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Giant extensional strain of magnetoactive elastomeric cylinders in uniform magnetic fields
Elongations of magnetoactive elastomers (MAEs) under ascending-descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics. © 2020 by the authors.
Robust homoclinic orbits in planar systems with Preisach hysteresis operator
We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.
On forward and inverse uncertainty quantification for models involving hysteresis operators
Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.
Hausdorff metric BV discontinuity of sweeping processes
Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.
Error estimates for nonlinear reaction-diffusion systems involving different diffusion length scales
We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling the microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1 other species may diffuse with the order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we derive quantitative error estimates.
Cartesian product of synchronization transitions and hysteresis
We present theoretical results when applying the Cartesian product of two Kuramoto models on different network topologies. By a detailed mathematical analysis, we prove that the dynamics on the Cartesian product graph can be described by the canonical equations as the Kuramoto model. We show that the order parameter of the Cartesian product is the product of the order parameters of the factors. On the product graph, we observe either continuous or discontinuous synchronization transitions. In addition, under certain conditions, the transition from an initially incoherent state to a coherent one is discontinuous, while the transition from a coherent state to an incoherent one is continuous, presenting a mixture state of first and second order synchronization transitions. Our numerical results are in a good agreement with the theoretical predictions. These results provide new insight for network design and synchronization control.
Topological boundaries between helical domains as a nucleation source of skyrmions in the bulk cubic helimagnet Cu2OSeO3
Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets with a tilted spiral and a low-temperature skyrmion phase arising for magnetic fields applied along the easy crystallographic (100) axes. Although the stabilization mechanism of these phases can be accounted for by cubic magnetic anisotropy, the skyrmion nucleation process is still an open question, since the stability region of the skyrmion phase displays strongly hysteretic behavior with different phase boundaries for increasing and decreasing magnetic fields. Here, we address this important point using micromagnetic simulations and come to the conclusion that skyrmion nucleation is underpinned by the reorientation of spiral domains occurring near the critical magnetic fields of the phase diagrams: HC1, the critical field of the transition between the helical and conical/tiled spiral phase, and HC2, the critical field between the conical/tiled spiral and the homogenous phase. By studying a wide variety of cases we show that domain walls may have a 3D structure. Moreover, they can carry a finite topological charge stemming from half-skyrmions (merons) also permitting along-the-field and perpendicular-to-the-field orientation. Thus, domain walls may be envisioned as nucleation source of skyrmions that can form thermodynamically stable and metastable lattices as well as skyrmion networks with misaligned skyrmion tubes. The results of numerical simulations are discussed in view of recent experimental data on chiral magnets, in particular, for the bulk cubic helimagnet Cu2OSeO3.
Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics
This note deals with the analysis of a model for partial damage, where the rate- independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading.
On forward and inverse uncertainty quantification for models involving hysteresis operators
Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied.