Optimal structural pattern for maximal compliance using topology optimization based on phasefields: Application to improve skin graft meshing efficiency

Abstract

This article focuses on the problem of maximal compliance design of a hyperelastic solid with the optimal design of human skin grafts as the application in mind. The solution method is a phasefield-based topology optimization method that supposes multiple local phasefields and a minimum distance constraint in order to prevent the phasefields from merging. Consequently, structurally disintegrating solutions such as by the coalescence of voids can be prevented. The method is used to find an optimal graft meshing pattern for a sample that is subjected to a biaxial extension of up to 150%, which corresponds to an expansion ratio of 1 : 2.25. Three prospective unitcell solutions that exhibit meta-material behavior are proposed for a periodic graft pattern. The results are a step toward improving the skin graft meshing efficiency. This work does not cover experimental validation.

Biomechanical modeling of novel high expansion auxetic skin grafts

“…Although the auxetic structures produced high expansions on the skin graft models, the excessive stretching may lead to high stress concentration factors at sharp corners in the patterns which could further lead to its fracture. Sutula et al 15 implemented phase fields in topology optimization for maximizing the compliance. Phase fields were considered as an efficient model to estimate the emergence of fractures or damage and optimal designs were suggested for the skin graft patterns, which can be useful in determining the optimizing parameters for a particular design.…”

“…Zhang et al 10 conducted high‐expansion experiments at various strain levels and achieved the NPR greater than −3.0 similarly, another study conducted by Grima et al 14 achieved NPR of approximately −4.8. In a recent computational study, Sutula et al 15 performed topology optimizations using maximal compliance approach by implementing phase field damage model and suggested the use of meta‐materials as repetitive patterns on the human skin graft. Owing to the high expansions produced by auxetic polymers, it is hypothesized that these patterns applied to skin grafting may be able to generate expansions larger than that produced by traditional split thickness skin grafts without generating induced stresses greater than ultimate tensile stress of skin.…”