Constitutive Relations Of Engineering Materials With Effects Of Microstructures

The materials mechanics nature relies on the material microstructure. In view of two kind of common engineering material, this paper has carried on following work:The first part has studied the relations of high polymer material visco-elasticity mechanical properties and the material microstructure. High Polymers is composed by the crystalline part and the non-crystalline part. Crystalline part is the set of chip; non-crystalline part is made of molecular chain. The Crystal itself has the anisotropic. The molecular chain in the principal direction is jointed by chemistry keying, vertical unifies in the molecular chain principal direction is connected by the van der Waals force, Therefore the crystalline orientation distribution and the molecular chain orientation distribution will intensely effect the material the macroscopic mechanical properties. We introduce orientation distribution function ODF, have respectively analyzed the crystalline elasticity theory nature and the crystalline orientation distribution relations under the Voigt model and the Reuss model, and then obtain the effective elastic rigidity tensor of crystalline. we has established molecular chain orientation distribution function CODF, and has inferred the non-crystalline state part under Kelvin model visco-elasticity mechanical properties and the chemical composition and the molecular chain orientation distribution relations. And gives containing the texture coefficient, the orientation coefficient, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation. And gives contains the texture effect, the molecular chain orientation effect, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation.The second part has studied the relations of elasto-plasticity composite materials mechanical properties and the microstructure. Two materials is composed which by the matrix/inclusions, the inclusions shape distribution can affect the condition which the material enters submits. Our supposition submits the criterion to rely on the stress and the shape distribution, inclusions effect the yield function, using the principle of material frame-indifference contains infers the general form. Assume that a composite material is an aggregate of numerous several phase elasto-plastic grains, where any grain in the composite material only belongs to one phase material. In this paper, any grain in the composite material is taken as an inclusion. By the equivalent inclusion method and the self-consistent method on eigen-strain, we give the macroscopic constitutive relation of the composite material of several phase elasto-plastic grains. We find out the relations of material properties between the composite material and its tiny grains.