Muscle performance in a soft-bodied terrestrial crawler: constitutive modelling of strain-rate dependency

Abstract

Experimental data on the passive mechanical properties of the ventral interior lateral muscle of the tobacco hornworm caterpillar, Manduca sexta, are reported. The stress-deformation response of the Manduca muscle is shown to be nonlinear pseudo-elastic, capable of large deformations and subject to stress softening during initial loading cycles. The muscle passive mechanical properties also depend on multiple time-dependent processes. In particular, we show new experimental data from cyclic loading tests of an unstimulated muscle with constant maximum stretch and different, constant engineering strain rates. Then, on the basis of these data a constitutive model is derived to reproduce the main characteristics of this behaviour. In formulating the constitutive model, we consider the muscle as a complex macromolecular structure with fibrous components at numerous size scales. The model uses a phenomenological approach to account for different mechanisms by which passive force changes during applied deformation and how the muscle properties recover after unloading.

Figure 1

Cyclic tension tests of a passive caterpillar muscle with a maximum stretch of λ_max=1.18 and engineering strain rates of (a) $\dot{ϵ}=0.0144$ s⁻¹, (b) $\dot{ϵ}=0.072$ s⁻¹, (c) $\dot{ϵ}=0.36$ s⁻¹ and (d) $\dot{ϵ}=1.8$ s⁻¹.

Figure 2

Comparison of the rate-dependent responses of a preconditioned Manduca muscle. Engineering strain rates are $\dot{ϵ}=$0.0144, 0.072, 0.36 and 1.8 s⁻¹.

Figure 3

Experimental and numerical loading–unloading data of a preconditioned Manduca muscle with λ_max=1.18 and an engineering strain rate of $\dot{ϵ}=1.8$ s⁻¹.

Figure 4

Numerical results of loading–unloading stress–strain data corresponding to engineering strain rates of $\dot{ϵ}$=0.0144, 0.072, 0.36 and 1.8 s⁻¹.