Entire Deformation Range Research Articles

Hot Working of an Fe-25Al-1.5Ta Alloy Produced by Laser Powder Bed Fusion

In the present work, hot working was used as a post-processing method for Fe-25Al-1.5Ta (at.%) alloy built using laser powder bed fusion (LPBF) to refine the undesirable columnar microstructure with heterogeneous grain sizes and strong textures in the build direction. The hot deformation behavior and workability were investigated using constitutive modeling and the concept of processing maps. Uniaxial compression tests were conducted up to a true strain of 0.8 at 900 °C, 1000 °C, and 1100 °C with strain rates of 0.0013 s−1, 0.01 s−1, and 0.1 s−1. The constitutive equations were derived to describe the flow stress–strain behavior in relation to the Zener–Hollomon parameter. Processing maps based on a dynamic materials model were plotted to evaluate the hot workability and to determine the optimal processing window as well as the active deformation mechanisms. The microstructure of the deformed specimens was characterized by scanning electron microscopy equipped with an electron backscatter diffraction detector. The results indicated a high degree of hot workability of the LPBF builds without flow instabilities over the entire deformation range tested. The epitaxially elongated grains of the as-built alloys were significantly refined after deformation through dynamic softening processes, and the porosity was reduced due to compressive deformation. The current study revealed a well-suited parameter range of 1000–1080 °C/0.004–0.012 s−1 for the safe and efficient deformation of the LPBF-fabricated Fe-25Al-1.5Ta alloys. The effectiveness of the process combination of LPBF with subsequent hot forming could be verified with regard to microstructure refinement and porosity reduction.

Hot Workability Investigation of an Fe-Al-Ta Alloy Using Deformation Processing Maps

Fe-Al-Ta alloys are expected to replace high-alloyed steels in steam turbine blades. However, the mechanical properties of the forged blades are still not optimal due to limited grain refinement during hot forging and the coarse-grained microstructure inherited from the as-cast precursor. It is, therefore, essential to investigate the hot deformation behavior of the alloy to identify the optimum range for the deformation parameters leading to good hot workability with significant grain refinement. The hot deformation behavior and hot workability of an Fe-25Al-1.5Ta (at.%) alloy were investigated in the present work using constitutive modeling and the concept of processing maps. Uniaxial compression tests were conducted in a strain rate range from 0.0013 s−1 to 1 s−1 and in a temperature range from 900 °C to 1100 °C, where a disordered A2 α-(Fe, Al) matrix phase along with a C14-(Fe, Al)2Ta Laves phase were confirmed by X-ray diffraction. The flow stress–strain curves showed a broad maximum followed by a slight drop in stress until a steady state was reached. The optimum processing window for the studied alloy was located at 910–1060 °C/0.0013–0.005 s−1, where the efficiency of the power dissipation (η) and strain rate sensitivity (m) reached 50% and 0.33, respectively. The material underwent a combination of dynamic recovery and dynamic recrystallization over the whole tested deformation range. No flow instabilities were predicted based on Prasad’s flow instability criterion when deformation was performed up to a true strain of 0.5 and 0.8, indicating a high degree of hot workability of the studied alloy over the entire deformation range tested. The current study reveals a well-suited parameter range for the safe and efficient deformation of Fe-Al-Ta alloys, which may contribute to the optimization of the thermomechanical processing of this alloy.

Variant of the deformation diagram of concrete under uniaxial and volumetric stress state

Variants of diagrams for the description of the stress-strain state of concrete under uniaxial and volumetric stress state at different levels and stages of deformation have been considered. A variant of nonlinear analytical dependence between stresses and relative deformations of concrete under uniaxial stressed state described by one continuous polynomial function over the entire range of deformation, including the description of the range of limiting deformations on the descending branch of the diagram, is proposed. The obtained dependence has a number of advantages for the calculation of reinforced concrete structures compared to other known variants of diagrams. The use of this dependence as the initial characteristics of concrete properties in the defining relations to describe the volumetric stress state of concrete more fully corresponds to the physical meaning of the law of deformation of concrete, has sufficient accuracy and can be recommended for practical use in the design of reinforced concrete structures.

