#### 5.3.5.2. Face Sheet Wrinkling

Wrinkling of sandwich face sheets is a local instability phenomenon, in which the face sheets can be modeled as plates on an elastic foundation formed by the core. Simple formulas for estimating wrinkling stresses of sandwich face sheets under uniaxial load have been presented in the literature ([ 23 ] and [ 33 ]). Linear elastic material behavior is assumed. Possible interaction of the top and bottom face sheets is not considered.

In the following, , , and refer to a coordinate system in which the -axis is in the direction of compression and the -axis is perpendicular to the face sheets. The subscripts F and C indicate the face sheet and the core, respectively.

For sandwich laminates with homogeneous cores, the wrinkling stress of a face sheet is:

| (5–114)

where the theoretical value of the wrinkling coefficient is 0.825. The effects of initial waviness and imperfections of the face sheet are normally accounted for by replacing the theoretical value of the wrinkling coefficient with a lower value. it is recommended that you use the value as a safe design value for homogeneous cores ([ 23 ] and [ 33 ]).

The wrinkling stresses for sandwich laminates with honeycomb cores are estimated with the expression:

| (5–115)

The theoretical value of is 0.816, whereas a safe design value is ([ 23 ] and [ 33 ]).

The prediction of wrinkling under multiaxial stress state is discussed in [ 33 ]. When in-plane shear stresses exist, it is recommended that the principal stresses are determined first. If the other of the two principal stresses is tensile, it is ignored and the analysis is based on the equations given above. When biaxial compression is applied, wrinkling can be predicted with an interaction formula. The condition for wrinkling is:

| (5–116)

where is the direction of maximum compression [ 33 ]. For orthotropic sandwich face sheets, is more logically interpreted as the most critical of the two directions. The wrinkling stresses and are computed from the formulas for uniaxial compression by considering the compressive stresses in the - and -direction independently.

The average face sheet stresses , , are obtained from the layer stresses of the face sheets. The following procedure for the computation of reserve factors is then used independently for the top and bottom face sheets.

If the shear stress of the face sheet is zero, the normal stresses and are used directly in the prediction of wrinkling. Otherwise, the principal stresses are determined first:

| (5–117)

The orientation of the normalized principal stresses with respect to the xy-coordinate system is

| (5–118)

where:

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