Purpose

A diffusion-reaction-deformation coupled model is employed and implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS.

Design/methodology/approach

Chemical reaction and diffusion are treated as two distinct processes by introducing the extent of reaction and the diffusion concentration as two kinds of independent variables, for which the independent governing equations for chemical reaction and diffusion processes are obtained. Furthermore, an exponential form of chemical kinetics, instead of the linearly phenomenological relation, between the reaction rate and the chemical affinity is used to describe reaction process. As a result, complex chemical reaction can be simulated, no matter it is around or away from equilibrium.

Findings

Two numerical examples are presented, one for validation of the model and another for the modeling of the deflection of a plane caused by a chemical reaction.

Originality/value

1. Independent governing equations for diffusion and reaction processes are given. 2. An exponential relation between the reaction rate and its driving force is employed. 3. The UEL subroutine is used to implement the finite element procedure.

中文翻译：

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扩散-反应-变形耦合问题的计算模型及其有限元实现

目的

在商业有限元软件包 ABAQUS 中采用扩散-反应-变形耦合模型并将其作为用户定义元 (UEL) 子程序实现。

设计/方法/方法

将反应程度和扩散浓度作为两种自变量引入，将化学反应和扩散视为两个不同的过程，得到化学反应和扩散过程的独立控制方程。此外，化学动力学的指数形式，而不是反应速率和化学亲和力之间的线性唯象关系被用来描述反应过程。因此，可以模拟复杂的化学反应，无论它是接近平衡还是远离平衡。

发现

给出了两个数值例子，一个用于验证模型，另一个用于模拟由化学反应引起的平面偏转。

原创性/价值

1. 给出了扩散和反应过程的独立控制方程。2.采用反应速率与其驱动力之间的指数关系。3. UEL 子程序用于执行有限元程序。