The possibility to perform advanced forming operations of initially plane paperboard paves the way to making products like food trays, plates, cups and other containers as a part of shifting towards a circular bioeconomy. As a part of the ongoing efforts of expanding the product range using paperboard, we performed analyses of the forming operation using simulations. An implicit non‐linear finite element model is built to more accurately than previous studies simulate the tray forming process of paperboard. Two different commercial paperboards are investigated. The use of an implicit solver enabled the inclusion of the creasing pattern into the geometry of the paperboard blank resolving the formation of wrinkles during forming. The material data is extracted from tensile test curves of the investigated paperboards and was fitted accurately using Hill's plasticity with difference in tension and compression accounted for with subsequent failure evaluation. The results showed that the inclusion of the creases in the geometry is vital for getting a correct shape of the formed tray and important for decreasing the risk of failure. The results also showed that friction has a big impact on the formed shape and hence on the stress levels, and therefore supports the means of lowering friction between the blank holder and the blank during the tray forming operation. A stochastic approach is proposed to determine the probability of failure for the boards. The performed failure evaluation is consistent with the field observations. The developed approach enables more precise simulations of paperboard tray forming.
The growth and resorption of bone are governed by interaction between several cells such as bone-forming osteoblasts, osteocytes, lining cells and bone-resorbing osteoclasts. The cells considered in this study reside in the periosteum. Furthermore, they are believed to be activated by certain substances to initiate bone growth. This study focuses on the role that stress driven diffusion plays in the transport of these substances from the medullary cavity to the periosteum. Calculations of stress driven diffusion are performed under steady state conditions using a finite element method with the concentration of nutrients in the cambium layer of the periosteum obtained for different choices of load frequencies. The results are compared with experimental findings, suggesting that increased bone growth occurs in the neighbourhood of relatively high nutrient concentration.
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