On the derivation of passive 3D material parameters from 1D stress-strain data of hydrostats

The present paper offers a novel equivalent-pressure approach to the derivation of isotropic passive muscle parameters from 1D stress-strain data sets. The approach aims specifically at the identification of material parameters in hydrostats, in which case the equivalent-force approach that is common for skeletal muscle generates suboptimal results. Instead, an equivalent-pressure hypothesis is formulated which provides more adequate boundary conditions for the concluding curve-fitting procedure. The choice of an appropriate constitutive description is decisive for the quality of the deduced parameter sets. Here, a Yeoh material law is chosen for the model of a squid tentacle. Parameters derived by both, equivalent-force and equivalent-pressure algorithms, are compared, illustrating the applicability limits of either. They are implemented in a finite element model of the tentacle. A prey-capture strike is simulated and compared to data from literature. The hydrostat-specific interpretation of the equivalent-pressure hypothesis is shown to match the reference very well.