Shakedown Analysis of Paper and Paperboard Materials: A Computational Framework for Predicting Structural Reliability
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Paper and paperboard materials are increasingly being adopted in sustainable engineering applications because of their renewability, low weight, and favorable mechanical performance. However, their heterogeneous, anisotropic microstructure and inelastic deformation behavior under variable loading introduce significant challenges for long-term structural assessment. This study presents a computational framework for lower bound shakedown analysis, aimed at predicting the endurance limits of paper-based structures under repeated mechanical loading. We apply Melan’s static shakedown theorem to determine the load capacity of structures made from paperboard that are subjected to mechanical loading. For that, an anisotropic elasto-plastic constitutive model is used, which is based on our previous work. The implementation follows a finite element-based constrained optimization formulation. Numerical case studies on representative paperboard geometries subjected to mechanical loading illustrate the effectiveness of the proposed framework in identifying elastic, plastic, and shakedown regimes. The results support the use of classical plasticity theory for modern orthotropic material systems and provide a practical computational tool for assessing structural reliability in sustainable design contexts.