Simplification of Hyperelastic Constitutive Model and Finite Element Analysis of Thermoplastic Polyurethane Elastomers

In this work, the simplified hyperelastic constitutive model and finite element analysis of thermoplastic polyurethane elastomers (TPUs) under uniaxial tension are studied. Based on a series of classical strain energy density function of hyperelastic materials, a "one-step" transformation algorithm from standard test data to the simplest constitutive model is proposed and a three-parameter simplified constitutive model is obtained. The simplified model has a high accuracy on the experimentally determined load-displacement curve with fitting errors of 0.95%, 0.81%, and 0.98% to three TPUs comprising different hard segment contents of 15.19, 22.54, and 38.51 wt%, respectively. By combining the simplified hyperelastic constitutive model with the finite element analysis, the mechanical behavior of TPUs in uniaxial tensile state is predicted accurately. The simplification algorithm and simulation method may be applicable to other hyperelastic materials with more complex shapes and working conditions and have certain practical engineering guiding significance for the subsequent material selection, design, and production.