Magneto-active polymers (MAPs) are composite materials composed of a polymeric matrix (specifically, an elastomer) embeddedwith magnetic particles. When subjected to an external magnetic field, these materials change shape, volume, and magneto-mechanical properties. In this work, we fabricate MAPs by embedding carbonyl iron particles into PDMS, with particle volumefractions ranging from 0% to 40%. We perform experiments to characterize the magneto-mechanical responses of MAPs, followedby microstructural analysis. Motivated by experiments, we further develop a filler-dependent coupled magneto-mechanical con-stitutive model. The model is then calibrated using a minimal set of filler fractions and magnetic field data. Moreover, the modelrequires a few material parameters to simulate various coupled MAP responses effectively. Finally, the model is validated with theremaining experimental data and is ready to predict stress variations across different combinations of filler concentrations andmagnetic fields under various loading conditions.

Hydrogels are cross-linked polymeric materials capable of undergoing large deformation in response to external stimuli, such as chemical gradients and mechanical loading. This article presents a coupled chemo-mechanical model of hydrogel undergoing substantial swelling. A multiplicative decomposition-based framework is adopted to represent simultaneous swelling and mechanical deformation in a consistent thermodynamic way. A nonlinear modified hyperelastic Yeoh–Fleming model is considered for the fully swollen hydrogel to describe the strain energy of the polymer network and is calibrated from the available experiments. After calibrating the model using uniaxial stretching for different volume fractions of the polymer network, the model is then benchmarked with equi-biaxial and pure shear responses. The model calibration at different polymer network volume fractions also allows evolution of the Yeoh–Fleming model parameters with polymer network concentration. Finally, we combine the free energy of mixing of solvent and polymer network and the strain energy of polymer network to solve a coupled boundary value problem (BVP) of free swelling. The solution predicts free swelling of hydrogel and the evolution of residual stresses induced by a slow diffusion phenomenon. The numerical results presented here may provide guidance for significant applications of hydrogels in soft robotics, drug delivery and biomedical systems.

This study focuses on creating novel magnetoactive polymers (MAP) by incorporating fabricated magnetic particles into elastomers, a unique approach to MAP preparation. We adopt a unified approach by integrating experimental characterization with a custom-built magneto-mechanical setup, along with modeling and finite element (FE) simulations, to investigate the magneto-mechanical responses of MAP. Our experiments discover a significantly high magneto-stiffening effect with a 20% filler fraction at 0.4 T, almost doubling the stiffness observed in most existing isotropic MAP responses. Based on this data, we propose a new finite deformation-based constitutive model of MAP, which captures the essential features of coupled magneto-mechanical responses. This model is calibrated using experimental data, and its predictions are benchmarked. We further present a 3D FE analysis to show the consistency between experiments and model responses. Finally, we perform a numerical study to demonstrate a stress-induced actuation mechanism using our uniquely fabricated soft magnetic particles which showcases the material’s elastic tunability. This significantly contributes to the theoretical understanding and practical implementation of magnetoactive polymer responses. 

This article presents a coupled magneto-thermo-mechanical model of pressure-dependent magneto-caloric effect (MCE) and magnetization responses for polycrystalline magnetic shape memory alloys (MSMA). Coupled constitutive equations are derived from a Helmholtz free energy function in a consistent thermodynamic way. The hysteretic and dissipative characteristics of phase transformations in MSMAs are captured by the internal state variables approach with their evolution equations. A relation of adiabatic temperature change is established for such a dissipative material system. The model is calibrated and validated with the existing experimental data. The validated constitutive model is then exploited to predict MCEs at different pressure and magnetic field level. Some predicted results are compared with the available experimental data. 

The impact forces due to accidental head impacts make the brain tissue distorted, twisted, and cause Traumatic Brain Injury (TBI). One way to predict the injury level is through simulations with appropriate material modeling and a computational framework. This work focuses on the Finite Element (FE) formulation of white matter responses to improve TBI predictions. Rate-dependent effects of white matter deformation are captured through the numerical implementation of an experimentally verified constitutive equation and nonlinear evolution equations of internal state variables. An ABAQUS UMAT is developed. One-element FE simulations are compared with the analytical and experimental results. Motivated by real-life scenarios, a few 3D Boundary Value Problems (BVPs) are solved to investigate the white matter responses.

