Abstract
Stress calculation problem in an elastically creeping layered array is solved by the method of homogenization. Exponential function of time is taken as the kernel of creep of each layer. Experiments prove that such functions are the best way to describe the creep of mountain ranges over long periods of time. Integrals of convolution type with such exponential kernels are used to describe the creep process. The article contains formulas for calculating effective elastic-creep coefficients. These formulas contain exponential functions with both initial parameters and with new ones, which are also negative real numbers. As a computational example, kernel creep graph is shown for one of the average environment's effective modulus. Obtained solution can be used in underground construction.
Highlights
Most of the existing in nature and man-made materials are characterized by a heterogeneous composition
As usual we denote by Oi,Pi Lame parameters, by J i specific weight, by Gi creeping kernel for each layer ( i 1,2 )
For example, we plotted creep kernel g11 containing exponential functions depending on time t for t [0;5000 ] (Fig. 2)
Summary
Most of the existing in nature and man-made materials are characterized by a heterogeneous composition. Numerous experimental studies show that the properties of structurally inhomogeneous materials (e.g., rocks, composite materials) can considerably differ from the properties of the individual components included in their structure These issues are important in solving practical problems that arise during the construction and exploitation of buildings, the operation of composite materials. The method of asymptotic averaging can be used to solve such problems This method allows to find the effective mechanical properties of heterogeneous material using the values of the mechanical characteristics of its components and their geometry. The investigated area is considered as a periodic system with known characteristics of the individual components To solve this problem, we can consider the environment as a macro-homogeneous, which obeys the averaged equations with constant coefficients. The obtained homogeneous medium is anisotropic, even if the original layers were isotropic This method of averaging is developed in the works [1-9]. Problems for layered materials with continuously changing characteristics have been solved in [10 -12]
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