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

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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.