Nonlinear Modeling of Contact Stress Distribution in Thin Plate Substrates Subjected to Aspect Ratio.

The foundation substrate's basal contact stresses are typically thought to have a linear distribution, although the actual form is nonlinear. Basal contact stress in thin plates is experimentally measured using a thin film pressure distribution system. This study examines the nonlinear distribution law of basal contact stresses in thin plates with various aspect ratios under concentrated loading, and it establishes a model for the distribution of contact stresses in thin plates using an exponential function that accounts for aspect ratio coefficients. The outcomes demonstrate that the thin plate's aspect ratio significantly affects how the substrate contact stress is distributed during concentrated loading. The contact stresses in the thin plate's base exhibit significant nonlinearity when the aspect ratio of the test thin plate is greater than 6~8. The aspect ratio coefficient-added exponential function model can better optimize the strength and stiffness calculations of the base substrate and more accurately describe the actual distribution of contact stresses in the base of the thin plate compared to linear and parabolic functions. The correctness of the exponential function model is confirmed by the film pressure distribution measurement system that directly measures the contact stress at the base of the thin plate, providing a more accurate nonlinear load input for the calculation of the internal force of the base thin plate.

Constitutive Relations of Anisotropic Polycrystals: Self-Consistent Estimates.

In this paper, the elastic constitutive relation of polycrystals contains the effect of the mesostucture coefficients. We consider a general case and derive the average elastic constitutive relation pertaining to polycrystals of cubic crystals with any symmetry of crystalline orientation in their statistical distribution. Following Budiansky and Wu, we used self-consistent estimates of eigenstrain to obtain the effective elastic constitutive relation of polycrystals in an explicit form. For the Voigt assumption and the Reuss assumption, the effective elastic constitutive relation of polycrystals on cubic crystals contains the the mesostructure coefficients up to linear terms. In general, the linear term expression works well for materials such as aluminum, the single crystal of which has weak anisotropy. However the same expression (which allows the anisotropic part of the effective elastic constitutive relation to depend only linearly on the mesostructure coefficients) does not suffice for materials such as copper, in which the single crystal is strongly anisotropic. Per the Taylor theorem, we expand the expression based on the self-consistent estimates with respect to the mesostructure coefficients up to quadratic terms for anisotropic polycrystals of cubic crystals. While our numerical data are very close to those of Morris, our expression is much simpler.