Fused deposition modeling (FDM) is highly commercialized Rapid Prototyping (RP) technology for its ability to build complex parts with low cost in a short period of time. The process parameters in the FDM play a vital role in the mechanical properties of the polymeric parts. Most of the research studies show that the variable parameters such as orientation, layer thickness, raster angle, raster width, and air gap are some of the key parameters that affect the mechanical properties of FDM-processed polymeric parts. However, no reports have been made regarding the influence of nozzle diameter with raster width on the tensile properties of FDM fabricated polymeric parts. This work was devoted to achieving improved and isotropic mechanical properties in polycarbonate (PC) and PC/carbon nanotube (PC/CNT) nanocomposites by investigating the effect of printing parameters in FDM process. The nozzle diameter to raster width ratio, α was found to significantly affect the mechanical properties. The printing direction dependency in tensile properties were studied with the ratio α < 1 and α≥ 1 at three different raster angles of 0°, 45°/−45° and 90°. For α < 1, Ultimate tensile strength and modulus of elasticity were higher for 0°, compared to 45°/−45° and 90° raster angles. However, for α ≥ 1, the ultimate tensile strength and the modulus of elasticity showed little dependency to print direction. This certainly determines the decrease in anisotropy at higher values of α. Mesostructure characterization with microscopy and image analysis were used to further explain the printing behavior and the resultant properties of the printed samples.

There have been various theoretical studies done on anisotropic neo-Hookean models; however, there have been limited experimental validations of these theories. In this study, a silicone/silicone laminate with a fiber volume fraction of 18% has been parameterized. Conventional neo-Hookean models have been modified for compressible in-plane deformations. Two-dimensional deformation limitations and a compressible constraint have been discussed. Material parameters have been calculated for three different anisotropic, neo-Hookean models from the literature.

This document condenses the results obtained when 3D printing lenses and their potential use as diffraction gratings using Digital Light Processing (DLP), as an additive manufacturing technique. This project investigated the feasibility of using DLP additive manufacturing for producing custom designed lenses and gratings. DLP was identified as the preferred manufacturing technology for gratings fabrication. Diffraction gratings take advantage of the anisotropy, inherent in additive manufacturing processes, to produce a collated pattern of multiple fringes on a substrate with completely smooth surfaces. The gratings are transmissive and were manufactured with slit separations of 10, 25 and 50 μm . More than 50 samples were printed at various build angles and mechanically treated for maximum optical transparency. The variables of the irradiance equation were obtained from photographs taken with an optical microscope. These values were used to estimate theoretical irradiance patterns of a diffraction grating and compared against the experimental 3-D printed grating. The resulting patterns were found to be remarkably similar in amplitude and distance between peaks when compared to theoretical values.

Artificial muscle systems have the potential to impact many technologies ranging from advanced prosthesis to miniature robotics. Recently, it has been shown that twisting drawn polymer monofilaments, such as nylon fishing line or sewing thread, can result in a biomimetic thermally activated torsional actuator. The actuation phenomenon in these twisted polymer actuators (TPAs) is thought to be a result of an untwisting that occurs about the fiber’s axis due to an anisotropic thermal expansion. Before being twisted, the precursor fibers are comprised of polymer chains that are aligned axially. During fabrication of TPAs, the polymer chains reorient as the precursor fiber is twisted about the central axis of the monofilament. At the end of the fabrication process, the TPA is annealed in order to relieve internal stresses and to keep the fiber in the twisted configuration. The mechanism of untwisting actuation is generally thought to be a result of radial expansion and axial contraction. After being twisted, these radial and axial expansion relationships remain relatively unchanged, but the polymer chain direction is no longer axially aligned. Thus, upon heating the twisted fibers of the TPA, the fibers untwist and torsional actuation occurs. This actuation phenomenon has been used in the past to create linear actuators, but can also be use directly as a torsional actuator. Compared to other torsional actuators TPAs are low cost, lightweight, and can actuate reasonably high torques per unit volume. However, because TPAs are thermally activated, they may not be suitable for all applications. In this work, we present a novel TPA design for use as a torsional actuator for miniature actuation and artificial muscle applications. Our design bundles twisted monofilaments to increase the torque. Both fabrication and testing methods of the new design are presented. Results for temperature versus torsional displacement under various loads give insights as to how these actuators may be used and the reversibility of the actuation process under different fabrication loads. Additionally, comparisons are made between these bundled actuators and similarly loaded single TPA monofilament actuation.

