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。将从理论的角度研究这个问题，并推导出解析解。基于均匀化方法和奇异摄动技术的渐近方法将被使用。所提出的方法不仅可以获得有效的特性，而且还可以研究不同材料和结构中的机械应力的非均匀分布，这对于评估其强度具有重要意义，将研究每个材料组分（基体，纤维和界面）对复合材料行为的影响。复合材料失效的三种可能的情况将被研究：基体的塑性失效，界面失效和纤维断裂，所提出的方法填补了数值方法之间的实质性差距缺乏一般性和把握所考虑的结构的行为的共同特征的可能性，近似设计方案，启发式假设的基础上。所提出的方法适用范围广，设计公式简单明了，可供实际分析使用。

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.