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# Compressive Stress-Strain Relationships of Layered Solid Foams

This Demonstration calculates and plots the sigmoid compressive stress-strain curve of hypothetical slabs composed of three layers of solid foams having different mechanical properties and thicknesses. It also calculates and displays, separately, the individual components’ stress-strain curves. Each layer is characterized by the foam’s compressibility model equation, whose coefficients can be adjusted, and by its initial thickness, which also can be adjusted.

### DETAILS

Snapshot 1: layered spongy baked product
Snapshot 2: two soft and one hard layer combination
Snapshot 3: two-layered sponge
This Demonstration calculates the compressive engineering stress-strain relationships of layered arrays of one to three solid foam slabs having the same cross sectional area stacked together. The sigmoid compressive stress-strain relationship of the individual foams is described by the three-parameter model , or , where is the engineering stress in kPa, the engineering strain (dimensionless), and , , and are constants; is primarily a scale factor and has kPa units, , which is dimensionless, primarily controls the shoulder’s height, and , also dimensionless, serves as a marker of the densification stage [1]. For alternative models, see [1] and [2].
The absolute deformation of each layer is given by , being the layer’s initial thickness.
In a layered array of foams , , and under uniaxial compression, the absolute deformation is . Therefore, the corresponding engineering strain of the array is [2]: , where the deformations and strains are calculated by the layers’ compressibility equations.
The compressive engineering stress-strain curves of the individual foams are calculated and displayed together on the top graph and that of the array on the bottom graph. Vary the stress slider to calculate the corresponding strain of the individual layers and of the array as a whole. The chosen conditions will be seen as a moving dot on each of the stress-strain curves and the corresponding values displayed in a table above the plots.
To eliminate a layer from the array, enter zero as its initial height.
To go back to the initial settings, click the plus sign in the upper right corner of the panel, then "Initial Settings".
References
[1] S. Swyngedau, A. Nussinovitch, I. Roy, M. Peleg, and V. Huang, "Comparison of Four Models for the Compressibility of Breads and Plastic Foams," Journal of Food Science, 56, 1991 pp. 756–759.
[2] S. Swyngedau, A. Nussinovitch, and M. Peleg, "Models for the Compressibility of Layered Polymeric Sponges," Polymer Engineering & Science, 31, 1991 pp. 140–144.

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