Mixed least-squares formulations within the framework of the theory of porous media for modeling ionic polymer-metal composites

多孔介质理论框架内的混合最小二乘公式用于模拟离子聚合物-金属复合材料

• 批准号: 445534800
• 负责人: Professor Dr.-Ing. Joachim Bluhm
• 金额: --
• 依托单位: Institut für Mechanik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/445534800?language=en
• 关键词: Mixed; least; squares; formulations; within

The objective of the proposed research project is the development of mixed Least-Squares finite element formulations for the analysis of the electromechanical behavior of ionic polymer-metal composites (IPMCs) within the framework of the theory of porous media (TPM). An incompressible four-phase model consisting of the phases polymer network, anions, cations and liquid is applied. The polymer network and the anions (fixed charges) have the same motion function, these two phases are combined to a solid phase. Furthermore, the same electrical potential is applied locally to all phases.A challenge in mixed Galerkin formulations is the robust approximations of the field quantities in space and time. Thus, the finite element ansatz spaces for the description of the coupled equations for the modeling of ionic polymer metal composites must satisfy certain stability conditions (LBB condition). Furthermore, simulations with real material parameters sometimes show large oscillations, e.g. in the fluid pressure.For these nonlinear, coupled boundary value problems the least squares method results in a minimization problem with symmetric positive semi-definite systems of equations. The ansatz spaces are not subjected to stability criteria, so that arbitrary conformal discretizations of the individual field quantities are possible and oscillation-free solution functions can be generated in principle.For ionic polymer metal composites, the temporal development of the concentration of the cations is described by a second order diffusion equation, which is transferred into a first order system within the LSFEM.The weighting of the residuals in the LSFEM is of particular importance with regard to the approximation quality and is systematically investigated. Furthermore, adaptive strategies in space and time are applied to achieve optimal convergence. We benefit from the fact that the LSFEM provides an a posteriori error estimator for mesh adaptivity as an inherent property of the method. The time adaptivity required for efficiency reasons is implemented by means of suitable Runge-Kutta methods.

拟议的研究项目的目的是开发混合最小二乘有限元的制剂，用于分析在多孔介质（TPM）框架内离子聚合物 - 金属复合材料（IPMC）的机电行为。应用了由相聚合物网络，阴离子，阳离子和液体组成的不可压缩的四相模型。聚合物网络和阴离子（固定电荷）具有相同的运动函数，这两个阶段合并到固相。此外，局部将相同的电势应用于所有阶段。混合盖尔金配方中的挑战是空间和时间中田间数量的稳健近似值。因此，用于描述离子聚合物金属复合材料建模的耦合方程的有限元ANSATZ空间必须满足某些稳定性条件（LBB条件）。此外，具有真实物质参数的模拟有时显示出较大的振荡，例如对于这些非线性，耦合边界值问题，最小二乘方法导致对称的半明确系统方程式导致最小化问题。 ANSATZ空间不符合稳定性标准，因此可以原理生成单个场数量的任意保形，无振荡的溶液功能。对于离子聚合物金属复合材料，阳离子浓度的时间开发是用二阶扩散方程式描述，该方程将其转移到LSFEM内的一阶系统中。在近似质量方面，LSFEM中残差的权重特别重要，并且正在系统地研究。此外，应用时空的自适应策略用于实现最佳收敛。我们受益于这样一个事实，即LSFEM为该方法的固有属性提供了网格适应性的后验误差估计器。出于效率原因所需的时间适应性是通过合适的runge-kutta方法实现的。