An optimization algorithm is proposed to determine the parameters of a discrete energy-averaged (DEA) model for Galfenol alloys. A new numerical approximation approach for partial derivative expressions is developed, which improves computational speed of the DEA model by 61% relative to existing partial derivative expressions. Initial estimation of model parameters and a two-step optimization procedure, including an-hysteresis and hysteresis steps, are performed to improve accuracy and efficiency of the algorithm. Initial estimation of certain material properties such as saturation magnetization, saturation magnetostriction, Young’s modulus, and anisotropy energies can improve the convergence and enhance efficiency by 41% compared to the case where these parameters are not estimated. The two-step optimization improves efficiency by 28% while preserving accuracy compared to one-step optimization. Proposed algorithm is employed to find the material properties of Galfenol samples with different compositions and heat treatments. The trends obtained from these optimizations can guide future Galfenol modeling studies.

The actuation mechanisms of cnt-based materials are still controversially discussed. It is not common sense whether it is a macroscopic volume effect caused by ion intercalation or electrostatic repulsion of equally charged cnts or a nanoscopic effect of filled electron anti-bonding orbitals of the carbon atom or interactions with ions docking on the carbon surface. In the presented paper arrays of highly aligned multi-walled carbon nanotubes (mwcnts) are used which are stabilized by a polypyrrole-coating. The samples are tested along the cnt-orientation and in perpendicular mode to analyze the influence of the structure-ion interaction. The mwcnt-arrays exhibit only a total length of approximately 2.8 mm but by coating with polypyrrole larger geometries can be tested. The actuation is analyzed using an in-plane test and an actuated tensile testing. Free strain can be detected using the first set-up, the second method is carried out to evaluate the mechanical stability of the samples. As might be expected, the material shows a strong anisotropic active behavior with the actuation along the tube axis being only half of the value detected at the perpendicular oriented samples. The findings point out that an intercalation of ions into the charged CNT-architecture seems here to be the dominating mechanism.

In this study, we demonstrate the electric and magnetic manipulation of nanoscale M-type Barium Hexaferrite (nBF) in polydimethylsiloxane (PDMS) to engineer a multifunctional nanocomposite with improved dielectric and magnetic properties. First, we synthesized the single crystal nBF via the hydrothermal synthesis route. The hydrothermal temperature, duration, and surfactant conditions were optimized to improve the magnetic properties of the nBFs, with further improvement achieved by post-annealing. The annealed nBFs were aligned dielectrophoretically (DEP) in the polymer matrices by applying an AC electric field. Under the influence of this electric field, nBFs were observed to rotate, align and form chains within the polymer matrix. Optical microscopy (OM) imaging was used to determine the electrical alignment conditions (duration, magnitude, and frequency) and these parameters were used to fabricate the composites. A Teflon setup with Indium Tin Oxide (ITO) coated Polyethylene Terephthalate (PET) was used, where the ITO coatings act as electrodes for the electric field-manipulation. To simultaneously apply the magnetic field, this Teflon setup is placed between two permanent magnets capable of generating a 0.6 T external magnetic field. Along with electric and magnetic fields, concurrent heating was applied to cure the PDMS and freeze the microstructure formed due to electric and magnetic fields. Upon completion of the curing step, parallel chain formation is observed under OM. The X-Ray Diffraction (XRD) results also confirm that the particles are magnetically oriented in the direction of the magnetic field within the chain. Vibrating Sample Magnetometry (VSM) measurements and dielectric spectroscopy are used to characterize the extent of anisotropy and improvement in dielectric and magnetic properties compared to random composites. We find that simultaneous electric and magnetic field alignment improves the dielectric properties by 12% compared to just magnetic alignment. We also observe 19% improved squareness ratio when both fields are applied. The possibility of simultaneous electrical and magnetic alignment of magnetic nanoparticles will open up new doors to manipulate and design particle-modified polymers for various applications.

