Computational homogenization of inelastic conventional and gradient-extended microstructures by a shear band approach

通过剪切带方法对非弹性常规和梯度延伸微结构进行计算均质化

基本信息

批准号：
310713160
负责人：
Professor Dr.-Ing. Stephan Wulfinghoff
金额：
--
依托单位：
Rektor der Universität Siegen
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/310713160?language=en
关键词：
Computational homogenization inelastic conventional gradient

项目摘要

This proposal is dedicated to a numerically efficient approach for the computation of the average stress response of periodic microstructures. The method exploits the fact that many heterogeneous microstructures with and without gradient effects mainly deform by the formation of shear bands. By introducing a small number of degrees of freedom on these bands, a computationally very cheap model is obtained being surprisingly accurate for a wide range of microstructures. Thus, the approach allows for efficient two-scale simulations, where a microstructural model is attached to each integration point of a macroscopic finite element model. In contrast to the classical FE²-method, the microscopic model has significantly less degrees of freedom. This makes the fast two-scale simulation of very complex macroscopic structures possible. The microscopic strains of the model are piecewise constant. Thus, the number of stress computations within the microstructure is significantly smaller than in many other order reduction methods being, e.g., based on the proper orthogonal decomposition (POD). As a result, the performance of the method may in certain situations be superior to these latter approaches. As another advantage, the implementation of the method is rather simple and does not require the input of certain data objects like the finite element stiffness matrix or the residual vector, which are needed for the POD but are not always easy to access in finite element programs. Since size effects play a significant role in many microstructures, a concept for the model extension to gradient plasticity is developed.

该建议专门用于计算周期性微观结构的平均应力响应的数值方法。该方法探讨了以下事实：许多具有和没有梯度效应的异质微观结构主要通过剪切带的形成而变形。通过在这些频段上引入少量自由度，可以在各种微观结构中获得一个非常便宜的计算非常便宜的模型。这是该方法允许进行有效的两尺度模拟，其中将微结构模型附加到宏观有限元模型的每个集成点。与经典的Fe²方法相反，微观模型的自由度明显较小。这使得对非常复杂的宏观结构进行了快速的两尺度模拟。模型的微观菌株是分段常数。这是，基于适当的正交分解（POD），微结构内的应力计算数量的可能性要小得多。作为另一个优点，该方法的实现非常简单，并且不需要输入某些数据对象（例如有限元刚度矩阵或残差向量），该对象是POD所需的，但在有限元程序中并不总是很容易访问。由于尺寸效应在许多微观结构中起着重要作用，因此开发了模型扩展到梯度可塑性的概念。

项目成果

期刊论文数量（4）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

An efficient reduced computational method for nonlinear homogenization problems: the Hashin–Shtrikman type Finite Element method (HSFE)

非线性均质化问题的高效简化计算方法：HashinâShtrikman 型有限元方法 (HSFE)

DOI：
10.1002/pamm.201800146
发表时间：
2018
期刊：
PAMM
影响因子：
0
作者：
F. Cavaliere;S. Wulﬁnghoﬀ;S.Reese
通讯作者：
S.Reese

A grain boundary model considering the grain misorientation within a geometrically nonlinear gradient-extended crystal viscoplasticity theory

DOI：
10.1098/rspa.2019.0581
发表时间：
2020-03-25
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
影响因子：
3.5
作者：
Alipour, Atefeh;Reese, Stefanie;Wulfinghoff, Stephan
通讯作者：
Wulfinghoff, Stephan

Model order reduction of nonlinear homogenization problems using a Hashin–Shtrikman type finite element method