A phenomenological constitutive model for predicting both the moderate and large deformation behavior of elastomeric materials

Constitutive models that describe nonlinear elastic mechanical behavior are indispensable in the design of engineering components fabricated of elastomeric materials. The main drawbacks of the existing models include complexities in calibrating the model to experimental data and erroneous descriptions of multi-axial response. These challenges motivate researchers to continually formulate new or improved models with better predictive capabilities. In this work, we propose a new polynomial-type phenomenological model with linear and logarithmic dependence on the first and the second invariants respectively. Model parameters were obtained by utilizing the Levenberg-Marquardt algorithm to fit the model expression to the strain energy density data calculated from the experimental data of uniaxial tension loading. The predictive performance of our proposed model in comparison to that of three popular existing models was determined by utilizing three sets of classical experimental data from the literature with varying deformation ranges. Quantities used to relate the predicted and the experimental data include the coefficient of determination, relative errors, and average relative error (for overall behavior). The computations demonstrated that the proposed model exhibits superior predictive capabilities for the entire deformation range whilst requiring minimum efforts in obtaining its parameters, thus, exhibits the desirable features of a phenomenological hyperelastic model.

Development of a Rheological Model of Hot Deformation as Exemplified by 1424 and В-1461 Aluminum Lithium Alloys

A variant of a rheological model of hot deformation is proposed: the law of hyperbolic sine, which, as opposed to standard law, accounts not only for the rate of deformation and temperature of the process, but also the degree of deformation. The material constants in the law of hyperbolic sine are substituted with polynomial functions of the degree of deformation; its coefficients are calculated using a specially developed procedure. The proposed rheological model has been applied for aluminum lithium alloys of lower density, grade 1424, Al–Mg–Li–Zn system, and grade V-1461, system Al–Cu–Li–Zn, for which, using physical simulation at the Gleeble-3800 facility, the flow curves were determined in the temperature range of 400–480°C and the rates of deformation of 1–60 s–1 to the degree of deformation of 0.6. In addition, the influence of the initial state of the material is studied: samples are taken both from the ingot and from hot rolled plates. The constants of the rheological model of hot deformation, including the Zener–Hollomon parameter and the law of hyperbolic sine for the overall range of stresses and deformations, are determined. After approximating the parameters of this model as a function of real deformations using the polynomial law of the 4th order, the rheological model was developed describing the behavior of an alloy in the considered range of temperatures and rates. The parameters of the law of hyperbolic sine are determined as a function of degree of deformation. It is demonstrated that the parameters for a cast material are higher than for a rolled material. A comparison of the standard model with the proposed one demonstrated that the use of a standard model gives overestimated flow stresses in the entire deformation range (up to 12%).

A new energy–momentum time integration scheme for non-linear thermo-mechanics

The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola–Kirchoff stress tensor and the entropy (or the absolute temperature). The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature-based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as the thermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable).

Hinged-3D metamaterials with giant and strain-independent Poisson\u2019s ratios

Current designs of artificial metamaterials with giant Poisson’s ratios proposed microlattices that secrete the transverse displacement nonlinearly varies with the longitudinal displacement, and the Poisson’s ratio depends on the applied strain (i.e., tailorable Poisson’s ratio). Whereas metamaterials with tailorable Poisson’s ratios would find many important applications, the design of a metamaterial with a giant Poisson’s ratio that is constant over all the material deformation range has been a major challenge. Here, we develop a new class of bimaterial-3D-metamaterials with giant and strain-independent Poisson’s ratios (i.e., Poisson’s ratio is constant over the entire deformation range). The unit cell is 3D assembled of hinged-struts. Specially designed spherical hinges were utilized to give constant Poisson’s ratios. This new class of metamaterials has been demonstrated by means of experimental and numerical mechanics. 15 material samples were 3D printed by Stereolithography (SLA) and tested. We revealed a robust anisotropy dependence of the Poisson’s ratio. A giant negative Poisson’s ratio of −16 was obtained utilizing a highly anisotropic unit cell of dissimilar materials and stiffnesses. Materials with giant and strain-independent Poisson’s ratios provide a new class of artificial metamaterials, which would be used to optimize the performance of many existing devices, e.g., strain amplifiers and gauges.

