Hyper-Elastic Characterization of Polydimethylsiloxane by Optimization Algorithms and Finite Element Methods

This study explores the mechanical properties of incompressible isotropic material polydimethylsiloxane (PDMS) using hyper-elastic constitutive models. It comprises two main parts: an experimental phase involving the creation of a new PDMS formulation and stress–strain evaluation through uniaxial tensile loading, and a theoretical phase where six hyper-elastic models are applied to the stress–strain data using finite element methods and optimization algorithms. Elastic compatibility and Drucker’s stability criterion provide the determination of material constants, integrated into the generalized reduced gradient and constrained particle swarm optimization (C-PSO) algorithm for optimization. The performance of these models is assessed via the coefficient of determination. The Reduced Polynomial model, with six material parameters optimized through C-PSO, emerges as the top choice, closely matching experimental data at various strain levels. Subsequent finite element simulations validate the behavior of the Reduced Polynomial model under the same conditions as the tensile testing, showing excellent agreement with experimental results. Analyzing rubber-like materials and their composites using commercial finite element software is challenging due to their non-linear properties, motivating the use of optimization algorithms to determine material properties accurately. This research’s novelty lies in using C-PSO and GRG solver to examine polymeric materials, yielding highly efficient and precise results.