双层球壳结构准静态线性化学弹性问题的位移势函数解

本文研究了各向同性固体的化学-力学耦合问题，在传统化学弹性理论描述的扩散-变形耦合关系基础上，进一步考虑了化学反应与固体变形的相互作用关系，发展了等温状态下固体-扩散-反应-变形耦合的线性化学弹性理论，拓展了化学弹性力学的应用范围．该理论能够同时描述固体内介质扩散和固体与介质之间化学反应两个不同时间尺度的化学过程，并给出由此引起的弹性范围内的应变和应力．为应用该模型求解具体化学弹性问题，本文通过构造扩散-反应位移势函数来获得位移特解形式，再与齐次Lamé方程通解叠加获得完整解；针对反应控制问题，引入化学弹性准静态假设，将反应-扩散-变形全耦合的瞬态过程分解为两个可解耦的相继过程，从而获得相应位移解．基于此解法，本文获得了反应控制的双层球壳结构化学弹性问题的解析解，并分析了化学反应、几何结构和弹性模量对应力分布的影响．

A Displacement Potential Solution for Quasi-Static Linear Chemo-Elastic Problems of Double-Layer Spherical Shell Structure

The chemo-elastic coupling problems of isotropic materials are studied, from which a linear diffusion-reaction-elastic deformation coupled model under isothermal condition is developed. The effect of chemical reaction on solid deformation is further considered on the basis of classical chemo-elasticity describing the diffusion-deformation coupling. Thus, the model can solve the elastic strains and stresses induced by species diffusion and chemical reaction simultaneously, and accurately portray these two chemical processes with distinct time scales. To solve the specific chemo-elastic problems, a diffusion-reaction displacement potential function is constructed to derive a particular solution of displacement, which is added to the general solution of homogeneous Lamé equation to form the complete solution. For the reaction-dominant problem, the quasi-static assumption of chemo-elasticity is introduced, and the transient process of fully coupled reaction, diffusion and deformation is decomposed into two decoupled processes to obtain the corresponding displacement solutions. Finally, a spherically symmetric chemo-elastic problem controlled by a quasi-static reaction process is analytically solved, based on which the influences of chemical reaction, geometry and material parameters are discussed.