Transverse Shear Deformation Limits in Structural Foamed High Yield Packaging Substrates
Low transverse shear modulus in foamed cores reduces effective bending stiffness and causes early compression collapse on short spans.
Cellular Solids Theory
Structural Framework
Analytical model for predicting the mechanical response of low density materials based on the geometry of their internal cell walls and the properties of the solid from which they are made. Application of cellular solids theory allows manufacturers to estimate the compressive strength and elastic modulus of paper based honeycomb or expanded foams by treating them as a network of interconnected beams or plates. The relationship between relative density and mechanical performance forms the foundation of this approach.
It identifies the transition points between elastic buckling, plastic yielding, cell wall fracture and brittle crushing.
Scaling Law
Mathematical functions describe how the bulk properties of a core material change as the density of the cells increases or decreases. For most open cell structures, the stiffness scales with the square of the relative density, while the strength scales with the three halves power. This predictive capability is indispensable when designing lightweight corrugated board that must withstand specific stacking loads without adding unnecessary mass.
Engineers use these equations to optimize the flute size and liner weight for specific protective packaging requirements.
Limit Condition
Models lose their predictive accuracy when the relative density exceeds approximately 0.3. This occurs because the cells can no longer be treated as thin walled structures.