Abstract
Accurate RF simulations of fusion systems like ITER require the definition of high-fidelity analysis geometries that include detailed antenna, reactor wall, and physics regions. This paper will describe a workflow for the execution of adaptive high-performance simulations of RF fusion systems. In this workflow, the simulation input consists of a CAD model attributed with the needed analysis attributes. The analysis mesh is automatically generated and the analysis steps are executed using the time-harmonic Maxwell's equations solved using high-order Nedelec finite elements. A patch recovery-based error estimator is used to drive a conforming mesh adaptation procedure. More ...

Abstract
This paper is concerned with the development of finite-strain constitutive models for electro-active composites consisting of initially aligned, rigid dielectric fibers of elliptical cross-section that are distributed randomly in a dielectric elastomer matrix. For this purpose, we make use of a variational approach that partially decouples the mechanical and electrostatic contributions to the overall energy and leads to a minimum principle for the average orientation of the fibers. The resulting macroscopic electroelastic constitutive model accounts for electric and mechanical torques on the fibers, as well as for the microstructure and its evolution under finite deformations. In particular, the model characterizes the rotation of the fibers for general externally applied electromechanical loadings, predicting bifurcation instabilities for the special case of aligned loadings. To elucidate the main features of the model, we consider the application to a dielectric elastomer composite actuator and investigate the effects of fiber aspect ratio and initial fiber orientation on its macroscopic response. In addition, the new results are compared with the predictions of an earlier model approximating the fiber rotations by purely mechanical effects. More ...

Abstract
This chapter is concerned with a homogenization framework for electroelastic composite materials at finite strains. The framework is used to develop constitutive models for dielectric elastomer composites consisting of initially aligned, rigid dielectric inclusions that are distributed randomly in a dielectric elastomeric matrix. A strategy is proposed to partially decouple the mechanical and electrostatic effects in the composite by writing the effective electroelastic energy of the composite in terms of a purely mechanical energy term together with a purely electrostatic energy term that are linked only by the unknown particle rotations. In addition to the macroscopic constitutive relation for the composite, estimates are also generated for the evolution of the average particle orientation as a function of the applied mechanical and electric fields. The resulting estimates account for the electric torques and dipolar forces on the particles that are generated as a consequence of externally applied electric fields. More ...

Abstract
Accurate RF simulations of fusion systems like ITER require the definition of high-fidelity analysis geometries that include detailed antenna, reactor wall and physics region representations. This poster will describe a workflow for the execution of adaptive high-performance FR fusion system simulations. The steps in the simulation workflow include; defeaturing of un-needed details from antenna CAD models; combining the antenna, reactor wall and physics components into a single analysis model geometry; applying physical attributes to the analysis model; automatically generating a graded mesh; and executing an adaptive finite element analysis that includes the application of a iterations of finite element solve, a posteriori error estimation, and mesh enrichment. More ...

Abstract
This paper is concerned with the generation of homogenization estimates for electroelastic composites consisting of initially aligned, rigid dielectric fibers that are distributed with random positions in a dielectric elastomeric matrix. For this purpose, use is made of a certain “partial decoupling strategy” resulting in the splitting of the macroscopic energy of the composite into a purely mechanical and a purely electrostatic component—coupled only by the average rotation of the fibers. In addition to the macroscopic electro-mechanical constitutive response for the composite, the procedure delivers estimates for the average fiber rotation as a consequence of the combined action of the mechanical stresses and electrical torques under general in-plane loading conditions. It is found that when large compressive stresses are applied along the long axes of the fibers, the composite may undergo a “macroscopic” (i.e., material) instability that is captured by loss of ellipticity of the overall incremental response and corresponds to spontaneous rotation of the fibers to relieve the large stresses. Moreover, when the electric field is aligned with the long axes of the fibers, it tends to stabilize the response, while when it is transverse to them, it tends to destabilize the response. Earlier estimates obtained by means of a simplifying “partial decoupling approximation” are compared with the new, more robust estimates and found to become less accurate with increasing electric field magnitudes. More ...

Abstract
Particle-reinforced rubbers are composite materials consisting of randomly distributed, stiff fibers/particles in a soft elastomeric material. Since the particles are stiff compared to the embedding rubber, their deformation can be ignored for all practical purposes. However, due to the softness of the rubber, they can undergo rigid body translations and rotations. Constitutive models accounting for the effect of such particle motions on the macroscopic response under prescribed deformations on the boundary have been developed recently. But, in some applications (e.g., magneto-active elastomers), the particles may experience additional torques as a consequence of an externally applied (magnetic) field, which, in turn, can affect the overall rotation of the particles in the rubber, and therefore also the macroscopic response of the composite. This paper is concerned with the development of constitutive models for particle-reinforced elastomers, which are designed to account for externally applied torques on the internally distributed particles, in addition to the externally applied deformation on the boundary of the composite. For this purpose, we propose a new variational framework involving suitably prescribed eigenstresses on the particles. For simplicity, the framework is applied to an elastomer reinforced by aligned, rigid, cylindrical fibers of elliptical cross section, which can undergo finite rotations in the context of a finite-deformation, plane strain problem for the composite. In particular, expressions are derived for the average in-plane rotation of the fibers as a function of the torques that are applied on them, both under vanishing and prescribed strain on the boundary. The results of this work will make possible the development of improved constitutive models for magneto-active elastomers, and other types of smart composite materials that are susceptible to externally applied torques. More ...

