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

在这个项目中，我们打算使用新开发的概念，isogeometric配置（IGA-C）与随机配置（SC）相结合，以实现稳定和计算效率高的高阶模型的不可逆多尺度行为在固体力学。基本假设是，一个异质固体的微观结构是不确定的，因此应该建模概率。为了描述微尺度不确定性不仅对平均宏观场的影响，而且对它们的可变性的影响，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是数量级大于简单的确定性分析，一个前所未有的计算效率，寻求在IGA-C的机械/确定性建模的组合，和一个SC计划与新的anonymous功能的随机离散化。要开发的数值框架包括局部和非局部弹性和塑性有限应变，以及接触，损伤和断裂模型。

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.