Magneto-active polymers are polymer-based composites consisting of magnetizable micro-particles embedded in an elastomeric matrix material. The presence of magnetic particles provides strong tunability to the stiffness and damping properties of the polymeric composites under the magnetic field. We propose here a novel free energy-based phenomenological modeling for magneto-active polymers. Coupled mechanical and magnetization constitutive equations are derived by considering magneto-viscoelasticity in a finite deformation framework. The model calibration takes into account the demagnetization effect, which depends on the specimen size, shape, and its own magnetization. The model prediction is verified with the available experimental data. Finally, a coupled simple shear problem is solved to demonstrate the influence of magnetic field on the Poynting effect. Classical nonlinear soft elastic material shows positive Poynting effect, i.e., shearing planes try to expand. We found the possibilities of field-induced reverse or negative Poynting effect in shear for magneto-active polymers. Such a negative Poynting effect could potentially affect a very diverse range of applications from the performances of miniature sensors and actuators to controlled drug delivery.

Magnetic shape memory alloys (MSMAs) have drawn significant research attention as potential high actuation energy multi-functional materials. Such a dissipative material system can be considered as a solid continuum interacting with a magnetic field. A continuum-based phenomenological model provides a magneto-mechanical system of equations that simulates and predicts primary MSMA behaviours. In this work, we investigate the local symmetries of the MSMA system equations through the Lie group analysis. Symmetry breaking due to stable-unstable transition is analysed. The conservation laws are derived, and their physical meaning is scrutinized.

This work presents a general methodology to analyze three-dimensional Freedericksz transitions in twisted-nematic liquid crystal (LC) bilayers. Using two equivalent coupled electromechanical variational formulations, the problem is treated as a bifurcation instability triggered by an externally applied electric field. Specifically, we consider LC bilayer materials anchored between two bounding plates and subjected to an electric field across the bilayer thickness. The plates are also twisted by an overall angle leading to different orientations of the directors in each layer. We first evaluate the corresponding ground state of the director field, and subsequently, we analyze the bifurcation problem by using a combined analytical-numerical method leading to a one-dimensional finite element discretization of the resulting stiffness matrix of the system. An analytical solution for the zero-twist bilayer is also obtained. The developed methodology is used to study the effect of the volume fraction of the constituents forming the bilayer upon the resulting critical electric field and corresponding eigenmodes. We find that by assembling a relatively thin 5CB layer with a thicker 7E layer, one can obtain periodic Freedericksz transitions (i.e. local modes) even for a zero-twist LC bilayer. We also show that when a 5CB material is assembled together with another electrically similar LC, such as a PCH12, the combined LC bilayer can exhibit an even lower Freedericksz transition than a LC of the same thickness consisting of any of the two constituents alone.

Generating high actuation frequency (∼1.0 kHz) is one of the potential applications of Magnetic Shape Memory Alloys (MSMAs). In this work, dynamic responses of single crystal MSMAs due to variant reorientation are investigated. Time dependent part of the Maxwell equations becomes significant for a high frequency regime. Generation of an electric field and magnetic flux linkage due to the motion of the material points during deformation create a complex electro-magneto-mechanical coupling mechanism. We perform a thermodynamically consistent study to capture the variation of electromagnetic fields due to the deformation in the presence of fluctuating magnetic field, mainly focusing on eddy current and Joule heating. A comparison of MSMA responses with a typical ferromagnet/magnetostrictive material responses is discussed.

This study aims constitutive modeling of rate dependent anisotropic viscoelastic brain tissue that experiences large deformation during accidental impact. Many experimental studies confirm that brain parenchyma mechanisms are strongly influenced by anisotropy, nonlinear viscoelasticity, rate dependent loading/unloading and tension-compression asymmetry of the soft brain tissues. We present a rigorous thermodynamically consistent phenomenological approach to capture these mechanisms in a single model. Model parameters are calibrated from the experiments, and mechanical responses are predicted for different loading conditions. We consider a 2-D fibrous circular tube geometry, an idealized form of a human head, to simulate shear stress distribution for a given boundary condition. Different orientations of the fibers are considered to investigate the influence of anisotropy on the shear stress. Finally, stretch rate dependency of stress responses for a particular fiber orientation is demonstrated.

This contribution is concerned with the embedding of constitutive relations for magneto-active polymers (MAP) into finite element simulations. To this end, a recently suggested, calibrated, and validated material model for magneto-mechanically coupled and rate-dependent MAP response is briefly summarized in its continuous and algorithmic settings. Moreover, the strongly coupled field equations of finite deformation magneto-mechanics are reviewed. For the purpose of numerical simulation, a finite element model is then established based on the usual steps of weak form representation, discretization and consistent linearization. Two verifying inhomogeneous numerical examples are presented in which a classical ‘plate with a hole’ geometry is equipped with MAP properties and subjected to different types of time-varying mechanical and magnetic loading.

Magnetic Shape Memory Alloys (MSMAs) have been the subject of much research in recent years as potential high-actuation-energy multifunctional materials. In this work we analyze coupled magneto-mechanical stability analysis of a variant reorientation mechanism for a single crystal based on a proposed 3-D magneto-mechanically coupled constitutive equations, derived in a consistent thermodynamic way. Discrete symmetry is considered to take into account single crystal anisotropy in the modeling. Analytical results are presented to demonstrate the influence of coupling and anisotropy in the stability of such a material system. Finally, a coupled Boundary Value Problem (BVP) using finite element analysis is performed by considering actual specimen geometry and boundary conditions that are used in the experiments. The numerical simulation reveals localization zones in the solutions due to the loss of ellipticity of the coupled magneto-mechanical problem.

A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

In this work, a continuum based model of the magnetic field induced phase transformation (FIPT) for magnetic shape memory alloys (MSMA) is developed. Hysteretic material behaviors are considered through the introduction of internal state variables. A Gibbs free energy is proposed using group invariant theory and the coupled constitutive equations are derived in a thermodynamically consistent way. An experimental procedure of FIPT in NiMnCoIn MSMA single crystals, which can operate under high blocking stress, is described. The model is then reduced to a 1-D form and the material parameter identification from the experimental results is discussed. Model predictions of magneto-thermo-mechanical loading conditions are presented and compared to experiments.

This paper is concerned with the finite element analysis of boundary value problems involving nonlinear magnetic shape memory behavior, as might be encountered in experimental testing or engineering applications of magnetic shape memory alloys (MSMAs). These investigations mainly focus on two aspects: first, nonlinear magnetostatic analysis, in which the nonlinear magnetic properties of the MSMA are predicted by the phenomenological internal variable model previously developed by Kiefer and Lagoudas, is utilized to investigate the influence of the demagnetization effect on the interpretation of experimental measurements. An iterative procedure is proposed to deduce the true constitutive behavior of MSMAs from experimental data that typically reflect the shape-dependent system response of a sample. Secondly, the common assumption of a homogeneous Cauchy stress distribution in the MSMA sample is tested. This is motivated by the expectation that the influence of magnetic body forces and body couples caused by field matter interactions may not be negligible in MSMAs that exhibit blocking stresses of well below 10 MPa. To this end, inhomogeneous Maxwell stress distributions are first computed in a post-processing step, based on the magnetic field and magnetization distributions obtained in the magnetostatic analysis. Since the computed Maxwell stress fields, though allowing a first estimation of the influence of the magnetic force and couple, do not satisfy equilibrium conditions, a finite element analysis of the coupled field equations is performed in a second step to complete the study. It is found that highly non-uniform Cauchy stress distributions result under the influence of magnetic body forces and couples, with magnitudes of the stress components comparable to externally applied bias stress levels.

Magnetic shape memory alloys have been the subject of much research in recent years as potential high actuation energy multifunctional materials. They can be considered as continua that deform under mechanical and magnetic forces. The constitutive magnetization response of such materials is highly non-linear with magnetic field. A boundary value problem where Maxwell’s equations of the magnetostatic problem are coupled with the non-linear constitutive behavior is solved using finite element analysis. The numerical simulation reveals localization zones of the field variables, which appear due to loss of ellipticity of the magnetostatic problem. Stability analysis is performed by considering the characteristics of the magnetostatic field equations.