Magneto-Active elastomers (MAEs) and magneto-rheological elastomers (MREs) are smart materials that consist of hard and soft magnetic particles, respectively, embedded in a flexible matrix. Their actuation capabilities are dependent on the arrangement of particles achieved during the fabrication process. Previous works have shown varying degrees of particle alignment and / or agglomeration as a function of fabrication process variable, most notably volume fraction of the particulates, their magnetic material type (hard vs soft), and the strength of the external field applied during curing. In this work, we simulated the dynamics of magnetic particles suspended in a fluid matrix to predict the evolution of microstructures resulting from these varying process conditions. The simulations accounted for the magnetic interaction of all particles using standard dipole-dipole interaction potentials along with dipole-field potentials developed from the Zeeman Energy. Additionally, the field local to each particle, on which magnetization depends, was determined by the sum of the external fields generated by each member of the ensemble and their demagnetizing fields. Fluid drag forces and short range particle-particle repulsion (non-overlapping) were also considered. These interactions determined the body forces and torques acting on each particle that drove the system of equations of motions for the ensemble of particles. The simulation was carried out over a nearest neighbor periodic unit cell using an adaptive time stepping numerical integration scheme until an equilibrium structure was reached. Structural parameters, related to the magnetic energy, spatial distribution, spatial alignment, and orientation alignments of the particle distributions were defined to characterize the simulated structures. The effect of volume fraction and intensity of the external magnetic field on the achieved particle distributions were studied. At low external field strengths, the particles formed long entangled chains that had very low alignment with the applied field. The remnant magnetic potential energy of these configurations was also significantly low. As the field is increased the length of the chains reduced and the alignment increased. The corresponding change in magnetic potential energy of the system with an increase in the applied field was found to follow a power law fit that spanned a wide range of magnetic field strengths. At low volume fractions the particles aligned rapidly with the field and formed short chains. As the volume fraction of the samples increased the chains grew longer and closer to each other, and magnetic potential of the structure became lower. Results of the simulations suggest that it is possible to tailor the microstructure and thus affect remanent magnetization and magnetization anisotropy, by judicious control of process parameters. This ability could have implications for newly emerging additive manufacturing techniques utilizing suspensions of magnetic particulates.

Recently, carbon fiber-reinforced thermoplastics (CFRTPs) have become popular choices in desktop-based additive manufacturing, but there is limited information on their effective usage. In Fused Deposition Modeling (FDM), a structure is created by layers of extruded beads. The degree of bonding between beads, bead orientation, degree of interlayer bonding, type of infill and the type of material, determines overall mechanical performance. The presence of chopped fibers in thermoplastics increases melt viscosity, changes coefficients of thermal expansion, may have layer adhesion issues, and causes increased wear on nozzles, which makes FDM fabrication of thermoplastic composites somewhat different from neat thermoplastics. In the current work, best practices and the effect of annealing and infill patterns on the mechanical performance of FDM-fabricated composite parts were investigated. Materials included commercially available PLA, CF-PLA, ABS, CF-ABS, PETG, and CF-PETG. Two sets of ASTM D638 tensile and ASTM D790 flexural test specimens with 3 different infill patterns and each material were fabricated, one set annealed, and all tested. Anisotropic behavior was observed as a function of infill pattern. As expected, strength and stiffness were higher when the beads were oriented in the direction of the load, even for neat resins. All fiber-filled tensile results showed an increase in stiffness, but surprisingly, not in strength (likely due to very short fiber lengths). Tests of annealed specimens resulted in clear improvements in tensile strength, tensile stiffness and flexural strength for PLA, CF-PLA, and PETG, CF-PETG but a reduction in flexural stiffness. Also, annealing resulted in mixed improvements for ABS and CF-ABS and is only useful in certain infill patterns. This work also establishes ‘Best Practices’ of FDM-type fabrication of thermoplastic composite structures and documents the minimum critical fiber lengths and fiber fractions of several CF-filled FDM filaments.

Patterned liquid crystal elastomer (LCE) has been shown to have significant promise in surface topography control. Large and diverse shapes and surface adaptive responses have been shown using LCE materials with patterned director profiles. Using various techniques, crystal orientation across the surface of the material as well as through the thickness can be achieved yielding the capability to design out-of-plane deformation. These topological features can be used as active flow effectors manipulating, among other things, drag on an object in cross-flow. It is well known that surface topography can have a large effect on skin friction drag by effecting the boundary layer transition, separation, and interfering with the shedding of vortices. In regards to a cylinder in a cross-flow, spatially manipulating surface topography, and thus drag, in this way gives rise to forces exerted by the fluid on the body. An imbalance of forces due to non-uniform surface topography can then be used to control the cylinder. Designing such a system requires optimization of the surface topography via optimization of the crystal orientation pattern over a wide range of environments. Key to this optimization, described in detail in the presented work, is an accurate material model validated against experimental data. By representing the strain energy of the material as a combination of contributions of the elastomer backbone and the liquid crystals separately, unique material properties can be properly modeled. This is achieved by combining a traditional isotropic 3 chain Arruda-Boyce hyperelastic equation modeling the elastomer backbone with an anisotropic extension modeling the patterned liquid crystals, resulting in an anisotropic hyperelastic material model. The model can then be used to predict the material response of various patterns and investigate the design space of possible surface topographies.

