A solid shell finite element formulation to simulate the behaviour of thin dielectric elastomer structures

This paper is concerned with a solid shell finite element formulation to simulate the behavior of thin dielectric elastomer structures. Dielectric elastomers belong to the group of electroactive polymers. Due to efficient electromechanical coupling and the huge actuation strain, they are very interesting for actuator applications. The coupling effect in the material is mainly caused by polarization. In the present work, a simple constitutive relation, which is based on an elastic model involving one additional material constant to describe the polarization state, is incorporated in a solid shell formulation. It is based on a mixed variational principle of Hu-Washizu type. Thus, for quasi-stationary fields, the balance of linear momentum and Gauss' law are fulfilled in a weak sense. As independent fields, the displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements are employed. The element has eight nodes with four nodal degrees of freedom, three mechanical displacements, and the electric potential. The surface oriented shell element models the bottom and the top surfaces of a thin structure. This allows for a simple modeling of layered structures by stacking the elements through the thickness. Some examples are presented to demonstrate the ability of the proposed formulation.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

This study is focusing on the finite element simulation of low velocity impact applied to glass fiber-reinforced composites. Elasto-visco-plasticity is adopted taking into account strain rate effect, with isotropic hardening. To avoid numerical locking, hexahedral solid shell finite element SS is developed. The formulation is based on the mixed Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods. A geometrical non linear condition is applied. The finite element is implemented in UEL subroutine via the commercial software ABAQUS/Standard. The numerical element proved its efficiency comparing to conventional element and previous experimental results in (Mars et al. 2018). Numerical simulations with solid element are conducted using Abaqus/standard via user material UMAT subroutine. In terms of computation time, the solid shell element is less time consuming when comparing to conventional solid element. This is due to the fact that a single element through the thickness direction is adopted. Element efficiency is assessed for various fibers contents.

A scaled thickness conditioning for solid- and solid-shell discretizations of thin-walled structures

This article focuses on the buckling response of columns formed by pre-twisting a flat, narrow and straight material strip of a rectangular cross section. The experimental analysis accomplished for birch plywood strips covers twisting up to 90 degrees. The corresponding computational analysis covers the twisting process (geometrically nonlinear analysis) and the subsequent compression (linear buckling analysis, including the residual stresses from the twisting process) and includes comparisons for 3D solid and 2D shell finite elements within orthotropic linear elasticity. A further finite element analysis provides findings up to twisting angles of 400 degrees and includes nonlinear post-buckling analyses for the compression subsequent to twisting, in addition to the linear buckling analyses. These sets of analyses reveal some new findings regarding this classical problem. Most importantly, there are four characteristic twisting angles which are associated to mode jumps in buckling, to a plateau in the curve relating the critical load and the twisting angle and, finally, to a loss of stability during the twisting process. The influence of the twisting-induced stresses on the buckling response is investigated as well.

Dielectric elastomer actuators are ideal drivers for next-generation soft robots due to their large electroactive deformations. However, conventional dielectric elastomers suffer from insufficient breakdown strength and high mechanical loss, which limits their ability to meet the demanding requirements of advanced robotics for high energy and power densities. Herein, we propose a versatile strategy for incorporating organic molecular semiconductors into the dielectric elastomer network. This design simultaneously achieves high breakdown strength (82 V μm-1), desirable modulus, elasticity, and large electro-actuation strain (174%). Consequently, the optimized elastomer delivers a high energy density (169 J kg-1) and an ultrahigh power density (3000 W kg-1), surpassing natural muscle by 8-fold and outperforming all reported dielectric elastomers. A demonstrated light-emitting, fast-moving soft robot further highlights the material's multifunctional application potential.

Dielectric elastomer membranes are one of the most promising transducers for developing soft large strain sensors. In this article, we describe the sensor response for a potential biomedical application. It is widely accepted that diseased arteries at various stages have a unique constitutive response. This means that ideally the output of an in situ artery sensor would have distinct profiles corresponding to various stages of unhealthiness. An in situ sensor can potentially allow access to information about the mechanical state of the artery that is not currently available. Furthermore, the potential to combine the functions of providing structural support (stent) and monitoring the mechanical state (sensor) is appealing. Traditional sensors such as strain gages and piezoelectric sensors are stiff and fail at low strains (<1%), whereas some dielectric elastomers are viable at strains up to and even surpassing 100%. Investigating the electromechanical response of a deformable tube sensor sandwiched between a pulsating pressure source and a nonlinear elastic distensible thick wall has not been attempted before now. The successful development of a multiphysics model that correlates the electrical output of a pulsatile membrane sensor to its state of strain would be a significant breakthrough in medical diagnostics. The artery is described using a structural model for a tubular membrane reinforced with two families of initially crimped fibers subjected to a pulsating pressure profile. In this article, the fundamental mechanics associated with electromechanical coupling during dynamic finite deformations of dielectric elastomers is derived. A continuum model for the dynamic response of tubular dielectric elastomer membranes configured for sensing is presented. The pressure profile leads to a nonlinear response of the artery sensor due to the nonlinear deformation behavior of the arterial wall. At pressures above 13 kPa, the artery undergoes infinitesimal deformation, which leads to very small changes in the sensor signal. In this range, fabricating thinner sensors and synthesizing hybrid polymers with higher dielectric constants can enhance the sensitivity.

