The analysis of the worst-case distribution of the damage in composite material imposed by a low velocity impact

Abstract

Low velocity impact causes barely visible impact damage (BVID) in composite material, which can be missed at technical inspection. Usual cases during composite product lifetime are the tool drop, hailstones, runway debris etc. The proposed approach avoids the direct modelling of impact process and realizes the minimum possible residual strength for specific damage based on the worst distribution of matrix, fiber and interface micro damages and its accumulation after impact. The minimum possible residual strength condition is fulfilled by the decreasing the stiffness of the laminate via energy absorption form the impactor and composite material collision. It is assumed, that the portion of the kinetic energy of an impactor is transformed into microcracks of fractured matrix materials by several damage modes but the other portion is transformed back to the impactor. The presented method gives as a result the distribution of damage parameters, which reduces stiffness of the material using gradient descent method and provides the worst distribution of damage densities, which associated with the stiffness and gives the direct analogue to the structural topology optimization algorithm. The simple explanation of presented method can be formulated as a search of the worst case of damage distribution in the material for residual strength of the structure with restriction on total energy spent on material damaging.