NiTi has been shown to be of great interest for bone implant applications. Introducing porosity to NiTi bone implants is an effective technique to tune their equivalent modulus of elasticity in order to acquire similar value to that of cortical bone. Moreover, such porous implants allow for better tissue ingrowth due to the interconnecting open pore structure. The effect of porosity percentage on the NiTi equivalent modulus of elasticity is well understood. However, the effect of porosity type on NiTi bone implant’s performance, in terms of the geometrical structure and other mechanical properties, has not yet been investigated. To this end, we simulated three porous structures made of shape memory Ti-rich Ni50.09Ti alloy. The effect of porosity type on the NiTi implant’s geometrical structure and mechanical properties was studied using numerical tests. The purpose is to compare three NiTi implants with different kinds of porosities, at a similar level of porosity (i.e., 69 %). The assigned porosity types in this study are Schwartz-type, Gyroid-type, and Diamond-type. Three triply periodic minimal surface (TPMS) models (9mm×9mm×9mm) with the assigned fixed level of porosity (69 %) were designed as CAD files using Solidworks. Each model was meshed, and the convergence study was conducted. The three models were then imported into a finite element package (ABAQUS). A UMAT code developed by IUT (Isfahan University of Technology) group was used to simulate the mechanical behavior of the shape memory NiTi alloy. All boundary conditions and loading conditions were applied to the models. Compressive mechanical tests were simulated in the finite element, and the resultant equivalent modulus of elasticity, elongations, stress, and strain was estimated. The results show anisotropic behavior within the three different porous structures. With the same level of porosity (i.e., 69 %), equivalent modulus of elasticity was observed to be 48.9, 34.8, and 30.2 GPa for Schwartz-type, Gyroid-type, and Diamond-type, respectively. Moreover, the Schwartz-type scaffold was seen to offer the highest stress at plateau start and the lowest residual strain after unloading, in comparison with the other two types of structure.

A two-dimensional phononic crystal (PC) can exhibit longitudinal-mode negative energy refraction on its lowest (acoustical) frequency pass band. The effective elastodynamic properties of a typical PC are calculated and it is observed that the components of the effective density tensor can achieve negative values at certain low frequencies on the acoustical branches for the longitudinal-mode pass-band, and that negative refraction may be accompanied by either positive or negative effective density. Furthermore, such a PC has a high anisotropy ratio at certain low frequencies, offering potential for application to acoustic cloaking where effective material anisotropy is essential.

Artificial muscle systems have the potential to impact many technologies ranging from advanced prosthesis to miniature robotics. Recently, it has been shown that twisting drawn polymer fibers such as nylon can result in torsional or tensile actuators depending on the final fiber configuration. The actuation phenomenon relies on the anisotropic nature of the fibers moduli and thermal expansion. They have high axial stiffness, low shear stiffness, and expand more radially when heated than axially. If a polymer fiber is twisted but not coiled, these characteristics result in a torsional actuator that will untwist when heated. During the fabrication process, these twisted polymers can be configured helically before annealing. In this configuration, the untwisting that occurs in a straight twisted fiber results in a contraction or extension depending on relative directions of twist and coiling. In these ways, these materials can be used to create both torsional or axial actuators with extremely high specific work capabilities. To date, the focus of research on twisted polymer actuators (TPAs) and twisted-coiled polymer actuators (TCPAs) has been actuator characterization that demonstrates the technologies capabilities. Our work focuses here on applying a 2D analysis of individual layers of the TPAs to predict thermally induced twisting angle and fiber length based on virgin (untwisted) material properties and actuator parameters like fiber length and inserted twist. A multi-axis rheometer with a controlled thermal environmental chamber was used to twist, anneal, and test thermally induced actuation. Experimentally measured angle of untwist and axial contraction after heating are compare the the model. In comparing the experimental results with the two dimensional model, it appears that the difference between the 2D model and experimental results can be explained by the longitudinal stresses that develop inside the material. Future work will aim to include these effects in the model in order to be able to use this model in the design of TPAs.

