A unified continuum mechanical model framework for initial and induced anisotropy - systematic investigations of anisotropic damage

许多与实践相关的材料--尤其是复合材料，其作用越来越重要--由于其生产，已经表现出明显的非弹性和方向依赖性（即各向异性）行为。如果强机械应力导致材料中的主要塑性变形和损坏，则这种方向依赖性可能变得更大。从实际和科学的角度来看，除了了解这种复杂材料行为的原因外，其建模也非常重要，例如，为了能够在模拟中对相应部件的使用寿命和承载能力进行现实的预测。因此，迫切需要一种能够同时以令人满意的方式表示上述材料现象的模型，因此，本项目的中心思想是开发一种新的、非常普遍适用的基于结构张量的连续介质力学模型框架，通过该方法，初看起来非常不同的材料现象-初始各向异性以及由于损伤和/或塑性引起的诱导各向异性-可以用一个统一的概念来描述。这将大大简化新的各向异性材料模型的未来发展。具体来说，该项目侧重于推导和系统研究两种不同类型的各向异性损伤模型，这两种模型都可以嵌入到新的连续介质力学框架中。使用单向纤维增强复合材料，将测试上述损伤概念的质量，以描述材料的实际物理行为。为此目的，将在中尺度上进行广泛的虚拟实验，在这些实验的帮助下，可以逐步发现各自建模战略的长处和不足。例如，复合材料中的裂纹形成可取决于基质中、纤维与基质之间的界面中或纤维本身中的组分的刚度和强度性质而发生。一个各向异性的连续介质力学损伤模型应该能够以一种物理意义上的方式来描述这三种情况下的脆性和韧性损伤。众所周知，变形局部化发生在软化材料行为的情况下，当使用标准离散化方法时，这可能导致病态的网格依赖解。为了规避这个问题，梯度扩展损伤建模，这是嵌入在相应的扩展有限元技术。

Many practice-relevant materials - especially composites, which are playing an increasingly important role - already exhibit a pronounced inelastic and direction-dependent (i.e. anisotropic) behavior due to their production. If strong mechanical stresses cause major plastic deformations and damage in the material, this directional dependence can become even greater. From a practical and scientific point of view, in addition to understanding the causes of such complex material behaviour, its modelling is also of enormous importance, e.g. in order to be able to make realistic forecasts of the service life and load-bearing capacity of corresponding components in simulations. There is an urgent need for models which can represent the above-mentioned material phenomena simultaneously and in a satisfactory way.The central idea of this project is therefore to develop a new and very generally applicable continuum mechanical model framework based on structural tensors, with which the at first sight very different material phenomena - initial anisotropy as well as induced anisotropy due to damage and / or plasticity - can be described by means of a unified concept. This will significantly simplify the future development of new anisotropic material models.Specifically, the project focuses on the derivation and systematic investigation of two different types of anisotropic damage modelling, both of which can be embedded in the novel continuum mechanical framework. Using unidirectional fibre-reinforced composites, the quality of the damage concepts described above will be tested to describe the actual physical behaviour of the materials. For this purpose, extensive virtual experiments on the mesoscale will be carried out, with the help of which the strengths and deficits of the respective modelling strategy can be gradually uncovered. For example, crack formation in a composite can occur depending on the stiffness and strength properties of the components in the matrix, in the interface between fiber and matrix or in the fiber itself. An anisotropic continuum mechanical damage model should be able to represent these three cases in a physically meaningful way for both brittle and ductile damage.A further challenge is related to the numerical implementation. It is well-known that deformation localization occurs in the case of softening material behavior, which can lead to pathologically mesh-dependent solutions when using standard discretization methods. In order to circumvent this problem, a gradient-extended damage modelling is pursued, which is embedded in a correspondingly extended finite element technology.