Multi-field modelling and simulation of fibre reinforced polymers

该项目的总体目标是开发一个数值框架，用于模拟大变形和大位移下纤维增强聚合物的热机械损伤和断裂。这将有助于我们预测和理解在高速和高能冲击情况下出现的瞬时断裂机制。为此，必须发展和结合几种新颖和复杂的数值方法。必须引入考虑各向异性材料行为以及局部损伤和热效应的相场断裂公式，以便对复杂的三维断裂模式进行实际预测。高阶相场公式提高了断裂能估计的准确性，但需要满足所需连续性条件的空间离散格式。在这种情况下，等距分析的概念能够提供足够的连续近似，并且必须与分层细化方案一起考虑以解决局部特征。为了建立一个稳定和稳健的数值框架，必须发展满足Ball意义下多凸性条件的高级混合变分原理。这种有希望的方法为新的多场配方的开发提供了极大的灵活性和清晰度，因为本构定律可以作为单独的场来求解。基于砂浆的接触公式已被证明优于经典的配置型方法，因此它们必须被考虑用于三维多物理接触界面。最终，必须开发稳定的二阶精度隐式时间积分格式。在这种情况下，结构保持积分器允许相对较大的时间步长，大大提高了手头给定问题的模拟的效率和稳健性。我们将在一个统一的数值框架中结合所有不同的方法，并进行几个静态和瞬时基准测试以进行验证，并最终将该框架应用于现实的工业应用。

The overall goal of this project is to develop a numerical framework for the simulation of thermomechanical damage and fracture in fibre reinforced polymers under large deformations and displacements. This will help us to predict and understand transient fracture mechanisms as they arise in high-velocity and high-energy impact situations. To this end, several novel and sophisticated numerical methods have to be developed and combined. A phase-field fracture formulation taking into account the anisotropic material behaviour as well as local damage and thermal effects has to be introduced for a realistic prediction of complex three-dimensional fracture patterns. Higher-order phase-field formulations increase the accuracy of the evaluation of the fracture energy but necessitates spatial discretization schemes which fulfil the required continuity conditions. In this context, the concept of isogeometric analysis is able to provide sufficient continuous approximations and has to be considered along with a hierarchical refinement scheme to resolve local features. Advanced mixed variational principles satisfying the polyconvexity condition in the sense of Ball have to be developed for a stable and robust numerical framework. This promising approaches enable great flexibility and clarity for the development of new multi-field formulations, since the constitutive laws can be solved as separate field. Mortar based contact formulations have shown to be superior against classical collocation type methods and thus they have to be considered for the three-dimensional multi-physical contact interface. Eventually, stable and second order accurate implicit time integration schemes have to be developed. In this context,structure-preserving integrators allow for comparatively large time steps, raising the efficiency and robustness of the simulation of the given problem at hand dramatically. We will combine all different approaches in a unified numerical framework and conduct several static as well as transient benchmark tests for verification purposes and apply this framework finally to realistic industrial applications.