材料生长与变形的连续介质模型:平衡方程与边界条件

Continuum Model for Growth and Deformation of Materials:Equilibrium Equations and Boundary Conditions

本文探讨了生长变形体连续介质模型的平衡理论框架。文中首先证明了广义输运定理,根据这个定理,推导了生长变形体广义平衡方程的一般形式及其生长边界条件,并导出反映生长边界面对平衡影响的生长耦合函数。在此基础上,具体讨论了质量、动量、动量矩以及能量平衡方程,并对其中相伴出现的一些新的物理量进行了评述;此外,还根据非平衡热力学理论的局域平衡假设建立了描述生长变形体热力学过程的熵不等式。这些方程唯象反映了生长变形体在运动、变形与生长过程中各物理量之间的耦合关系与平衡规律。

The equilibrium equations of growing deformable body based on the continuum model were established. Firstly, the so-called material accretion derivative was defined. Based on this definition, a general form of the equilibrium equation and its growing boundary condition describing motion of the growing deformable body were deduced. From the process of deduction, the concept of coupling function of growth was derived, which reflects the influence of the accretive boundary surface. Then, the equilibrium equations, including the equation of mass, momentum, moment of momentum and energy, were discussed. Also, the entropy inequality was given according to the assumption of local equilibrium of non-equilibrium thermodynamics. These equations characterize the equilibrium relationships in the growth and motion of body.