In this work, aspects considering material modeling of electro-mechanical coupling in fiber reinforced electro-active polymers (EAP) and the corresponding finite element implementation are considered. We propose a constitutive model that takes into account the electro-viscoelastic behavior of the isotropic matrix and the influence of unidirectional fibers on both the hyperelastic response and the viscous behavior of the whole composite. Two distinct existing models that describe the electro-mechanical coupling, are demonstrated and implemented, moreover, a numerical link between both models for three-dimensional continua in terms of tensor calculus, is identified. We propose the extended-tube model for the elastic response with some of its parameters evolving in response to the electric field, in order to fit electro-viscoelastic experiments. Regarding the finite element implementation, in addition to the deformation field and the electric potential, two pairs of field variables are introduced on the element level, to enforce quasi-incompressibility and quasi-inextensibility. It is shown that using the mixed finite element improves the convergence behavior for the simulation of soft EAP with relatively stiff fibers. Moreover, the choice of the model that expresses the nature of the underlying coupling is shown to noticeably affect the degree of simulated actuation in fiber reinforced actuators.

The concept of merging pre-processed textile materials with tailored mechanical properties into soft matrices is so far rarely used in the field of soft robotics. The herein presented work takes the advantages of textile materials in elastomer matrices to another level by integrating a material with highly anisotropic bending properties. A pre-fabricated textile material consisting of oriented carbon fibers is used as a stiff component to precisely control the mechanical behavior of the robotic setup. The presented robotic concept uses a multi-layer stack for the robot’s body and dielectric elastomer actuators (DEAs) on both outer sides of it. The bending motion of the whole structure results from the combination of its mechanically adjusted properties and the force generation of the DEAs. We present an antagonistic switching setup for the DEAs that leads to deflections to both sides of the robot, following a biomimetic principle. To investigate the bending behavior of the robot, we show a simulation model utilizing electromechanical coupling to estimate the quasi-static deflection of the structure. Based on this model, a statement about the bending behavior of the structure in general is made, leading to an expected maximum deflection of 10 mm at the end of the fin for a static activation. Furthermore, we present an electromechanical network model to evaluate the frequency dependent behavior of the robot’s movement, predicting a resonance frequency of 6.385 Hz for the dynamic switching case. Both models in combination lead to a prediction about the acting behavior of the robot. These theoretical predictions are underpinned by dynamic performance measurements in air for different switching frequencies of the DEAs, leading to a maximum deflection of 9.3 mm located at the end of the actuators. The herein presented work places special focus on the mechanical resonance frequency of the robotic setup with regard to maximum deflections.

Dielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuation response with relatively large deformation capability. The properties of DEA make them suitable to be used in the form of major active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active material properties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneous DEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of the material’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling and numerical simulation, we propose a material model and a computational framework using the finite element method, which is capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description with the electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation. Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with only density-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is a suitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrate analytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and the extended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate several heterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volume fraction and ellipsoidal inclusions with varying aspect ratio.

Hyperelastic constitutive relations form the basis of advanced models for novel materials. Such elastic deformation potentials are the backbone for complex material formulations at elastic and inelastic deformations, especially when embedded into powerful frameworks like generalized standard materials, as well as multiphysical and multiscale formulations. With the focus on electroactive polymers, the article at hand demonstrates the derivation of a variational, rate-dependent electromechanical model for quasi-incompressible polymers and the derivation of an electromechanical model for regularized fracture mechanics by means of the phase-field method. Starting at the prominent Ogden and the extended tube model, some developments from the last decades are revisited and presented via the principle of virtual power, for instance, the established mixed element formulation, nonlinear viscoelasticity and electromechanical coupling. An electromechanically fully coupled representative crack element is used to derive a novel phase-field model for fracture. A key property of the proposed model is the ability to describe the electrical free-space behaviour inside the crack gap, which is demonstrated by adopting three common crack-face conditions. This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.

In this contribution, a computational thermo-electro-mechanical framework is considered, to simulate coupling between the mechanical, electrical and thermal fields, in nonhomogeneous electro-active materials. A thermo-electro-mechanical material model and a mixed Q1P0 finite element framework are described and used for the simulations. Finite element simulations of the response of heterogeneous structures consisting of a soft matrix and a stiff incluison are considered. The behavior of the composite material is studied for varying initial temperatures, different volume fractions and various aspect ratios of the inclusion. For some of the examples, the response of the structure beyond a limit point of electro-mechanical instability is traced. Regarding the soft matrix of the composite, thermal properties of silicone rubber at normal conditions have been obtained by molecular dynamics (MD) simulations. The material parameters obtained by MD simulations are used within the finite element simulations.