The Poynting effect in elastomeric bars undergoing chemo-mechanical evolution

This work considers a rubber cylinder under zero axial force that elongates in response to the normal stresses produced during torsion (the Poynting effect). The combined elongation and twisting deformation occurs at an elevated temperature at which the rubber undergoes time-dependent scission and re-crosslinking of its macromolecular network junctions. A constitutive theory accounting for this microstructural change is used in an analytical and numerical study of the interaction of the deformation and the scission or re-crosslinking process. Examples show the time-dependence of elongation for several twist histories.

Experimental study of the Poynting effect in a soft unidirectional fiber-reinforced material under simple shear

Shear and normal responses of a soft unidirectional fiber-reinforced material subjected to simple shear.

Dimensional changes during shear without normal tractions (the Poynting effect) in nonlinear viscoelastic fiber-reinforced solids

When a rectangular block of a nonlinear material is subjected to a simple shearing deformation, specific normal tractions are required to ensure that the distances between the faces of the block, i.e. its dimensions, do not change. This work investigates the time-dependent dimensional changes during shear in the absence of these normal tractions (the Poynting effect) that occur in a block composed of an incompressible nonlinearly viscoelastic fiber-reinforced solid. The material is modeled using the Pipkin–Rogers nonlinear single integral constitutive equation for viscoelasticity. This constitutive equation is used because (1) it exhibits the essential features of nonlinear viscoelasticity; (2) it is straightforward to include the material symmetry restrictions due to the reinforcing fibers. A system of nonlinear Volterra integral equations is formulated for the dimensional changes in the block. Numerical solutions are presented for the case when the standard reinforcing model for nonlinearly elastic fiber-reinforced materials is incorporated in the Pipkin–Rogers constitutive framework. The results illustrate how the time-dependent dimensional changes depend on the fiber orientation and the viscoelastic properties of the fibers relative to those of the matrix.

A minimal-length approach unifies rigidity in underconstrained materials

We present an approach to understand geometric-incompatibility–induced rigidity in underconstrained materials, including subisostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal lengthℓ¯min, determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise magnitudes for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of 3. We propose that this factor of 3 is a general hallmark of geometrically induced rigidity in underconstrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Finally, our results may lay important foundations for ways to estimateℓ¯minfrom measurements of local geometric structure and thus help develop methods to characterize large-scale mechanical properties from imaging data.

Poynting effect of brain matter in torsion

We investigate experimentally and model theoretically the mechanical behaviour of brain matter in torsion.