Abstract
In this work we investigate the possible development of instabilities in a certain class of dielectric elastomer composites (DECs) subjected to all-around dead electromechanical loading. The DECs consist of a dielectric elastomer matrix phase constrained to plane strain deformations by means of aligned, long, rigid-dielectric fibers of elliptical cross section that are also aligned but randomly distributed in the transverse plane. Two types of ``material'' instabilities are considered: loss of positive definiteness (LPD), and loss of strong ellipticity (LE). Loss of positive definiteness simply corresponds to the loss of local convexity of the homogenized electro-elastic stored-energy function for the DECs and can be of two types depending on the resulting instability modes. When the modes are aligned with the ``principal'' solution, the instability corresponds to a maximum in the nominal electric field, possibly followed by snapping behavior. Alternatively, when the modes are orthogonal to the principal solution, the instability corresponds to a bifurcation from the principal solution. The loss of strong ellipticity, on the other hand, corresponds to loss of positive definiteness of the electromechanical acoustic tensor and manifests itself by the onset of highly localized shear band instabilities. Our results show that the stability, as well as the type of instability (when stability is lost), of the DECs depend sensitively on the loading conditions and are also affected by the microstructure of the DECs (i.e., the volume fraction of the fibers and their aspect ratio). In particular, it is found that the non-aligned LPD instabilities typically precede aligned LPD and LE instabilities, especially for in-plane isotropic microstructures, but aligned (limit load) LPD and LE instabilities are also possible for composites with anisotropic microstructures. In this context, it should be noted that the possible development of non-aligned LPD bifurcation instabilities appears to have been ignored by prior works. Fortunately, however, such instabilities can usually be avoided by orienting the long (in-plane) axis of the fibers parallel to the tensile stress direction and orthogonal to the applied electric field. More ...

Abstract
This paper presents homogenization estimates for the finite-strain effective response of a certain class of dielectric elastomer composites (DECs) subjected to electromechanical loading conditions. The DECs consist of a dielectric elastomer matrix phase constrained to undergo plane strain deformations by means of aligned, long, rigid-dielectric fibers of elliptical cross section that are also aligned but randomly distributed in the transverse plane. The estimates for the effective electro-active response are obtained by means of available estimates for the purely mechanical response of such composites, together with a partial decoupling strategy/approximation. Such homogenization estimates can then be used to assess the effect of various microstructural parameters, such as the concentration and cross-sectional shape of the fibers, on the overall electromechanical response of the DECs, when subjected to an electric potential difference across suitably positioned soft electrodes. In addition, three different instability and failure mechanisms are investigated: loss of positive definiteness, loss of strong ellipticity and dielectric breakdown, with the objective of finding an optimal design of the microstructure and constituent properties for maximal electrostriction before failure. More ...

Abstract
We provide estimates for the effective response of Electro-Active Polymer Composites (EAPCs) consisting of aligned ellipsoidal inclusions of a stiff dielectric material which are distributed randomly in an soft elastomeric matrix with “ellipsoidal” two-point statistics. The derivation of the results for the electro-mechanical response assumes linearized deformations, but includes non-linear (quadratic) terms in the electric fields. We investigate three different physical mechanisms contributing to the macroscopic electro-mechanical response of the composite: the intrinsic effect of the particles on the Maxwell stress, the inter-particle (dipole) interactions which are accounted for by evaluating the effect of changes in the “shape” of the two-point probability functions with the deformation, and the effect of particle rotations and torques when the geometric and/or anisotropy axis of the particles are not aligned with the applied electric field. Several illustrative examples are provided to emphasize the relative importance of the different effects on the overall electrostriction of the composites. In particular, for the “compliant electrode” boundary conditions that are widely used in applications, it is shown that inter-particle interactions are synergistic with the intrinsic effect of the particles on the Maxwell stress, leading to significant enhancements in the electro-mechanical coupling of the EAPCs, especially at high particle concentrations. On the other hand, the effect of electric torques on non-aligned particles is generally deleterious for electrostriction. More ...

Abstract
This article deals with the problem of an isolated, rigid inclusion with linear-magnetic behavior embedded in a linear-elastic matrix. Under the hypothesis of infinitesimal deformations, an analytical expression is obtained for the equilibrium rotation of the magnetic inclusion under general magneto-mechanical loading conditions. The results show that the inclusion undergoes an ‘extra’ rotation due to the presence of non-aligned magnetic fields (even in the absence of mechanical loadings). Moreover, this extra rotation is found to depend on the shape of the inclusion, as well as on its magnetic anisotropy. Thus, the extra rotation increases monotonically to an asymptote with increasing magnetic anisotropy of the inclusion, while, for fixed magnetic behavior of the inclusion, the extra rotation increases up to a maximum with increasing aspect ratio, and then decays to zero. More ...

Abstract
This paper presents a homogenization framework for electro-elastic composite materials at finite strains. The framework is used to develop constitutive models for electro-active composites consisting of initially aligned, rigid dielectric particles distributed periodically in a dielectric elastomeric matrix. For this purpose, a novel strategy is proposed to partially decouple the mechanical and electrostatic effects in the composite. Thus, the effective electro-elastic energy of the composite is written in terms of a purely mechanical component together with a purely electrostatic component, this last one dependent on the macroscopic deformation via appropriate kinematic variables, such as the particle displacements and rotations, and the change in size and shape of the appropriate unit cell. The results show that the macroscopic stress includes contributions due to the changes in the effective dielectric permittivity of the composite with the deformation. For the special case of a periodic distribution of electrically isotropic, spherical particles, the extra stresses are due to changes with the deformation in the unit cell shape and size, and are of order volume fraction squared, while the corresponding extra stresses for the case of aligned, ellipsoidal particles can be of order volume fraction, when changes are induced by the deformation in the orientation of the particles. More ...