Effect of lattice deformation on electronic and optical properties of CuGaSe2: Ab-initio calculations

In this study, we have investigated the effect of bi-axial, ϵab, and uni-axial, ϵc, strains on the optoelectronic properties of chalcopyrite semiconductor CuGaSe2 through first-principles full potential linearized augmented plane wave method. These materials have recently attracted much interest within the materials science community. The results are obtained in the framework of Density Functional Theory (DFT), using the Generalized Gradient Approximation based on the minimization of total energy, together with the modified Becke-Johnson exchange-correlation potential, as implemented in the WIEN2k code. Our results show that unstrained CuGaSe2 is a direct band gap semiconductor with a energy of 1.16 eV, thus improving the results of some previous DFT calculations, but still below the accepted experimental data. The incorporation of biaxial and uniaxial strain results in a monotonous decreasing behavior of the energy band gap when both ϵab and ϵc change between -8% and +8%, with unstrained value being, approximately, at the middle of the variation range. It is also found that strain causes modifications in the index of refraction of the material, with modifications of its static value that rank above 10% over the entire range of deformations considered.

Experimental Determination and Comparative Analysis of the PPH030GP, ABS and PLA Polymer Strength Characteristics at Different Strain Rates

Nowadays the field of application of products made from polymer materials is constantly increasing. These products find their wide application in the most high-tech industries such as automotive, aerospace and medical industry. Modern trends in the development of the automotive industry predicts that 75 % of the total car mass will be replaced with polymer materials by 2020 and other industries demonstrate similar trends. Regarding to this information, engineering companies that design parts of the automotive industry should have polymer material characteristics over an entire range of deformations up to destruction for their performance prediction. However, strength characteristics of products from polymers are different and depend not only on a polymer grade but also on technology used for part production. Existing literature review on this problematic area is rather rare. The purpose of this paper is to determine and analyze mechanical characteristics of widely used PPH030GP polymer obtained by extrusion and ABS, PLA polymers applied while manufacturing samples using an additive method (3D-printing) depending on the rate of high-elastic deformation. All the samples have been made according to the requirements of GOST 11262–80 and subjected to uniaxial stretching on a tensile machine UIT STM 050/300 at different speeds of clamp expansion. According to experimental results, stretching diagrams in conditional coordinates s–e have been obtained up to the point of failure for different rates of clamp expansion. It has been shown that while using the additive method, a direction of layers and adhesion between them, which depends on 3D-print parameters, have a significant effect on the part strength. Printing settings are indicated in accordance with the selected mode and a 3D-printer model. As a result of data processing, strength characteristics of PPH030GP polymer and ABS and PLA polymers have been determined to a sufficient extent, depending on the direction of printing layers and rate of high-elastic deformation. These data can be used to calculate strength of products by numerical methods and a finite element method in various software products.

Entropic Network Model for Star Block Copolymer Thermoplastic Elastomers

Uniaxial tensile deformation of star block polymer elastomers with up to 10 arms is studied with molecular dynamics simulations of a bead–spring representation at two different deformation rates. The mechanical response is rationalized in terms of an entropic network model, which we generalize from linear to star polymers. The model universally accounts for the stress in the entire deformation range well into the nonlinear regime. As the strain rate is increased, we find additional hardening as the number of arms increases, which can be attributed to the breakup of physical cross-links.

A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers

This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.

High Strain Rate Compression Testing of Hot-Pressed TRIP/TWIP-Matrix-Composites

Metal matrix composites with ceramic reinforcements such as particles or fibers have come into focus during the past decades due to rising requirements on engineering materials. In this work, composite materials out of high-alloy CrMnNi-steel matrices with varying Ni-contents (3 wt.% and 9 wt.%) and 10 vol.% Mg-PSZ were processed by hot-pressing. The variation in Ni-content resulted in a change in stacking fault energy (SFE) which significantly influenced the deformation mechanisms. The mechanical behavior of the developed composites was investigated in a wide strain rate range between 0.0004 s-1 and 2300 s-1 under compressive loading. This was done by a servohydraulic testing system, a drop weight tower, and a Split-Hopkinson Pressure Bar for the high strain rates. To study the influence on the deformation mechanisms such as martensitic transformations and/or twinning, interrupted tests were also carried out at 25 % compressive strain. Subsequent microstructural examinations were done by a magnetic balance to measure the quantity of α’-martensite as well as by scanning electron microscopy (SEM). The results show an increase of strength and strain hardening with decreasing SFE of the matrix due to increased α’-martensite formation. The addition of the Mg-PSZ particles resulted in further strengthening over almost the entire deformation range for all investigated composites. At high strain rates quasi-adiabatic heating suppressed the martensite transformation and reduced the strain hardening capacity of the matrix. Nonetheless the particle reinforcement retains its strengthening effect.

