Simplified theory for contact indentation of sandwich panels

Abstract

Previous attempts to analyze indentation of sandwich panels have been based on small deflection theory and an assumed elastic core behaviour. The agreement with experiments was poor. The present work includes core crushing and large deflections of the face sheets in a simplified model of sandwich contact indentation. The model assumes transverse isotropy with respect to the load axis and is based on an infinite, elastic face sheet on a core bonded to a rigid foundation. The core is assumed to be elastic in tension and elastic-ideally plastic in compression. After initiation of core yielding the problem is separated in two regions. In the inner, plastic region, the core has yielded and exert a constant reactive pressure on the face sheet. In the outer region the core acts as an elastic foundation. The plastic radius is found by matching boundary conditions for the two regions.The outer region is modeled as a plate on an elastic foundation. The inner region is modeled using three different approaches. For small deflections classical plate theory with shear corrections is used. For intermediate deflections an upper limit of the contact force is given by first order large deflection plate theory and a lower limit by small deflection plate theory. The asymptotic behaviour at large deflections is given by an approximate solution based on membrane theory. The three solutions, which all require iteration, have been put in dimensionless form and tabulated. The approach due to Hertzian contact has been included in the plate solution. Bounds have been given for the residual indentation after unloading. Approximate expressions are given for analysis of orthotropic face sheets.Good agreement with experiments was found for sandwich panels of different materials and thickness. The often observed, approximately linear, load-indentation relation is found to be the combined effect of softening due to core crushing and stiffening due to face sheet membrane effects. A limited parametric study indicates a strong influence of the core yield stress and the face sheet properties, and a relatively weak influence of the thickness and elastic properties of the core. The local indentation model may be used in a global impact model to predict impact response of sandwich panels, or as a starting point for more detailed stress analyses for prediction of damage due to impact and contact loads.

Localized Impact on Sandwich Structures With Laminated Facings

“…The motion of the projectile is governed by Newton's law and combining the equations of motion of the plate with that of the projectile we obtain the global set of second order differential equations The submatrices in Eqs (46,47) are the modal mass and stiffness matrices for modes i = 1,n and are given in Eq (43). M e is the mass of the projectile and where X represents the displacement of the projectile.…”

Impact analysis of I-Lam sandwich system for over-height collision protection of highway bridges

“…Thomsen [14] presented the results from a combined theoretical and experimental investigation of local bending effects in a clamped circular foam core sandwich plate subjected to a central point load, and a simple two-parameter elastic foundation model was used in order to include the shear interaction between the skin and core. Olsson and McManus [15] developed a simplified theory describing the contact indentation of sandwich plates based on a single-parameter foundation model for the core. Lee et al [16] investigated the impact dynamic response of composite sandwich plates impacted by a rigid ball.…”

Indentation Study of Foam Sandwich Structures Reinforced by Fiber Columns

“…Later on, this model was sophisticated using the concept of linear elastic perfectly plastic foundation [9]. Olsson and McMannus [10] showed that the large deflection of plate theory, membrane theory, and core yielding significantly improve analytical predictions of the local load-indentation response of sandwich panels when compared to previous models assuming small deflection and elastic core response. But indentation analysis of the foam sandwich structures reinforced by fiber columns have not been addressed up to now.…”