Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis

Polymer gels are widely accepted as candidate materials for tissue engineering, drug delivery, and orthopedic load-bearing applications. In addition, their mechanical and physical properties can be tailored to meet a wide range of design requirements. For soft gels whose elastic modulus is in the kPa range, mechanical characterization by bulk mechanical testing methods presents challenges, for example, in sample preparation, fixture design, gripping, and/or load measurement accuracy. Nanoindentation, however, has advantages when characterizing the mechanical properties of soft materials. This study was aimed at investigating the application of an inverse finite element analysis technique to identify material parameters of polymer gels via nanoindentation creep testing, optimization, and finite element simulation. Nanoindentation experiments were conducted using a rigid circular flat punch, and then simulated using the commercial software ABAQUS™. The optimization (error minimization) procedure was integrated in the parameter determination process using a Matlab™ shell program, which makes this approach readily adaptable to other test geometries and material models. The finite element results compare well with a derived analytical viscoelastic solution for a rigid circular flat punch on a Kelvin–Voigt half-space.