Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness

By A. Spencer, K. Soldatos. 2007

138 citations recorded by the source corpus.

Abstract In the conventional theory of finite deformations of fibre-reinforced elastic solids it is assumed that the strain-energy is an isotropic invariant function of the deformation and a unit vector A that defines the fibre direction and is convected with the material. This leads to a constitutive equation that involves no natural length. To incorporate fibre bending stiffness into a continuum theory, we make the more general assumption that the strain-energy depends on deformation, fibre direction, and the gradients of the fibre direction in the deformed configuration. The resulting extended theory requires, in general, a non-symmetric stress and the couple-stress. The constitutive equations for stress and couple-stress are formulated in a general way, and specialized to the case in which dependence on the fibre direction gradients is restricted to dependence on their directional derivatives in the fibre direction. This is further specialized to the case of plane strain, and finite pure bending of a thick plate is solved as an example. We also formulate and develop the linearized theory in which the stress and couple-stress are linear functions of the first and second spacial derivatives of the displacement. In this case for the symmetric part of the stress we recover the standard equations of transversely isotropic linear elasticity, with five elastic moduli, and find that, in the most general case, a further seven moduli are required to characterize the couple-stress.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/858e339598a40d56c98dcfa7edafa8650b9c0a6d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A Two-Dimensional Gradient-Elasticity Theory for Woven Fabrics (2015, result): “This is consistent with the model adopted by Spencer and Soldatos [18], who assumed, in the case of a single family of fibers, that the dependence of the strain energy on G occurs through g.”
Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching (2015, methodology): “[19], we forego such refinements for the sake of simplicity.”