Equivalent constitutive equations of honeycomb material using micro-polar theory to model thermo-mechanical interaction

For describing the properties for micro-polar cellar material, the definitions of representative element as well as the corresponding equivalent physical quantities in cellular are introduced in this paper. It involves the Cauchy stress, couple stress, displacement gradient, strain, torsion tensor, temperature gradient and the heat flux respectively. The general principle and mode of solving the boundary value problem with respect to the construction of the equivalent constitutive equations is investigated, and the thermo-mechanical interaction is modeled for the micro-polar cellar material. In the context, a standard method for formulizing the boundary value problem in accordance with the specified representative element volume (REV) is developed, and thereupon the equivalent constitutive equations are deduced. For honeycomb materials, the analytical formula for the equivalent elastic coefficient tensor, temperature coefficients of equivalent stress, equivalent Fourier coefficients and the temperature gradient coefficients of couple stress of the honeycomb materials would be formed.