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。我们将从理论的角度来研究这个问题，并推导出解析解。将使用基于齐次化方法和奇异摄动技术的渐近技术。该方法不仅可以获得材料和结构的有效特性，而且可以研究不同材料和结构中机械应力的非均匀分布，这对于评估它们的强度具有重要意义。本文将研究复合材料失效的三种可能情形：基体塑性失效、界面失效和纤维断裂。该方法填补了缺乏通用性的数值方法和基于启发式假设的近似设计方案之间的巨大空白。所提出的方法应用范围广，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.