Formulation of constitutive relations for nonlinear elastic media using a mechanical–geometric model with diagonal bonds
The formulation of constitutive relations for hyperelastic materials is one of the important problems of nonlinear mechanics. A new approach - the method of mechanical-geometric modeling - is proposed. This method makes it possible to derive constitutive relations for a nonlinear medium based on a chosen geometry of the model and specified mechanical parameters. The properties embedded in the model at the construction stage are subsequently transferred to the simulated continuum. This enables the formulation of a strain energy density function of the continuum corresponding to the selected model. This paper presents an algorithm for such construction using the model in the form of a rectangular parallelepiped as a case study. The initial stages of the model development are described, such as the selection of geometry and mechanical parameters that determine the properties of the model. The explicit constitutive relations connecting the nominal (engineering) stresses with the principal elongation ratios are obtained. The strain energy density function is then derived for a compressible nonlinear elastic material in terms of a symmetric dependence on three principal elongation ratios. Forms of the energy function are presented for both anisotropic and isotropic elastic media. Graphs of the strain energy function for an isotropic medium are plotted for several stress-strain states, i.e., uniaxial, biaxial, and equibiaxial tension, under the incompressibility constraint. References are given to the articles describing other initial geometric shapes and mechanical parameters of the model, which lead to different types of strain energy density functions. Possible directions for the further development of the mechanical-geometric modeling method are outlined.
Keywords
hyperelastic materials,
constitutive relations,
hyperelasticity,
strain energy density,
elastic potential,
continuous medium,
mechanical-geometric model,
incompressibilityAuthors
| Azarov Daniil A. | Don State Technical University | danila_az@mail.ru |
Всего: 1
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