A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory

In this paper, a new computational framework for the analysis of incompressible Electro Active Polymer (EAP) shells subjected to large strains and large electric fields is presented. Two novelties are incorporated in this work. First, the variational and constitutive frameworks developed by the authors in recent publications (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016; Ortigosa et al., 2016) in the context of three-dimensional electromechanics are particularised/degenerated to the case of geometrically exact shell theory. This formulation is computationally very convenient as EAPs are typically used as thin shell-like components in a vast range of applications. The proposed formulation follows a rotationless description of the kinematics of the shell, enhanced with extra degrees of freedom corresponding to the thickness stretch and the hydrostatic pressure, critical for the consideration of incompressibility. Different approaches are investigated for the interpolation of these extra fields and that of the electric potential across the thickness of the shell. Crucially, this allows for the simulation of multilayer and composite materials, which can display a discontinuous strain distribution across their thickness. As a second novelty, a continuum degenerate approach allows for the consideration of complex three-dimensional electromechanical constitutive models, as opposed to those defined in terms of the main strain measures of the shell. More specifically, convex multi-variable (three-dimensional) constitutive models, complying with the ellipticity condition and hence, satisfying material stability for the entire range of deformations and electric fields, are used for the first time in the context of shell theory.

A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation

Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain energies which depend on non-strain based variables introducing other physical measures such as the electric displacement. Six key novelties are incorporated in this work. First, a new definition of the electro-mechanical internal energy is introduced expressed as a convex multi-variable function of a new extended set of electromechanical arguments. Crucially, this new definition of the internal energy enables the most accepted constitutive inequality, namely ellipticity, to be extended to the entire range of deformations and electric fields and, in addition, to incorporate the electro-mechanical energy of the vacuum, and hence that for ideal dielectric elastomers, as a degenerate case. Second, a new extended set of variables, work conjugate to those characterising the new definition of multi-variable convexity, is introduced in this paper. Third, both new sets of variables enable the definition of novel extended Hu–Washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro-elasticity. Fourth, some simple strategies to create appropriate convex multi-variable energy functionals (in terms of convex multi-variable invariants) by incorporating minor modifications to a priori non-convex multi-variable functionals are also presented. Fifth, a tensor cross product operation (de Boer, 1982) used in Bonet et al. (2015) to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro-mechanical framework, leading to insightful representations of otherwise complex algebraic expressions. Finally, under a characteristic experimental setup in dielectric elastomers, the behaviour of a convex multi-variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction, is numerically studied.

Mechanism-based modelling of plastic deformation in magnesium alloys

The plastic deformation of two different rolled magnesium sheets (AZ31 and ZE10) under quasi-static tensile and compressive loading conditions at room temperature is studied. Beside glide by dislocation motion, deformation twinning leads to evolving flow stress asymmetry and evolving plastic anisotropy in these alloys. These mechanisms cause a significant change in the shape of the yield surface with accumulated plastic deformation which cannot be described by traditional hardening concepts. A phenomenological plasticity model in which the primary deformation mechanisms, slip and (extension) twinning, are treated separately is developed here and incorporated in the finite element framework. Deformations caused by these mechanisms are modelled by a symmetric and an asymmetric plastic potential, respectively. The hardening functions are coupled to account for the latent hardening. The necessary input for model parameter calibration is provided by mechanical tests along different orientations of the rolled sheets. Tensile tests of notched samples and shear tests are furthermore incorporated in the parameter optimisation strategy, which is based on minimising the difference between experimental behaviour and FE prediction over the entire deformation range up to failure. The model accounts for the characteristic tension-compression asymmetry and the evolution of strain anisotropy. Both, the convex-up and the concave-down shaped stress–strain response are predicted. The computational model is exemplified by studying the evolution of the plastic multipliers during a shear test. It is shown that despite its phenomenological character, the model predicts the dominant deformation mechanism present at monotonous loading of the magnesium sheets investigated.

