Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties
Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties
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DOI：
10.1016/j.cma.2004.04.004
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发表时间：
2004-11
影响因子：
7.2
通讯作者：
S. Ganapathysubramanian;N. Zabaras
中科院分区：
文献类型：
--
作者：
S. Ganapathysubramanian;N. Zabaras
讨论了控制多晶材料材料性能的技术的发展，这些材料性能内在地依赖于择优取向(织构)。为了考虑微结构特征的无限自由度，引入了一种微观尺度的模型降阶。利用取向空间的有限元离散，建立了由取向分布函数描述的微结构演化的降维模型。这种降阶建模方法是基于本征正交分解(POD)技术和快照法。此外，还介绍了基于真实多晶塑性的微观结构控制的新的设计问题。具体地说，利用多尺度连续灵敏度方法(CSM)引入了一个基于梯度的优化框架。模型降阶被推广到灵敏度分析，是变形过程计算设计成功的关键因素。数值算例突出了连续介质灵敏度方法和模型降阶的优点。此外，通过在材料点控制面心立方铜的弹性模数，展示了所提出的技术在工艺设计中获得所需材料性能的潜力。通过对速度梯度的优化选择，可以获得理想的弹性模量值分布。
Development of techniques for the control of material properties of polycrystal materials that are inherently dependent on preferred orientations (texture) is addressed. To account for the infinite degrees of freedom of microstructural features, a model reduction on the micro-scale is introduced. Reduced-order models are developed to model the evolution of microstructure described by an orientation distribution function using a finite element discretization of the orientation space. This reduced-order modeling approach is based on the technique of proper orthogonal decomposition (POD) and the method of snapshots. Furthermore, novel design problems are introduced for the control of microstructure based on realistic polycrystalline plasticity. Specifically, a gradient based optimization framework is introduced using a multi-length scale continuum sensitivity method (CSM). The model reduction is extended to the sensitivity analysis and is a key element for the success of computational design of deformation processes. Numerical examples that highlight the benefits of the continuum sensitivity method and model reduction are presented. In addition, the potential of the presented techniques towards process design for obtaining desired material properties is demonstrated with the control at a material point of the elastic modulus in fcc copper. A desired distribution of the elastic modulus is achieved through an optimal selection of the velocity gradient.