Magnetorheological Elastomers

National audienceMagnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. In this work, we present a combined experimental and theoretical study of the macroscopic response of a particular MRE consisting of a rubber matrix phase with spherical carbonyl iron particles. The MRE specimens used in this work are cured in the presence of strong magnetic fields leading to the formation of particle chain structures and thus to an overall transversely isotropic composite. The MRE samples are tested experimentally under uniaxial stresses as well as under simple shear in the absence or in the presence of magnetic fields and for different initial orientations of their particle chains with respect to the mechanical and magnetic loading direction. Using the theoretical framework for finitely strained MREs introduced earlier by the author, we propose a transversely isotropic energy density function that is able to reproduce the experimentally measured magnetization, magnetostriction and simple shear curves under different prestresses, initial particle chain orientations and magnetic fields. Microscopic mechanisms are also proposed to explain i) the counterintuitive effect of dilation under zero or compressive applied mechanical loads for the magnetostriction experiments and ii) the importance of a finite strain constitutive formulation even at small magnetostrictive strains. The model gives an excellent agreement with experiments for relatively moderate magnetic fields but has also been satisfactorily extended to include magnetic fields near saturation

Failure of elasto-plastic porous materials subjected to triaxial loading conditions

National audienceThis work makes use of the recently proposed second-order nonlinear homogenization model (SOM) for (visco)plastic porous materials [1] to study the influence of the Lode parameter and the stress triaxiality on the failure of metallic materials. This model is based on the "second-order" or "generalized secant" homogenization method [2] and is capable of handling general "ellipsoidal" microstructures (i.e., particulate microstructures with more general orthotropic overall anisotropy) and general three-dimensional loading conditions.See http://hal.archives-ouvertes.fr/docs/00/59/26/93/ANNEX/r_A1B5O25U.pd

Influence of the Lode parameter and the stress triaxiality on the failure of elasto-plastic porous materials

International audienceThis work makes use of a recently developed ''second-order'' homogenization model to investigate failure in porous elasto-plastic solids under general triaxial loading conditions. The model incorporates dependence on the porosity and average pore shape, whose evolution is sensitive to the stress triaxiality and Lode parameter L. For positive triaxiality (with overall tensile hydrostatic stress), two different macroscopic failure mechanisms are possible, depending on the level of the triaxiality. At high triaxiality, void growth induces softening of the material, which overtakes the intrinsic strain hardening of the matrix phase, leading to a maximum in the effective stress-strain relation for the porous material, followed by loss of ellipticity by means of dilatant shear localization bands. In this regime, the ductility decreases with increasing triaxiality and is weakly dependent on the Lode parameter, in agreement with earlier theoretical analyses and experimental observations. At low triaxiality, however, a new mechanism comes into play consisting in the abrupt collapse of the voids along a compressive direction (with small, but finite porosity), which can dramatically soften the response of the porous material, leading to a sudden drop in its load-carrying capacity, and to loss of ellipticity of its incremental constitutive relation through localization of deformation. This low-triaxiality failure mechanism leads to a reduction in the ductility of the material as the triaxiality decreases to zero, and is highly dependent on the value of the Lode parameter. Thus, while no void collapse is observed at low triaxiality for axisymmetric tension (L=-1), the ductility of the material drops sharply with decreasing values of the Lode parameter, and is smallest for biaxial tension with axisymmetric compression (L=+1). In addition, the model predicts a sharp transition from the low-triaxiality regime, with increasing ductility, to the high-triaxiality regime, with decreasing ductility, as the failure mechanism switches from void collapse to void growth, and is in qualitative agreement with recent experimental work

Magnetorheological Elastomers: Experiments and Modeling

National audienceMagnetorheological elastomers (MREs) are ferromagnetic particle impregnated elastomers whose mechanical properties are altered by the application of external magnetic fields. Due to their magnetoelastic coupling response MREs are finding an increasing number of engineering applications. The objective of this work is : (a) the experimental study of transversely isotropic MREs (i.e., the particles form chains along a certain direction) that are subjected to prestressing and arbitrary magnetic fields and (b), the phenomenological modeling of these materials using transversely isotropic energy functions.See http://hal.archives-ouvertes.fr/docs/00/59/26/92/ANNEX/r_NHEKI0N4.pd