Thermal and strain rate sensitive compressive behavior of polycarbonate polymer - experimental and constitutive analysis

The mechanical behavior of polycarbonate (PC) polymer was investigated under the effect of various temperatures and strain rates. Characterization of polymer was carried out through uniaxial compression tests and split Hopkinson pressure bar (SHPB) dynamic tests for low and high strain rates respectively. The experiments were performed for strain rates varying from 10 −3 to 103 and temperature range of 213 to 393 K. By conducting these experiments, the true stress–strain (SS) curves were obtained at different temperatures and strain rates. The results from experiments reveal that the stress–strain behavior of polycarbonates is different at lower and higher strain rates. At higher strain rate, the polymer yields at higher yield stress compared to that at low strain rate. At lower strain rate, the yield stress of the polymer increases with the increase in strain rate while it decreases significantly with the increase of temperature. Likewise, initial elastic modulus, yield and flow stress increase with the increase in strain rate while decreases with the increase in temperature. The yield stress increases significantly for low temperature and higher strain rates. On the basis of experimental findings, a phenomenological constitutive model was employed to capture the mechanical behavior of polymer under temperature and loading rate variations. The model predicted the yield stress of polymer at varying strain rate and temperature also it successfully predicted the compressive behavior of polymer under entire range of deformation.

Two Chain-Packing Transformations and Their Effects on the Molecular Dynamics and Thermal Properties of α-Form Isotactic Poly(propylene) under Hot Drawing: A Solid-State NMR Study

The chain packing, crystal thickness, molecular dynamics, and melting temperature of α-form isotactic polypropylene (iPP) drawn uniaxially at high temperatures of 100–150 °C were investigated using solid-state (SS) NMR and DSC. Two types of iPP samples with disordered (α1) and relatively ordered (α2-rich) packing structures were prepared via different thermal treatments and drawn up to an engineering strain (e) of approximately 20. High-resolution 13C NMR detected continuous α2 → α1 transformations in the original α2-rich samples over the entire deformation range at all drawing temperatures (Tds). A sudden α1 → α2 transformation was found to occur in the original α1 sample in the small e range of approximately 3–7 at Td = 140 °C. Then, in the late stage, the newly grown α2 structure reversely transformed into α1 structure with further increase in e, as observed in the original α2-rich sample. These results indicate that at least two different processes are involved in large deformations. On the basis of c...

A Novel Constitutive Formulation for Rubberlike Materials in Thermoelasticity

The objective of this paper is to present a new framework to formulate thermoelastic constitutive relations for initially isotropic rubberlike materials undergoing finite deformations. The strain-energy function for incompressible materials is extended to include the effects of compressibility and temperature changes. The novelty of this framework is that only a few material functions and material parameters to be fitted with the experimental data are required, and these functions and parameters have clear physical meaning. In order to validate the proposed formulation, the Gent–Gent model for incompressible rubbers is chosen as an illustrative example. A new expression of the Helmholtz free energy of rubberlike materials, which takes into account the material compressibility and thermal effect, is then derived. In this generalized Gent–Gent model, only one material function and six material parameters are introduced. It is shown that the generalized Gent–Gent model can be used to predict the stress-strain behavior over the entire range of deformation. Even for incompressible materials, the strain-energy function in this paper is different from that given by Gent himself. The generalized Gent–Gent model can also adequately describe the thermal-mechanical coupling effect, in which thermoelastic inversion phenomena occur.

Electromagnetic transition strengths in soft deformed nuclei

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $<\Delta \vec{J}^2>$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.

Investigating new symmetry classes in magnetorheological elastomers: cantilever bendingbehavior

This work defines and examines four classes of magnetorheological elastomers(MREs) based upon permutations of particle alignment–magnetization pairs.Particle alignments may either be unaligned (e.g. random) or aligned. Particlemagnetizations may either be soft-magnetic or hard-magnetic. Together, thesedesignations yield four material types: A–S, U–S, A–H, and U–H. Traditional MREscomprise only the A–S and U–S classes. Samples made from 325-mesh iron and40 µm barium hexaferrite powders cured with or without the presence of a magneticfield served as proxies for the four classes. Cantilever bending actuating testsmeasuring the magnetically-induced restoring force at the cantilever tip on50 mm × 20 mm × 5 mm samplesyielded ∼ 350 mN at μ0H = 0.09 T for classes A–H, A–S, and U–S while class U–H showed only ∼ 40 mN. Furthermore, while classes U–S and A–S exerted forces proportional to tip deflection,they exerted no force in the undeformed state whereas class A–H exerted a relativelyconstant tip force over its entire range of deformation. Beam theory calculations andmodels with elastic strain energy density coupled with demagnetizing effects in themagnetic energy density were used to ascertain the magnitude of the internal bendingmoment in the cantilever and to predict material response with good results. Thiswork highlights the ability of the newly developed A–H MRE materials, andonly that material class, to operate as remotely powered bidirectional actuators.