论文标题
一个通用，隐性的大型Fe $^2 $框架，用于模拟两个量表的动态问题
A General, Implicit, Large-Strain FE$^2$ Framework for the Simulation of Dynamic Problems on Two Scales
论文作者
论文摘要
在本文中，我们提出了一种完全耦合的两尺度均质化方法，用于以Fe $^2 $方法的精神进行动态载荷。该框架考虑了线性动量的平衡，其中包括微观的惯性，以捕获微异质性引起的可能的动态效应。有限型制剂的配方适用于几何非线性，以实现研究，例如。可塑性或纤维拔出，可能与大变形有关。一致的运动量表链接被确定为整个代表体积元素的位移约束。一致的宏观材料切线模量被得出，包括封闭形式的微惯性。这些可以通过在所有显微镜有限元素上的循环轻松计算，只能应用现有的组装和求解程序。因此，使其适用于标准有限元程序架构。给出了分层周期材料的数值示例，并将其与直接数值模拟进行了比较，以证明所提出的框架的能力。
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible dynamic effects arising from micro heterogeneities. A finite-strain formulation is adapted to account for geometrical nonlinearities enabling the study of e.g. plasticity or fiber pullout, which may be associated with large deformations. A consistent kinematic scale link is established as displacement constraint on the whole representative volume element. The consistent macroscopic material tangent moduli are derived including micro inertia in closed form. These can easily be calculated with a loop over all microscopic finite elements, only applying existing assembly and solving procedures. Thus, making it suitable for standard finite element program architectures. Numerical examples of a layered periodic material are presented and compared to direct numerical simulations to demonstrate the capability of the proposed framework.
