Nonlinear behaviour and failure analysis of fibre-reinforced composites (Nichtlineares Verhalten und Versagensanalyse von Faserverbundwerkstoffen)

本课题的研究对象是周期性纤维增强复合材料的失效分析问题。这个问题将从理论角度进行研究，并推导出解析解。本文将采用一种基于均匀化方法和奇异摄动技术的渐近方法。该方法不仅可以获得有效特性，而且可以研究不同材料和结构中机械应力的非均匀分布，这对评估其强度具有重要意义。将研究每种材料成分（基体、纤维和界面）对复合材料行为的影响。本文将研究复合材料破坏的三种可能情况：基体塑性破坏；界面失效和纤维断裂。所提出的方法填补了缺乏通用性的数值方法与掌握所考虑结构行为的共同特征的可能性之间的实质性空白，以及基于启发式假设的近似设计方案。所提出的方法适用范围广，设计公式简单明了，便于实际分析。

Object of this project is the problem of failure analysis of periodic fibre-reinforced composites. The problem will be studied from theoretical point of view and analytical solutions will be derived. An asymptotic technique, based on the homogenization method and singular perturbation technique, are going to be used. The proposed method allows not only to obtain effective characteristics but also to investigate non-homogeneous distributions of mechanical stresses in different materials and structures which is of great significance for evaluating their strength.The influence of each material component (matrix, fibre and interface) on the behaviour of the composite will be investigated. Three possible scenarios of composite failure will be studied: plastic failure of matrix; interface failure and breaking of fibres.The proposed approach fills the substantial gap between numerical methods lacking in generality and the possibility to grasp the common features of the behavior of the considered structures, and approximate design schemes, based on heuristic hypotheses. The proposed methods are wide-ranged in applications and lead to simple and clear design formulae, useful for practical analyses.