Isogeometric and stochastic collocation methods for nonlinear probabilistic multiscale problems in solid mechanics

固体力学中非线性概率多尺度问题的等几何和随机配置方法

• 批准号: 255747201
• 负责人: Professorin Dr. Laura De Lorenzis
• 金额: --
• 依托单位: Departement Maschinenbau und Verfahrenstechnik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/255747201?language=en
• 关键词: Isogeometric; stochastic; collocation; methods; nonlinear

In this project, we intend to use the newly developed concept of isogeometric collocation (IGA-C) in combination with stochastic collocation (SC) to achieve stable and computationally efficient higher-order modeling of irreversible multiscale behaviour in solid mechanics. The basic assumption is that the microstructure of a heterogeneous solid is uncertain and hence should be modeled probabilistically. In order to describe the effects of the microscale uncertainty not only on the mean macroscopic fields, but also on their variability, a probabilistic treatment of the scale transition is also needed. As the computational cost of such stochastic computations may be orders of magnitude larger than that of simple deterministic analyses, an unprecedented computational efficiency is sought in the combination of IGA-C for the mechanical/deterministic modeling, and of an SC scheme with novel ansatz functions for the stochastic discretization. The numerical framework to be developed encompasses local and non-local elasticity and plasticity with finite strains, as well as contact, damage and fracture models.

在本项目中，我们打算将新发展的等几何配置（IGA-C）概念与随机配置（SC）相结合，以实现固体力学中不可逆多尺度行为的稳定和计算效率高阶建模。基本假设是，非均质固体的微观结构是不确定的，因此应该以概率方式建模。为了描述微观尺度不确定性不仅对平均宏观场的影响，而且对其变异性的影响，还需要对尺度转换进行概率处理。由于这种随机计算的计算成本可能比简单的确定性分析大几个数量级，因此，在机械/确定性建模的IGA-C和随机离散化的具有新颖ansatz函数的SC方案的组合中，需要寻求前所未有的计算效率。要开发的数值框架包括有限应变下的局部和非局部弹性和塑性，以及接触、损伤和断裂模型。

项目成果

Inverse Problems in a Bayesian Setting

贝叶斯环境中的反问题

• DOI: 10.1007/978-3-319-27996-1_10
• 发表时间: 2016
• 期刊: arXiv: Probability
• 作者: H. G. Matthies;E. Zander;B. Rosić;A. Litvinenko;O. Pajonk
• 通讯作者: O. Pajonk

Variational formulation with error estimates for uncertainty quantification via collocation, regression, and sprectral projection

通过搭配、回归和谱投影进行不确定性量化的误差估计的变分公式

• DOI: 10.1002/pamm.201710024
• 发表时间: 2017
• 期刊: PAMM
• 作者: J. Rang;H. G. Matthies
• 通讯作者: H. G. Matthies

Uncertainty Quantification and Bayesian Inversion

不确定性量化和贝叶斯反演

• DOI: 10.1002/9781119176817.ecm2071
• 发表时间: 2017
• 作者: H. G. Matthies

Comparison of Numerical Approaches to Bayesian Updating

贝叶斯更新数值方法的比较

• DOI: 10.1007/978-3-319-27996-1_16
• 发表时间: 2016
• 作者: B. Rosić;J. Sýkora;O. Pajonk;A. Kučerová;H. G. Matthies
• 通讯作者: H. G. Matthies

Parameter estimation via conditional expectation: a Bayesian inversion

• DOI: 10.1186/s40323-016-0075-7
• 发表时间: 2016-06
• 期刊: Advanced Modeling and Simulation in Engineering Sciences
• 作者: H. Matthies;E. Zander;B. Rosic;A. Litvinenko