Figure 1: A fifth instar Manduca sexta
illustrating the position of the ventral
muscle in the third abdominal body
Muscle Performance in a Soft-Bodied Terrestrial Crawler
In this project 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 behavior
of particle reinforced rubber. Both materials are capable of large
nonlinear elastic deformations, show a hysteretic behavior 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. There is,
however, one important difference. Biological tissues are composed
of an isotropic matrix embedding multiple oriented families of
protein fibers. Therefore, the material response is best described
as anisotropic. Rubber response, on the other hand, is generally
We develop a constitutive model to describe the nonlinear mechanical
response of a preconditioned Manduca muscle both for the
passive and the stimulated conditions. The muscle consists of a
microfibrillar matrix material with an embedded fibrous network of
elastic proteins and the proposed model accounts for its nonlinear
mechanical properties, including finite deformation
pseudo-elasticity, anisotropy and energy dissipation associated with
hysteresis. We further assume incompressibility since changes in
volume for deformations within the physiological range are
infinitesimal and therefore negligible. The model is fitted to
available data and its predictions are assessed.
Figure 2: Pre-conditioning of a caterpillar
the passive state with maximum
stretch of λ = 1.15.
Figure 3: Pre-conditioning of a caterpillar
the active state with maximum
stretch of λ = 1.15. Data
for the stimulated
condition were obtained during the
seconds of a 10 seconds stimulus, corresponding
to the period during which the same muscle
sustained force within 90 % of
peak values under tetanic
- Ahamed T, Rubin MB, Trimmer BA, Dorfmann L (2016)
The time-dependent behavior of passive skeletal muscle.
Continuum Mech Therm 28:561-577.
- Paetsch C, Dorfmann L (2015) Stability of active muscle
tissue. J Eng Math 95:193-216.
- Paetsch C, Dorfmann A (2013) Non-linear modeling
of active biohybrid materials.
Int J Nonlinear Mech 56:105-114.
- Paetsch C, Trimmer BA, Dorfmann A (2012) A constitutive model for
active-passive transition of muscle fibers. Int J Nonlinear
- Lin HT, Paetsch CR, Slate D, Dorfmann L,
Trimmer BA (2011) Ontogenetic scaling of caterpillar body
properties and its biomechanical implications on the use
of hydrostatic skeleton. J Exp Biol
- Lin HT, Dorfmann A, Trimmer BA (2009) Soft
Cuticle Biomechanics: A Constitutive Model
of Anisotropy for Caterpillar Integument. J Theor Biol
- Bose K., Dorfmann A (2009) Computational
Aspects of a Pseudo-Elastic Constitutive
Model for Muscle Properties in a Soft-Bodied
Arthropod. International Journal of
Non-Liner Mechanics 44:42-50.
- Dorfmann A, Trimmer BA, Woods W.A (2008) Muscle Performance in a
Soft-Bodied Terrestrial Crawler: Constitutive Modeling of
Strain-Rate Dependency. J Roy Soc Interface 5:349-362.
- Dorfmann A, Trimmer BA, Woods W.A (2007) A Constitutive Model for Muscle
Properties in a Soft Bodied Arthropod. J Roy Soc Interface