Anisotropic Criterion
Structural analysis of orthotropic materials requires a mathematical tool to predict when a sheet will break under complex loading conditions. Hill quadratic failure offers a specialized equation that accounts for the different strengths of paper in the machine direction and the cross direction. This approach expands on simpler isotropic theories by incorporating six distinct parameters to describe the yielding of the fiber network.
Stress Analysis
Applying the model involves measuring the tensile and compressive limits of the board along its primary axes. When hill quadratic failure is calculated for a heavy shipping container, it identifies whether the vertical or horizontal stresses will cause the corners to buckle first. The formula is essential for finite element analysis of corrugated structures where the liner and medium have vastly different mechanical properties.
Paperboard Specification
Accurate material testing provides the data needed to populate the failure surface in a simulation. Designers use hill quadratic failure to optimize the grammage of individual layers in a laminated board without compromising the final structural integrity of the package. This optimization reduces material waste while ensuring that the product survives the vibration and impact of long distance shipping.
Because the fiber orientation in a fourdrinier machine creates significant directional bias, this specific model is more reliable than general criteria for predicting the actual performance of the final box.
