A genetic algorithm optimization framework for the characterization of hyper-viscoelastic materials: application to human articular cartilage

Abstract

This study aims to develop an automated framework for the characterization of materials which are both hyper-elastic and viscoelastic. This has been evaluated using human articular cartilage (AC). AC (26 tissue samples from 5 femoral heads) underwent dynamic mechanical analysis with a frequency sweep from 1 to 90 Hz. The conversion from a frequency- to time-domain hyper-viscoelastic material model was approximated using a modular framework design where finite element analysis was automated, and a genetic algorithm and interior point technique were employed to solve and optimize the material approximations. Three orders of approximation for the Prony series were evaluated at N = 1, 3 and 5 for 20 and 50 iterations of a genetic cycle. This was repeated for 30 simulations of six combinations of the above all with randomly generated initialization points. There was a difference between N = 1 and N = 3/5 of approximately ~5% in terms of the error estimated. During unloading the opposite was seen with a 10% error difference between N = 5 and 1. A reduction of ~1% parameter error was found when the number of generations increased from 20 to 50. In conclusion, the framework has proved effective in characterizing human AC.

Keywords

• articular cartilage
• dynamic mechanical analysis
• finite element analysis
• genetic algorithm
• Prony series
• viscoelastic