非平衡态/不可逆过程的热力学理论(Ⅱ)

THERMOMECHANICS OF NONEQUILfBRIUM AND IRREVERSIBLE PROCESSES ( Ⅱ)

7 解的唯一性 如果不考虑非平衡态和不可逆性,则等能密度理论中的基本命题与经典弹性理论中的在形式上完全相同。无论整个系统的动能是大还是小,图6中(sumform)_o上的面力T_i和在(sumform)_c和在的位移u_i将始终在空间坐标系x_i和时刻i下给出。与一般力学中相同,必须知道有关位移u_i及其时间导数的初始条件。它们的影响则可通过(38)和(39)向等能面转化。

Reconciliation of thermal and mechanical interdependence is made possible by casting away the concept of heat. Defined are the dissipation and available energy density as two mutually exclusive quantities; thermal and mechanical changes become two aspects of the same process that coexist and are in continual operation. This is accomplished by interlacing the rotation, deformation and change in element size into one single operation; irreversibility is embedded inherently into the theory. No a priori assumption needs to be made on the constitutive relations which are, in fact, derived for each individual element and time increment. Only the initial slope of the reference material and load history need to be specified. Instead, the surface and volume energy density are assumed to be exchangeable without letting the change of volume with surface area to vanish in the limit, a simplification of classical physics and continuum mechanics that results in the decoupling of thermal and mechanical effects. Complete nonlinearity and finiteness of deformation are retained such that boundary problems can be solved directly by specifying the tractions and/or displacements. Nonequilibrium/irreversible solutions are shown to possess definite limits and to be bounded by the equilibrium/irreversible states whose solutions are proved to be unique. The existence of the isoenergy density function provides an elegant means of resolving the multidimensionality of the problem; the translation of unidimensional data to multidimensional states.