Abstract
This contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior ...components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically, and open hysteresis loops arise with noticeable difference between the first load cycle and the following ones. The Preisach operator plays an important role in describing the input-output relation in hysteresis behaviours, and it can be expressed as a superposition of relay operators. Hence, a mathematical formulation of the problem is introduced, and a first attempt is made to determine the hysteresis behaviour that describes the relation between curvature and bending moment. Therefore, a suitable kernel function is identified in a way that its integration over the Preisach plane results in the bending moment of the specimen, and a comparison between different kernel functions is performed.
We deal with a one-dimensional temperature dependent model for fatigue accumulation in a moving visco-elasto-plastic material in contact with an elasto-plastic obstacle. The problem for the unknown ...displacement and temperature is formulated using hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this problem, consisting of the momentum and energy balance equations and an evolution equation for the fatigue, is obtained using a priori estimates established for the space discretized problem. The uniqueness result follows from the Lipschitz continuity of the nonlinearities.
•New 2-D hysteresis operator for the simulation of Goss-textured ferromagnets at macromagnetic scale-length.•The operator is derived from the classic Stoner–Wohlfarth but the in-plane magnetic ...anisotropy is cubic.•The single hysteron model is defined exploiting only one “moving” hysteresis operator.•Results are especially promising for FEM based calculations, where the magnetization state in each point must be recalculated at each time step.•Numerical accuracy is proved by comparison with measured data.
A new hysteresis operator for the simulation of Goss-textured ferromagnets is here defined. The operator is derived from the classic Stoner–Wohlfarth model, where the anisotropy energy is assumed to be cubic instead of uniaxial, in order to reproduce the magnetic behavior of Goss textured ferromagnetic materials, such as grain-oriented Fe–Si alloys, Ni–Fe alloys, and Ni–Co alloys. A vector hysteresis model based on a single hysteresis operator is then implemented and used for the prediction of the rotational magnetizations that have been measured in a sample of grain-oriented electrical steel. This is especially promising for FEM based calculations, where the magnetization state in each point must be recalculated at each time step. Finally, the computed loops, as well as the magnetic losses, are compared to the measured data.
We propose to model the lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal ...time-periodic process with gas exchange between the interior and exterior of the body. The main result consists in proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.
A problem of motion of a piezoelectric actuator in contact with an elasto-plastic obstacle is reformulated as a PDE in one spatial dimension with hysteresis in the bulk and on the contact boundary. ...The model is shown to dissipate energy in agreement with the principles of thermodynamics. The main result includes existence, uniqueness, and continuous data dependence of solutions.
The focus of this work is on fatigue estimation and data-based controller design for wind turbines. The main purpose is to include a model of the fatigue damage of the wind turbine components in the ...controller design and synthesis process. This study addresses an online fatigue estimation method based on hysteresis operators, which can be used in control loops. The authors propose a data-based model predictive control (MPC) strategy that incorporates an online fatigue estimation method through the objective function, where the ultimate goal in mind is to reduce the fatigue damage of the wind turbine components. The outcome is an adaptive or self-tuning MPC strategy for wind turbine fatigue damage reduction, which relies on parameter identification on previous measurement data. The results of the proposed strategy are compared with a baseline model predictive controller.
This paper focuses on a dynamical model for the motion of a visco-elasto-plastic body in contact with an elasto-plastic obstacle. The elastoplastic constitutive laws as well as the contact boundary ...condition are stated in terms of hysteresis operators. Under appropriate regularity assumptions on the initial data, we show that the resulting partial differential equation with hysteresis possesses a unique solution which is constructed by Galerkin approximations and the Minty trick. In the 1D case, the existence and uniqueness proof can be carried out without the viscosity assumption, and the necessary a priori estimates are derived from a hysteresis second order energy inequality.
The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the ...third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.
We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This ...constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well‐posed under the hypothesis that hysteretic effects take place only in one preferred direction. We prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.
The authors propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well‐posed under the hypothesis that hysteretic effects take place only in one preferred direction. They prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.
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