Structural Representation
Finite element analysis of thin-walled structures like corrugated boxes uses specialized solid-like formulations to capture both in-plane and out-of-plane mechanics. The utilization of continuum shell elements allows engineers to simulate the complex deformation of paperboard without the computational cost of fully three-dimensional solid elements. These mathematical formulations discretize the board through its thickness while retaining the displacement degrees of freedom of standard solid bodies.
This structural discretization supports the integration of non-linear material models that are essential for predicting crease behavior during carton conversion. It enables accurate representation of contact interactions on both the top and bottom faces of the sheet.
Stress Analysis
Calculations in this domain must account for the highly anisotropic nature of paperboard materials. Since the paperboard exhibits distinct properties in the primary directions, the stress tensor must be evaluated at multiple integration points through the thickness. This localized analysis captures the bending and stretching deformation that occur during folding or crushing.
It ensures that the onset of material failure is predicted accurately.
Thickness Formulation
Out-of-plane strain behavior requires particular attention because paperboard is susceptible to delamination under loading. Standard shell formulations often ignore these thickness-direction strains, whereas continuum shell elements compute them directly to improve accuracy. This feature proves useful when analyzing the crushing of flutes in corrugated boards.
The calculation finishes when the element reaches its critical deformation limit.
