Hyper-elastic materials

An important aspect of soft robotics in general is to accurately describe large nonlinear deformations of inertial continuum bodies in motion. Yet, due to these large deformations, many classical Hookean elasticity models may not be accurate for elastomer materials.

To address this, Sorotoki provides a library of hyper-elastic constitutive material models: Neo-Hookean (NH), Mooney-Rivlin (MR), and Yeoh model (YH). The strain energy densities for these models are derived based on the strain invariants \(I_1\), \(I_2\), and \(I_3\) provided in Table \ref{tab:C5:strain_measures} and are shown in Table

The material models presented in Table \ref{tab:C5:elasticitymodels} are implemented in \textit{Sorotoki} under the class \class{Material}, but have specific constructors tailored towards each material, \texttt{NeoHookeanMaterial}, \texttt{MooneyMaterial}, and \texttt{YeohMaterial}. Regarding their parameters, the work of Marechal et al. \cite{Marechal2021Jun} provides an open-source database that includes a broad collection of soft materials commonly used in soft robotics, gathered through uniaxial material tests. Based on their dataset and relevant other literature \cite{Xavier2022Jun,Smith2018,Kim2018,Goury2018}, \textit{Sorotoki} offers some preset material models of soft materials commonly used in soft robotics, such as the Ecoflex30/50 series, Dragonskin10/30 series, NinjaFlex, and Formlabs Elastic50A/80A material. These material classes also include the physical data for density, viscosity, and tangential contact friction. Following \eqref{eq:C5:fem_hyper}, the first Piola-Kirchhoff (PK1) stress tensor is evaluated analytically using the function call \code{P = Material.PiollaStress(F)}.