A constitutive model for muscle properties in a soft-bodied arthropod

Abstract

In this paper, we examine the mechanical properties of muscles in a soft-bodied arthropod under both passive and stimulated conditions. In particular, we examine the ventral interior lateral muscle of the tobacco hornworm caterpillar, Manduca sexta, and show that its response is qualitatively similar to the behaviour of particle-reinforced rubber. Both materials are capable of large nonlinear elastic deformations, show a hysteretic behaviour and display stress softening during the first few cycles of repeated loading. The Manduca muscle can therefore be considered as different elastic materials during loading and unloading and is best described using the theory of pseudo-elasticity. We summarize the basic equations for transversely isotropic pseudo-elastic materials, first for general deformations and then for the appropriate uniaxial specialization. The constitutive relation proposed is in good agreement with the experimental data for both the passive and the stimulated conditions.

A constitutive description of the anisotropic response of the fascia lata

“…where the term W iso represents the isotropic matrix and W fib accounts for the directional reinforcements (Qiu and Pence, 1997;Holzapfel et al, 2000;Merodio and Ogden, 2005;Horgan and Saccomandi, 2005;Dorfmann et al, 2007Dorfmann et al, , 2008. Based on the structure of fascia lata outlined in Section 3.1 and following the simplification suggested by Holzapfel et al (2000), we reduce the number of invariants and consider the form…”

Dynamic properties of a locomotory muscle of the tobacco hornwormManduca sextaduring strain cycling and simulated natural crawling

“…VIL, like other muscle, shows pseudoelasticity, a characteristic in which a material behaves as one kind of elastic when being lengthened and another when being shortened. It also shows a Mullins effect, or stress-softening under repeated constant-velocity strain cycling (Dorfmann et al, 2007). With respect to these characteristics, VIL's dynamic properties are qualitatively similar to those of synthetic elastomers (Dorfmann and Ogden, 2003;Dorfmann and Ogden, 2004) and have been described using a constitutive modeling approach (Dorfmann et al, 2007).…”

“…It also shows a Mullins effect, or stress-softening under repeated constant-velocity strain cycling (Dorfmann et al, 2007). With respect to these characteristics, VIL's dynamic properties are qualitatively similar to those of synthetic elastomers (Dorfmann and Ogden, 2003;Dorfmann and Ogden, 2004) and have been described using a constitutive modeling approach (Dorfmann et al, 2007). Additionally, these characteristics are dependent upon strain rate 8,9), indicating viscoelasticity (Fung, 1993;Wineman and Rajagopal, 2000).…”

“…Separate preparations were subjected to strain cycles and stimulation simulating those recorded during horizontal crawling (see below). Stress values were based upon muscle cross-sectional areas calculated using a relationship determined from imaging of individual muscle fibers in a separate set of preparations, as described by Dorfmann et al (Dorfmann et al, 2007). Data were analyzed in Aurora DMA, SigmaPlot 2000 (SAS Institute Inc., Cary, NC, USA) and Systat 10.0 (Systat Software Inc., Richmond, CA, USA).…”

Kinematics of horizontal and vertical caterpillar crawling

“…Because caterpillars crawl slowly (0.241-0.310 cm s -1 on average in the present study), and forward momentum is small and episodic, there is no sustained acceleration and the effect of gravity is therefore minimized during vertical climbing. Another reason for the high costs of caterpillar locomotion is that muscles and body wall have low resilience, dissipating a large proportion of mechanical work (40-60%) during cycles of strain Dorfmann et al, 2007;Lin et al, 2008;Woods et al, 2008). This inability to store elastic energy makes caterpillar locomotion less efficient.…”