Elastic Foundation Constants for Sandwich Composites

Abstract

Elastic foundation models are often used in fracture mechanics applied to face/core debonds in sandwich composites or in face wrinkling studies. The elastic constants to be used in these models are the most important element in these formulations. This paper presents closed-form solutions for the determination of these constants based on 1) the extended high-order sandwich panel theory and 2) the elasticity theory. The extended high-order sandwich panel theory results in a system of seven algebraic equations, which can be directly solved for the seven real constants that enter into the formulas (all calculations are in real variables). The elasticity solution results in a system of 12 linear algebraic equations, which can be directly solved for the twelve complex constants that enter into the formulas, and it also involves the direct solution of three characteristic equations (for the 2 faces and the core). In the elasticity approach, the calculations are done in complex variables. Direct formulas are derived for both the normal and the shear spring constants. The definition of the elastic foundation constants and possible misconceptions surrounding them are discussed. New simple formulas are also suggested, which are variations of “crude” formulas existing in the literature.