved by use of replacement of the original material by some other material (a model material), which is homogeneous and has known characteristics. Such a replacement is based on the particular criteria. In the general case, these criteria presume that an element made of model material is subjected to the same loads as that made of original material, and the averaged strains of the model homogeneous substance, in some sense, are equivalent to the strains of the original substance, though, the local strains and stresses of these two substances may differ greatly. Estimation of the effective characteristics of composite materials using the characteristics of their components is a principal problem of mechanics of composites. Similar problems appear when estimating stiffness and strength characteristics of materials, in which microdamages are accumulated. A problem of estimation of effective characteristics of two-phase substances seems to be of great importance. Thus, for example, most of materials with the memory of shape undergo phase austenitic-martensitic transformations. At that, the properties of such two-phase materials change significantly, since the modulus of elasticity of different phases can differ in several times. In order to estimate average effective characteristics of a two-phase material with a system of distributed microdefects, it is proposed to apply the relationships, which follow from the description of heterogeneous substance by variational equation, when applying the expanded Lagrangian.

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