Enhanced local maximum-entropy approximation for stable meshfree simulations

We introduce an improved meshfree approximation scheme which is based on the local maximum-entropy strategy as a compromise between shape function locality and entropy in an information-theoretical sense. The improved version is specifically designed for severe, finite deformation and offers significantly enhanced stability as opposed to the original formulation. This is achieved by (i) formulating the quasistatic mechanical boundary value problem in a suitable updated-Lagrangian setting, (ii) introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability, (iii) spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency, (iv) truncating shape functions at interfaces in order to stably represent multi-component systems like composites or polycrystals. The new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy (as compared to exact solutions and, where applicable, finite element simulations) and efficiency. Importantly, the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes, as shown for stable simulations of, e.g., the inhomogeneous extension of a hyperelastic block up to 100% or the torsion of a hyperelastic cube by 200° –both in an updated Lagrangian setting and without the need for remeshing

Failure of elasto-plastic porous materials due to void shape effects and void growth

This work makes use of the recently proposed second-order nonlinear homogenization model (SOM) for (visco)plastic porous materials to study the influence of the Lode parameter and the stress triaxiality on the failure of metallic materials. This model is based on the second-order or generalized secant homogenization method and is capable of handling general ellipsoidal void shapes (i.e., particulate microstructures with more general orthotropic overall anisotropy) and general three-dimensional loading conditions

Experimental and theoretical inverstigation of magnetorheological elastomers

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated elastomers whose mechanical properties are altered by the application of external magnetic fields. Due to their magnetoelastic coupling response, MREs are finding an increasing number of engineering applications. The objective of this work is (a) the experimental study of transversely isotropic MREs (i.e., particles form chains along a certain direction) that are subjected to prestressing and arbitrary magnetic fields and (b) the continuum modeling of these materials using transversely isotropic energy functions

Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle

International audienceThis work provides a rigorous analysis of the effective response, i.e., average magnetization and mag-netostriction, of magnetoelastic composites that are subjected to overall magnetic and mechanical loads. It clarifies the differences between a coupled magnetomechanical analysis in which one applies a Eulerian (current) magnetic field and an electroactive one where the Lagrangian (reference) electric field is usually applied. For this, we propose an augmented vector potential variational formulation to carry out numerical periodic homogenization studies of magnetoelastic solids at finite strains and magnetic fields. We show that the developed variational principle can be used for bottom-up design of microstructures with desired magne-tomechanical coupling by properly canceling out the macro-geometry and specimen shape effects. To achieve that we properly treat the average Maxwell stresses arising from the medium surrounding the magnetoelastic representative volume element (RVE) while at the same time we impose a uniform average Eulerian–and not Lagrangian–magnetic field. The developed variational principle is then used to study a large number of ideal as well as more realistic two-dimensional microstructures. We study the effect of particle volume fraction, particle distribution and particle shape and orientation upon the effective magnetoelastic response at finite strains. We consider also unstructured isotropic microstructures based on random adsorption algorithms and we carry out a convergence study of the representativity of the proposed unit cells. Finally, three-phase two-dimensional auxetic microstructures are analyzed. The first consists of a periodic distribution of voids and particle chains in a polymer matrix, while the second takes advantage of particle shape and chirality to produce negative and positive swelling by proper change of the chirality and the applied magnetic field

Bifurcation of magnetorheological film–substrate elastomers subjected to biaxial pre-compression and transverse magnetic fields

International audienceThis work investigates the primary sinusoidal bifurcation wrinkling response of single-and multi-layered magne-torheological elastomer (MRE) film-substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic properties upon the bifurcation response of the system. The analysis is built in a highly versatile manner using a finite-element discretization approach along the direction of the applied magnetic field and Fourier expansions along the infinite in-plane layer directions. This allows for a seamless investigation of various multi-layered structures. First, we analyze the effect of biaxial pre-compression upon the critical magnetic field for a film-substrate system and for various mechanical stiffness ratios. We observe a kink in the critical magnetic curves and a reflection in the corresponding wave numbers as they cross the equi-biaxial pre-compression regime. Subsequently, we consider a MRE film bonded to a MRE substrate and study the effect of the particle volume fraction ratios in those two parts. As a result, we obtain sharp pattern transitions, i.e., long to short wavelengths changes with only minor perturbations of the applied pre-compression. The presence of a magnetic sub-strate changes qualitatively and quantitatively the bifurcation response of the film/substrate system. Finally, we carry out a data-mining exercise to minimize the critical magnetic field at bifurcation by using three different topologies, i.e., a monolayer, a bilayer and a sandwich film. We find that the topologies resembling closely the monolayer one lead to the lowest critical magnetic fields for a given biaxial pre-compression

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

International audienc