Damage nucleation and growth can be complex in hybrid structures composed of layers of metal and laminated composites. Presently there are limited reliable damage growth analytical and empirical methods to evaluate the bond integrity of such structures and to quantify the state of bonding in such joints. Depending on the geometry and accessibility of hybrid joints, ultrasonic nondestructive testing (NDT) techniques are available for inspection of these structures. However there are some limitations for the usage of typical bulk or guided waves to quantify the integrity of bondline in hybrid structures. This work suggests the use of specific forms of ultrasonic guided waves that propagate along the bondline of these hybrid structures. This study is dedicated to modeling of interface guided waves for the purpose of disbond crack damage assessment. The nature of interface waves is discussed and the numerical simulation based on the material properties and geometries of hybrid interfaces as well as composite stacking sequence is verified. A finite element model of a hybrid structure with isotropic and anisotropic multilayer composites is constructed. The behavior of interface guided waves influenced by disbond cracks at free edges of hybrid bonded joints is numerically studied. The propagation characteristics of interface waves is shown to be sensitive to the size of disbond cracks. The velocity of interface waves is shown to have an inverse relation to the disbond damage size. Results show the speed is also a function of the interfacing ply orientation at the bondline. These results suggest that interface waves can be used to monitor the condition of bonded joints in hybrid structures.

ZnO based polymer composite materials are of great interest because of their excellent electrical, optical, semiconductor and biocompatible properties. In this study, we synthesize anisotropic composites of aligned ZnO rods in polydimethylsiloxane (PDMS) elastomer and study their dielectric properties as a function of applied electric field and frequency. Submicron ZnO rods are synthesized using an inexpensive, high yield chemical route. Washed and purified ZnO rods are then aligned in uncured PDMS at different electric field and frequency. We find that under electric field, ZnO rotates with their long axis in the direction of the electric field and before coalescing form chains in the silicone elastomer. From the optical microscopy images and in situ dielectric measurements, the best alignment parameters are found at 4 kV/mm and 10 kHz. These conditions are then selected to prepare aligned ZnO-PDMS composites. Complete curing of composites is confirmed using dynamic mechanical analysis (DMA). Our results show that aligned ZnO in uncured PDMS exhibit higher dielectric permittivity compared to random dispersion with the same composition. For the cured ZnO-PDMS composites, dielectric permittivity increases by 80% compared to random composites.

This paper presents a novel experimental apparatus and a test method for measuring simultaneously quasi-static average longitudinal and shear magnetic-field-induced strain (MFIS) of Ni-Mn-Ga single crystals. The apparatus consists of an aluminum casing, a weight-controlled plunger, two displacement probes (one vertical and one lateral), and a torsion guide etc. Three Ni-Mn-Ga square prism samples were tested. Twin boundary bands were clearly visible after the application of magnetic field. A range of material properties were measured. These include: (a) magnetic anisotropy constant; (b) single variant magnetization curves for the easy and hard axes; (c) nonlinear compressive stress-strain curves for all three samples at room temperature; and (d) average longitudinal and shear MFIS curves versus magnetic field strength for three prism samples subject to various compressive external stresses.

