Finite Elements in Analysis and Design ( IF 3.5 ) Pub Date : 2024-01-12 , DOI: 10.1016/j.finel.2023.104105 Lennart Sobisch , Tobias Kaiser , Tim Furlan , Andreas Menzel
The solution of multi-field problems and the numerical implementation by means of the finite element method constitute a sophisticated part of the characterisation of industrial processes. A comprehensive implementation framework for such a system of coupled field equations into a non-linear large strain finite element formulation is provided. The procedure is derived for a micromorphic approach in a thermo-mechanical setting. Although the provided framework contributes to a particular three-field problem it is not limited to a specific application or a specific number of coupled field equations from a conceptual point of view. The solution of the considered system of equations is separated into two coupled domains, with the balance of linear momentum and a balance equation of heat equation-type being solved on each of them. Since both, the balance of micromorphic momentum and the heat balance equation, are partial differential equations of Laplace-type, the resulting two-instance problem can be solved in the framework of commercial finite element software, such as Abaqus, based on a thermo-mechanical user material. To assess the framework for a particular constitutive model, a gradient-enhanced damage model in a thermo-mechanical setting is applied and representative simulation results are discussed. The Abaqus framework is made available as an open-source code on GitHub (https://github.com/InstituteOfMechanics/Thermomechanical_Gradient_Enhanced_Damage_UMAT).
中文翻译:
在 Abaqus 中解决多场问题的用户材料方法:理论基础、梯度增强损伤力学和热机耦合
多领域问题的求解和有限元方法的数值实现构成了工业过程表征的复杂部分。提供了将耦合场方程系统转化为非线性大应变有限元公式的综合实施框架。该程序是针对热机械环境中的微形态方法而推导的。尽管所提供的框架有助于解决特定的三场问题,但从概念的角度来看,它并不限于特定的应用或特定数量的耦合场方程。所考虑的方程组的解被分成两个耦合域,在每个域上求解线性动量平衡和热方程类型的平衡方程。由于微态动量平衡和热平衡方程都是拉普拉斯型偏微分方程,因此所产生的双实例问题可以在商用有限元软件(例如 Abaqus)的框架中基于热平衡方程求解。机械用户材料。为了评估特定本构模型的框架,应用了热机械环境中的梯度增强损伤模型,并讨论了代表性的模拟结果。Abaqus 框架作为开源代码在 GitHub ( https://github.com/InstituteOfMechanics/Thermomechanical_Gradient_Enhanced_Damage_UMAT ) 上提供。