Yangkun Du

Fracture and instability may occur separately or concurrently, severely impairing the reliability of flexible electroactive devices. Based on the nonlinear theory of electroelasticity and incremental field theory, this work establishes general solutions to the governing equations for a soft electroelastic body subjected to particular yet common biasing fields. We use potential theory method to obtain and validate explicit analytical solutions of the resulting integrodifferential equations for both crack and anti-crack problems under various elementary loading conditions. We examine two types of surface instabilities in pre-deformed cracked electroactive bodies for perturbations in the x-z and ρ-z planes. To quantitatively describe the fracture and stability behavior, we further introduce incremental intensity factors and incremental energy release rates to assess crack propagation, together with a buckling topological number to classify crack-face buckling and persistent stability. The derived bifurcation equations further reveal re-entrant phenomena as pre-stretch and initial electrical displacement vary. Overall, the proposed framework provides unified, quantitative analysis for electromechanically coupled fracture and instability in soft electroelastic materials.

Soft materials exhibit significant nonlinear geometric deformations and stress-strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau's and Murnaghan's formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in powers of epsilon, where epsilon is defined as the square root of the inner product of H with itself, epsilon = sqrt(H * H), and epsilon is between 0 and 1. Here, H represents the perturbation to the deformation gradient tensor, where the deformation gradient F is given by F = I + H. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.

Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [ ], where [ ] and [ ], and [ ] is the perturbation to the deformation gradient tensor [ ]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).