Whether serving as mounts, isolators, or dampers, elastomer-based supports are common solutions to inhibit the transmission of waves and vibrations through engineered systems and therefore help to alleviate concerns of radiated noise from structural surfaces. The static and dynamic properties of elastomers govern the operational conditions over which the elastomers and host structures provide effective performance. Passive-adaptive tuning of properties can therefore broaden the useful working range of the material, making the system more robust to varying excitations and loads. While elastomer-based metamaterials are shown to adapt properties by many orders of magnitude according to the collapse of internal void architectures, researchers have not elucidated means to control these instability mechanisms such that they may be leveraged for on-demand tuning of static and dynamic properties. In addition, while magnetorheological elastomers (MREs) exhibit valuable performance-tuning control due to their intrinsic magnetic-elastic coupling, particularly with anisotropic magnetic particle alignment, the extent of their properties adaptation is not substantial when compared to metamaterials. Past studies have not identified means to apply anisotropic MREs in engineered metamaterials to activate the collapse mechanisms for tuning purposes. To address this limited understanding and effect significant performance adaptation in elastomer supports for structural vibration and noise control applications, this research explores a new concept for magnetoelastic metamaterials (MM) that leverage strategic magnetic particle alignment for unprecedented tunability of performance and functionality using non-contact actuation. MM specimens are fabricated using interrelated internal void topologies, with and without anisotropic MRE materials. Experimental characterization of stiffness, hysteretic loss, and dynamic force transmissibility assess the impact of the design variables upon performance metrics. For example, it is discovered that the mechanical properties may undergo significant adaptation, including two orders of magnitude change in mechanical power transmitted through an MM, according to the introduction of a 3 T free space external magnetic field. In addition, the variable collapse of the internal architectures is seen to tune static stiffness from finite to nearly vanishing values, while the dynamic stiffness shows as much as 50% change due to the collapsing architecture topology. Thus, strategically harnessing the internal architecture alongside magnetoelastic coupling is found to introduce a versatile means to tune the properties of the MM to achieve desired system performance across a broad range of working conditions. These results verify the research hypothesis and indicate that, when effectively leveraged, magnetoelastic metamaterials introduce remarkably versatile performance for engineering applications of vibration and noise control.

The goal of this study is to examine the theoretical capability of bimaterial lattices as thermally driven actuators. The lattices are composed of planar non-identical cells. Each cell consists of a skewed hexagon surrounding an irregular triangle; the skew angles of the hexagon and the ratio of the coefficients of thermal expansion (CTEs) of the two component materials determine the overall performance of the actuator. Such a cell has three tailorable CTEs along the lines connecting the points where adjoining cells are connected. Each individual cell and a lattice consisting of such cells can be strongly anisotropic in terms of thermal expansion. While these lattice cells have been used as stress-free connectors for components with differing CTEs, they have not been explored for their actuation capacity. This paper develops models for bimaterial lattices that can be used as mechanical actuators for valves, switches and differential motion. A general procedure for lattice design includes drawing of its skeleton, which identifies the points at which a lattice cell is connected to other cells or substrates; calculation of three CTEs in each cell depending upon the functionality desired; choosing lattice materials; and finding of the skew angles for each cell as solutions of three nonlinear algebraic equations. By changing materials and geometry, we can determine the change of their configuration when the temperature changes. This paper illustrates the concepts with several examples: a two-cell lattice that is connected to a substrate that functions as a lever in a switch; a three-cell lattice that serves as a valve; and a lattice that controls the maximum total deflection of two adjoining parts of a structure.

The realisation of morphing requires an efficient internal structure capable of significant shape adaptations, implying vastly anisotropic stiffness properties. In this context, introducing variable stiffness elements into distributed compliance systems shows great promise. Specifically, bi-stable laminates demonstrate stiffness variability characteristics arising from the markedly different properties of each equilibrium configuration. This paper presents a novel concept of a morphing wing section based on a distributed arrangement of embeddable variable stiffness bi-stable composites. The final configuration emerges from parameter studies into positioning distinct optimised bi-stable elements within a NACA 0012 profile. The structural response of the aerofoil is assessed numerically, with a particular focus on the global stiffness modification potential as well as exploring the snap-through behaviour of the component laminates. Final specimen manufacturing and testing validates the numerical strategy developed, confirming the feasibility of the innovative morphing approach based on variable stiffness bi-stable elements integrated into a selectively compliant system.

This paper presents an energy relaxation-based approach for the modeling of single crystalline magnetic shape memory alloy response under general two-dimensional magneto-mechanical loading. It relies on concepts of energy relaxation in the context of non-convex free energy landscapes whose wells define preferred states of straining and magnetization. The constrained theory of magnetoelasticity developed by DeSimone and James [1] forms the basis for the model development. The key features that characterize the extended approach are (i) dissipative effects, accounted for in an incremental variational setting, and (ii) finite magnetocrystalline anisotropy energy. In this manner, important additional response features, e.g. the hysteretic nature, the linear magnetization response in the pre-variant reorientation regime, and the stress dependence of the maximum field induced strain, can be captured, which are prohibited by the inherent assumptions of the constrained theory. The enhanced modeling capabilities of the extended approach are demonstrated by several representative response simulations and comparison to experimental results taken from literature. These examples particularly focus on the response of single crystals under cyclic magnetic field loading at constant stress, and cyclic mechanical loading at constant magnetic field.