A new stabilized method is presented for coupled chemo-mechanical problems involving chemically reacting fluids flowing through deformable elastic solids. A mixture theory model is employed wherein kinematics is represented via an independent set of balance laws for each of the interacting constituents. A significant feature of the mixture model is the interactive force field in the momentum balance equations that couples the constituents implicitly at the level of the governing system of equations. The constitutive relations for the constituents in the mixture model are based on maximization of the rate of entropy production. Since each constituent is not discretely modeled and the interactive effects are mathematically coupled at the local continuum level, the resulting system serves as a physics-based reduced-order model for the complex microstructure of the material system. When constitutive equations are substituted into the balance laws, they give rise to a system of coupled nonlinear PDEs. Evolving nonlinearity and coupled chemo-mechanical effects give rise to spatially localized phenomena, namely boundary layers, shear bands, and steep gradients that appear at the reaction fronts. For large reaction rates, the balance of mass of the fluid becomes a singularly perturbed equation (reaction-dominated), which may exhibit boundary and/or internal layers. Likewise, for large reaction rates and/or low diffusivity, the balance of linear momentum for the fluid constituent also becomes a singularly perturbed PDE. Presence of these features in the solution requires stable numerical methods, and we present a variational multiscale (VMS)-based stabilized finite element method for the initial-boundary value problem. Mathematical attributes of the method are investigated via a range of numerical test cases that involve diffusion of chemically reacting fluids through nonlinear elastic solids. Enhanced stabilization features and higher spatial accuracy of the models and the methods are highlighted.

中文翻译：

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具有反应流体前沿的有限变形固体的化学-机械耦合和材料演化

针对化学反应流体流经可变形弹性固体的耦合化学机械问题，提出了一种新的稳定方法。采用混合理论模型，其中运动学通过一组独立的平衡定律来表示，用于每个相互作用的成分。混合模型的一个显着特征是动量平衡方程中的相互作用力场，它在控制方程系统的水平上隐式地耦合了成分。混合模型中各成分的本构关系基于熵产生率的最大化。由于每个成分都不是离散建模的，并且交互效应在局部连续体水平上以数学方式耦合，由此产生的系统用作材料系统复杂微观结构的基于物理的降阶模型。当本构方程代入平衡定律时，它们会产生耦合非线性偏微分方程系统。不断发展的非线性和耦合的化学-机械效应会产生空间局部现象，即出现在反应前沿的边界层、剪切带和陡峭梯度。对于大的反应速率，流体的质量平衡变成一个奇异扰动方程（反应主导），它可能表现出边界和/或内部层。同样，对于大反应速率和/或低扩散率，流体成分的线性动量平衡也变成奇异扰动的偏微分方程。解决方案中存在这些特征需要稳定的数值方法，我们针对初始边界值问题提出了一种基于变分多尺度 (VMS) 的稳定有限元方法。该方法的数学属性通过一系列数值测试案例进行研究，这些案例涉及化学反应流体通过非线性弹性固体的扩散。强调了模型和方法的增强稳定功能和更高的空间精度。