“Segment-wise model” for theoretical simulation of barely visible indentation damage in composite sandwich beams: Part I – Formulation

Investigation on the indentation behavior of sandwich beams using crushable and hyperelastic foam cores

“…The indentation behaviour beyond the elastic limit of the foundation has been generally treated by representing the yielding behaviour of the foam as perfectly-plastic ("Crushable" foam) and solutions are provided in [2][3][10][11][12][13]15] based on different solutions to the differential equations problem. Solutions for the important estimation of residual dents after core yielding are more rare to find [3,4], while the segment-wise approach proposed in [14] has good but yet unexplored potentials for dealing with the evaluation of residual dents in foamed core sandwiches. Recently the sandwich panels higher order theory approach [16] has also been used to derive the indentation law in the core elastic compression range for both fully backed and edge supported beams, with interesting results as compared to those of classic approaches [17].…”

“…The main cases proposed regard: x Point loaded sandwich beams where the lower skin is resting on a rigid surface, i.e. a fully backed sandwich beam (FB) [2,3,5,[11][12][13][14]; x Point loaded and edge supported sandwich beams, i.e. three point bending scheme (TPB) [10]; x Core material behaving as a rigid perfectly plastic foundation (RPP) [10,12]; x Core material behaving as a pure linear elastic foundation (E) [2,3,5,13,14]; x Core material behaving as an elastic-perfectly plastic foundation (EPP) [2,3,10,11,15].…”

“…The general expression for the equilibrium equation of the beam is a fourth order linear differential equation [2,3,14], whose coefficients are functions of the core and skin geometric, elastic and constitutive properties. This equation can be written as: c…”

“…In this study analytical models for the point loaded sandwich beam indentation problem are reviewed by presenting a unified approach based on the segment-wise model recently proposed by Minakuchi et al [14]. It is shown in particular that solutions based on elastic and elastic-perfectlyplastic constitutive laws can be derived as particular cases of this approach.…”

“…In [6,7,9] a two parameters elastic foundation approach is used able to include also shear forces at the face-core interface while a justification for neglecting them in the case of sandwich beams, thus considering only normal forces (assumption found in the in the majority of works) is provided in [10]. Solutions are most frequently provided for the fully backed sandwich where the unloaded face is resting against a rigid foundation [2,3,5,9,[11][12][13][14]. Solutions for edge supported beams (e.g.…”