材料生长与变形的连续介质模型:弹性本构方程

本文着重探讨了生长变形体连续介质理论中的本构模型。首先列出了描述生长变形体能量平衡的微分方程以及熵不等式；以此为基础，通过将密度演化的历史作为独立的本构变量扩展了理性力学的因果性公理与决定性公理，具体而详细地推导了简单材料的生长弹性本构方程，给出了这些本构方程中的相关本构变量之间的约束不等式，得到了“生长变形体的自由能与其密度成反比”的结论，并从热力学上对这一结果进行了定性的解释。最后，文中对几个尚待解决的问题进行了说明，并指出了今后的发展方向。

Continuum Model for Growth and Deformation of Materials Constitutive Equations Based on First-order Gradient Theory

The constitutive models of growing deformable body based on the continuum theory were emphatically discussed. Firstly, the differential equations for describing the energy equilibrium of growing deformable body and the entropy inequality were discussed briefly. On the basis of them, the axioms of causality and determinism were extended by means of selecting the evolving history of density as an independent constitutive variable. The constitutive-equations characterizing the elastic response of growing deformable body were derived in detail, and the inequality restricting the dependent constitutive variables was established. Accomplished was the result that the free energy of the growing deformable body was inversely proportional to the mass density, on which a qualitative interpretation in thermodynamics was given. Finally, it is pointed out that the problems were waiting to be further solved.