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.

该提案致力于计算周期性微结构的平均应力响应的数值方法，该方法利用了许多具有或不具有梯度效应的异质微结构主要通过引入少量剪切带而有效变形的事实。由于这些带上的自由度，获得了一个计算成本非常低的模型，对于各种微观结构来说都非常准确，因此，该方法允许有效的两尺度模拟，其中微观结构模型附加到每个积分点。与经典的 FE² 方法相比，微观模型的自由度显着降低，这使得可以对非常复杂的宏观结构进行快速两尺度模拟，因此模型的微观应变是分段恒定的。，微观结构内的应力计算数量明显小于许多其他降阶方法，例如基于适当正交分解（POD）的方法，因此，该方法的性能在某些情况下可能会降低。优于后面这些方法的另一个优点是，该方法的实现相当简单，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，这些数据对象是 POD 所需的，但并不总是那么容易。由于尺寸效应在许多微观结构中发挥着重要作用，因此开发了梯度塑性模型扩展的概念。

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