A non-linear cubic spline layerwise time domain spectral finite element for the analysis of impacts on sandwich structures

Abstract

The present work addresses the non-linear impact dynamic response of sandwich composite plates with Hertzian contact interaction between the impactor and the plate. Initially, a well-established Cubic Spline Layerwise Theory is employed for the precise description of complex through the thickness kinematics of sandwich composite plates. Furthermore, the expressions of Green Lagrange non-linear strain terms, along with the Deshpande-Fleck flow rule for polymeric crushable foams are presented for non-linear explicit impact dynamics. The material and geometric non-linearities as well as the layerwise mechanics, are integrated into a Time Domain Spectral Element which possesses the attributes of high-order Lagrangian polynomial shape functions and node collocation with the integration points due to the Gauss-Legendre-Lobbato integration scheme. The aforementioned numerical package provides a fast and accurate non-linear explicit integration dynamic module for the prediction of the impact response of sandwich plates, demonstrating the universality and validity of using Hertzian contact in sandwich and laminated composite structures. The proposed novel non-linear numerical model is correlated with experimental results and also with a high-fidelity three-dimensional solid finite element model in terms of accuracy and computationally efficiency.