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

在这个项目中，我们打算使用新发展的等距配置法(IGA-C)与随机配置法(SC)相结合来实现对固体力学中不可逆多尺度行为的稳定和计算高效的高阶建模。基本的假设是，非均质固体的微观结构是不确定的，因此应该以概率的方式建模。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确定性分析的计算量大几个数量级，因此将用于机械/确定性建模的IGA-C和用于随机离散化的具有新的ANSAZ函数的SC格式的组合寻求前所未有的计算效率。拟开发的数值框架包括有限应变的局部和非局部弹性和塑性，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.