Various issues raised by the mechanics of an octopus’s arm

Abstract

Various issues raised by the mechanics of an octopus’s arm are presented from the point of view of continuum mechanics. First, we study the conditions for a mixture of a number of fiber bundles to span the space of stress tensors. The geometry of a fiber bundle, as reflected in the direction and density of the fibers, is described by a vector field, or, more precisely, by a differential two-form. For the stress analysis, we propose a three-dimensional continuum model of the arm that is based on constitutive data available for muscle fibers. An analysis of small deformations superimposed on an activated configuration of the muscle bundles reveals the stiffening mechanism which enables the arm to support various external loadings, even if the geometry and the number of the fiber groups does not allow the tensions in them to span the space of stress tensors.