The principle of robot based incremental sheet metal forming is based on flexible shaping by means of a freely programmable path-synchronous movement of two tools, which are operated by two industrial robots. The final shape is produced by the incremental infeed of the forming tool in depth direction and its movement along the geometry’s contour in lateral direction. The main problem during the forming process is the influence on the dimensional accuracy resulting from the compliance of the involved machine structures and the springback effects of the workpiece. The project aims to predict these deviations caused by resiliences and to carry out a compensative path planning based on this prediction. Therefore a planning tool is implemented which compensates the robot’s compliance and the springback effects of the sheet metal. Finite element analysis using a material model developed at the Institute of Applied Mechanics (IFAM) [1] has been used for the simulation of the forming process. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamical setting. It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening which is widely adopted as capable of representing the above metal hardening effects. The major problem of low-order finite elements used to simulate thin sheet structures, such as used for the experiments, is locking, a non-physical stiffening effect. Recent research focuses on the large deformation version of a new eight-node solid-shell finite element based on reduced integration with hourglass stabilization. In the solid-shell formulation developed at IFAM ([2], [3]) the enhanced assumed strain (EAS) concept as well as the assumed natural strain (ANS) concept are implemented to circumvent locking. These tools are very important to obtain a good correlation between experiment and simulation.

Dielectric Elastomers (DE) are incompressible dielectrics which can experience deviatoric (isochoric) finite deformations in response to applied large electric fields. Thanks to the strong electro-mechanical coupling, DE intrinsically offer great potentialities for conceiving novel solid-state mechatronic devices, in particular linear actuators, which are more integrated, lightweight, economic, silent, resilient and disposable than equivalent devices based on traditional technologies. Such systems may have a huge impact in applications where the traditional technology does not allow coping with the limits of weight or encumbrance, and with problems involving interaction with humans or unknown environments. Fields such as medicine, domotic, entertainment, aerospace and transportation may profit. For actuation usage, DE are typically shaped in thin films coated with compliant electrodes on both sides and piled one on the other to form a multilayered DE. DE-based Linear Actuators (DELA) are entirely constituted by polymeric materials and their overall performance is highly influenced by several interacting factors; firstly by the electromechanical properties of the film, secondly by the mechanical properties and geometry of the polymeric frame designed to support the film, and finally by the driving circuits and activation strategies. In the last decade, much effort has been focused in the devolvement of analytical and numerical models that could explain and predict the hyperelastic behavior of different types of DE materials. Nevertheless, at present, the use of DELA is limited. The main reasons are 1) the lack of quantitative and qualitative models of the actuator as a whole system 2) the lack of a simple and reliable design methodology. In this thesis, a new point of view in the study of DELA is presented which takes into account the interaction between the DE film and the film supporting frame. Hyperelastic models of the DE film are reported which are capable of modeling the DE and the compliant electrodes. The supporting frames are analyzed and designed as compliant mechanisms using pseudo-rigid body models and subsequent finite element analysis. A new design methodology is reported which optimize the actuator performances allowing to specifically choose its inherent stiffness. As a particular case, the methodology focuses on the design of constant force actuators. This class of actuators are an example of how the force control could be highly simplified. Three new DE actuator concepts are proposed which highlight the goodness of the proposed method.

