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首页> 外文期刊>Applied Mathematical Modelling >Large deformation analysis of a gel using the complex variable element-free Galerkin method
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Large deformation analysis of a gel using the complex variable element-free Galerkin method

机译：无复变元Galerkin方法对凝胶进行大变形分析

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Deformation of a gel is a complicated multiphysical process involving the diffusion of solvent and the mechanical stretching of polymeric networks. This process leads to a mechanical and diffusional equilibrium after a certain period of evolution. Here we present a large deformation analysis of a gel in the equilibrium state under environmental triggers using the complex variable element-free Galerkin (CVEFG) method. The work mainly addresses the numerical challenges encountered while a gel in contact with a solvent deforms only with the geometric constraints but without any force boundary conditions (implying that the force column in the final standard algebraic equations equals zero) and emphasizes the implementation of a different CVEFG approach. The material model is based on the work of Hong et al. (2008) and incorporates our previous efforts in the numerical implementation. The discretized equation system is derived from the complex variable moving least squares approximation and the Galerkin method. The essential boundary conditions are imposed through the penalty method. The proposed approach is verified by the simulation of the swelling-induced large deformation and surface instability of a confined single gel layer.
机译：凝胶的变形是一个复杂的多物理过程，涉及溶剂的扩散和聚合物网络的机械拉伸。经过一定的演化过程后，该过程导致了机械平衡和扩散平衡。在这里，我们提出了使用复杂的无变量元素Galerkin（CVEFG）方法在环境触发条件下处于平衡状态的凝胶的大变形分析。这项工作主要解决了与溶剂接触的凝胶仅在几何约束条件下变形而没有任何力边界条件（暗示最终标准代数方程中的力列等于零）时发生的数值挑战，并强调了实现不同CVEFG方法。物质模型是基于Hong等人的工作。 （2008年），并结合了我们在数值实施中的先前努力。离散方程组是从复变量移动最小二乘近似和Galerkin方法得出的。基本边界条件是通过惩罚方法施加的。该仿真方法通过模拟有限的单凝胶层的膨胀引起的大变形和表面不稳定性而得到验证。

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