Adaptive-equivalent Mechanical And Thermal Analysis Of Heterogeneous Material In Time Domain

The time-dependent solution of mechanical and heat conduction for heterogeneous material often appeared in various fields of engineering. These problems are thus of great importance for engineering and theory. A direct way is to consider the geometrical and mechanical property of component in the heterogeneous material, respectively, and then discretize the problem in space/time domain, but this caused a huge computational cost or would be impossible. Another way is to consider the heterogeneous material as macroscopical homogenous material and equivalent analysis, the computational cost will reduce sharply. Based on an adaptive algorithm in the time domain and different space-homogenization method, this paper presented a numerical method for time-dependent equivalent analysis of heterogeneous material by concerning the viscoelastic jointed rock and linear transient heat conduction problem of heterogeneous material, especially focused on the computing accuracy and cost in time domain. The main works are as follows:Expanded the stress/strain, constitutive equation and equivalent stress/strain of the jointed rock in base cell, recursive equivalent constitutive models of unidirectional /orthogonal viscoelastic jointed rock and recursive finite element model of the related equivalent fields are proposed based on different equivalent assumptions. Regarding to the different joint density/dip angel, different combinations of constitutive relationships for rock and joint, different geometrical and different time step sizes, numerical examples are presented to verify the proposed model and the results are compared with the FE based heterogeneous solutions via ANSYS.The simple equivalent assumption is easy to understand and operate, however, it is not very enough strict in the frame of mathematics and physics. An equivalent finite element model for the transient thermal field of heterogeneous material with periodic microstructure is obtained by introducing a more strict equivalent method—asymptotic expansion homogenization (AHE), and the derivation of the related equivalent thermal properties and the formulation of the equivalent governing equation are given. The comparisons between the proposed model and the heterogeneous solutions via ANSYS verified its efficiency and accuracy considering different unit cell and ratio of components. Numerical examples show that the proposed equivalent models of unidirectional /orthogonal viscoelastic jointed rock and transient thermal field of heterogeneous material with periodic microstructure. This method can interface with different spatial numerical method such as mesh less method and DEM (Discrete Element Method), as well as FEM (Finite Element Method), and avoid the error accumulation caused by the change of the time interval. Finally, we hope this thesis will provide valuable reference for the research on time-dependent equivalent analysis of heterogeneous material.