In this paper, the connection stiffness between a thin-walled Z-beam and a sandwich panel is investigated by means of laboratory experiment, analytical approach, and numerical simulation. The scheme of the conducted experiment refers to a double lap shear test. The two thicknesses of the sandwich panel (100 mm and 60 mm) and two groups of fasteners (four and three) were investigated. The laboratory tests allowed for the determination of the failure mechanisms and the prediction of the reliability of the restraint of the thin-walled beam, provided by sandwich panels. The assumed finite element model created in Abaqus/CAE consisted of solid finite elements (core layer of the sandwich panel, roller support) and shell finite elements (thin-walled beam, facings of the sandwich panel). The fasteners were modeled implicitly, i.e. using spring connectors. The stiffness of the spring connector was determined on the basis of the derived analytical expression and the laboratory test results. The kinematical response of the adopted finite element model was in agreement with the laboratory results. Such a model can be used to verify more complex finite element models with explicitly introduced fasteners.

Actuation devices made of dielectric elastomers are prone to compression induced wrinkling instabilities, which can adversely affect their performance and may lead to device failure. On the other hand, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. The idea of taut states and the natural width under simple tension plays an important role in the analysis of compression generated instability (wrinkling). In case of electrically driven DE membranes, the domain of taut states in the plane of principal stretches is influenced substantially by the applied voltage and the film's constitutive properties. In the recent past, there has been an increasing interest in exploiting anisotropy in the material behavior of dielectric elastomers for improving their actuation performance. Spurred with these ongoing efforts, this paper presents a continuum mechanics based electromechanical model for predicting the thresholds on the domain of taut states of transversely isotropic planar dielectric elastomers. The developed analytical framework uses an amended energy function that accounts for the electromechanical coupling for a class of incompressible transversely isotropic dielectric membranes. The required expressions for the total Cauchy stress tensor and the associated principal stress components are evaluated utilizing the amended energy function. Finally, the concept of natural width under simple tension is implemented to obtained the nonlinear coupled electromechanical equation that evaluates the associated taut states domain of the transversely isotropic planar dielectric elastomers. Our results indicate that the extent of taut domain can be controlled by modifying the level and the principal direction of the transverse isotropy. The taut states domain for a particular level of applied electric field increases with increase in the anisotropy parameter, while the taut domains depleted with the increase in fiber orientations from 00to 900for an applied level of electrical loading. The fiber-reinforced wrinkle-tunable surfaces can be effectively designed and developed using the underlying analytical framework and the trends obtained in this study.

In this article, we present a nonlinear theory for thin plates, which are made of incompressible electroded dielectric elastomer layers. The layers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of the electrostatic forces is taken into account by means of the electrostatic stress tensor. A plane state of stress is imposed on the total stress tensor, based on which two-dimensional constitutive relations for the plate are derived. A geometrically nonlinear formulation for the plate as a material surface is devloped, and solutions are computed using nonlinear finite elements. The numerical results are compared to available results from the literature verifying our approach, and an additional nonsymmetric example problem is studied with respect to stability.

Combination of Hexahedral and Prismatic Solid-shell Finite Elements

Dielectric oil coated single-walled carbon nanotube electrodes for stable, large-strain actuation with dielectric elastomers

A number of engineering applications involve contact with bodies modeled using specialized theories of solid mechanics like beams or shells. While computational models for contact in 2D and 3D solid mechanics have been extensively developed in the literature, problems involving contact with beams or shells have received less attention. When modeling contact between a solid body represented with beam or shell theory and a domain discretized with solid finite elements, the contact model faces the typical challenges of enforcing geometric compatibility and the transfer of a complete pressure field along the contact interface, with the added complications stemming from the different underlying mathematical formulations and finite element discretizations in the connecting domains. Resultant-based beam and shell theories do not provide direct estimates of surface tractions, therefore rendering the issue of pressure transfer on beam–solid and shell–solid interfaces more problematic. In the absence of specialized contact formulations for solid–beam and solid–shell interfaces, contact models have relied almost exclusively on the Node-To-Surface (NTS) geometric compatibility approach. This formulation suffers from well-known drawbacks, including instability, surface locking and incomplete pressure fields on the interface. The NTS approach, however, remains the method most readily applicable to contact with beam or shell elements among the vast variety of available methods for computational contact modeling using finite elements. The goal of this paper is to bridge the gap in the literature on coupling domains with beam and solid finite element discretizations. We propose an interface formulation for beam–solid interfaces that ensures the transfer of a complete pressure field while enforcing geometric compatibility using standard NTS constraints. The formulation uses a stabilization approach, based on a special form of the Discontinuous Galerkin method, to enforce weak continuity between the stress fields on the solid side of the interface, and the moment and shear resultants in the contacting beam. We show that the proposed formulation is a robust approach for satisfying compatibility constraints while ensuring the transfer of a complete pressure field on beam–solid finite element interfaces that can be used with bilinear and quadratic interpolations in the solid, and Euler or Timoshenko formulations for the beam.