Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab

We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled shape of the slab at the onset of buckling. Our analysis is valid for dielectrics modeled by a general free energy function. We then present illustrative numerical calculations for ideal neo-Hookean dielectrics. In that case, we provide an explicit treatment of the boundary value problem of the finite bending and derive closed-form expressions for the stresses and electric field in the body. For the incremental deformations, we validate our analysis by recovering existing results in more specialized contexts. We show that the applied voltage has a destabilizing effect on the bending instability of the slab, while the effect of the axial load is more complex: when the voltage is applied, changing the axial loading will influence the true electric field in the body, and induce competitive effects between the circumferential instability due to the voltage and the axial instability due to the axial compression. We even find circumstances where both instabilities cohabit to create two-dimensional patterns on the inner face of the bent sector

Nonlinear response and axisymmetric wave propagation in functionally graded soft electro-active tubes

Soft electro-active (SEA) materials can be designed and manufactured with gradients in their material properties, to modify and potentially improve their mechanical response in service. Here, we investigate the nonlinear response of, and axisymmetric wave propagation in a soft circular tube made of a functionally graded SEA material and subject to several biasing fields, including axial pre-stretch, internal/external pressure, and through-thickness electric voltage. We take the energy density function of the material to be of the Mooney-Rivlin ideal dielectric type, with material parameters changing linearly along the radial direction. We employ the general theory of nonlinear electro-elasticity to obtain explicitly the nonlinear response of the tube to the applied fields. To study wave propagation under inhomogeneous biasing fields, we formulate the incremental equations of motion within the state-space formalism. We adopt the approximate laminate technique to derive the analytical dispersion relations for the small-amplitude torsional and longitudinal waves superimposed on a finitely deformed state. Comprehensive numerical results then illustrate that the material gradients and biasing fields have significant influences on the static nonlinear response and on the axisymmetric wave propagation in the tube. This study lays the groundwork for designing SEA actuators with improved performance, for tailoring tunable SEA waveguides, and for characterizing non-destructively functionally graded tubular structures

Tunable morphing of electroactive dielectric-elastomer balloons

Designing smart devices with tunable shapes has important applications in industrial manufacture. In this paper, we investigate the nonlinear deformation and the morphological transitions between buckling, necking, and snap-through instabilities of layered DE balloons in response to an applied radial voltage and an inner pressure. We propose a general mathematical theory of nonlinear electro-elasticity able to account for finite inhomogeneous strains provoked by the electro-mechanical coupling. We investigate the onsets of morphological transitions of the spherically symmetric balloons using the surface impedance matrix method. Moreover, we study the nonlinear evolution of the bifurcated branches through finite element numerical simulations. Our analysis demonstrates the possibility to design tunable DE spheres, where the onset of buckling and necking can be controlled by geometrical and mechanical properties of the passive elastic layers. Relevant applications include soft robotics and mechanical actuators

Causality-based Dual-Contrastive Learning Framework for Domain Generalization

Domain Generalization (DG) is essentially a sub-branch of out-of-distribution generalization, which trains models from multiple source domains and generalizes to unseen target domains. Recently, some domain generalization algorithms have emerged, but most of them were designed with non-transferable complex architecture. Additionally, contrastive learning has become a promising solution for simplicity and efficiency in DG. However, existing contrastive learning neglected domain shifts that caused severe model confusions. In this paper, we propose a Dual-Contrastive Learning (DCL) module on feature and prototype contrast. Moreover, we design a novel Causal Fusion Attention (CFA) module to fuse diverse views of a single image to attain prototype. Furthermore, we introduce a Similarity-based Hard-pair Mining (SHM) strategy to leverage information on diversity shift. Extensive experiments show that our method outperforms state-of-the-art algorithms on three DG datasets. The proposed algorithm can also serve as a plug-and-play module without usage of domain labels

Pattern evolution in bending dielectric-elastomeric bilayers

We propose theoretical and numerical analyses of smart bending deformation of a dielectric-elastic bilayer in response to a voltage, based on the nonlinear theory of electro-elasticity and the associated linearized incremental field theory. We reveal that the mechanism allowing the bending angle of the bilayer can be tuned by adjusting the applied voltage. Furthermore, we investigate how much can the bilayer be bent before it loses its stability by buckling when one of its faces is under too much compression. We find that the physical properties of the two layers must be selected to be of the same order of magnitude to obtain a consequent bending without encountering buckling. If required, the wrinkles can be designed to appear on either the inner or the outer bent surface of the buckled bilayer. We validate the results through comparison with those of the classical elastic problem