A Large-Deformation Phase-Field Approach for the Modeling of Magneto-Sensitive Elastomers

Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magneto-mechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1, 7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A simple 1D model of inviscid fluid-solid interaction

We analyze a one-dimensional fluid-particle interaction model, composed by the Burgers equation for the fluid velocity and an ordinary differential equation which governs the particle movement. The coupling is achieved through a friction term. One of the novelties is to consider entropy weak solutions involving shock waves. The difficulty is the interaction between these shock waves and the particle. We prove that the Riemann problem with arbitrary data always admits a solution, which is explicitly constructed. Besides, two asymptotic behaviors are described: the long-time behavior and the behavior for large friction coefficients.     

Homogenization of a three-phase flow model in porous media

We give homogenization results for an immiscible and incompressible three-phase flow model in a heterogeneous petroleum reservoir with periodic structure, including capillary effects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection–diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the flow. The determination of effective properties require the numerical resolution of local problems in a standard cell.     

A phenomenological constitutive model for magnetostrictive materials and ferroelectric ceramics

The contribution is concerned with a thermodynamic consistent constitutive model for magnetostrictive materials and ferroelectric ceramics. It captures the nonlinear phenomenological behavior which is described by hysteresis effects. Magnetostrictive alloys and ferroelectric ceramics belong to the multifunctional materials. In recent years these materials have become widely–used in actor and sensor applications. They characterize an inherent coupling between deformation and magnetic or electric field. Due to the similarities of the coupled differential equations a uniform approach is applied for both phenomena. The presented three–dimensional material model is thermodynamically motivated. It is based on the definition of a specific free energy function and a switching criterion. Furthermore an additive split of strain and the magnetic or electric field in a reversible and an irreversible part is suggested. The irreversible quantities serve as internal variables, which is analog to plasticity theory. A one–to–one–relation between the two internal variables provides conservation of volume for the irreversible strains. The presented material model can approximate the ferromagnetic or ferroelectric hysteresis curve and the related butterfly hysteresis. Furthermore an extended approach for ferrimagnetic behavior, which occurs in magnetostrictive materials, is presented. Some numerical simulations demonstrate the capability of the presented model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An anisotropic viscoelastic soft tissue model at large strains

Soft biological tissues represent complex inhomogeneous, and as a rule multiphase materials subjected to large strains under in vivo mechanical conditions. Apart from a number of other structural-related features they are characterized by a ratedependent material behavior which is attributed to fluid-solid interactions as well as intrinsic viscoelastic properties of the solid matrix. The authors propose to model rate-dependent phenomena of the solid phase of soft biological tissues within the context of a thermodynamically consistent phenomenological material approach resulting from an overstress concept. Due to the presence of directed fibrous constituents soft tissues should be considered as anisotropic materials. Therefore, the viscous overstress model has been completed by a transversely isotropic approach. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于断裂能的岩土节理弹性-软化塑性本构模型

基于准脆性材料的断裂力学和塑性理论,提出了用于岩土节理软化行为描述的弹性软化塑性本构模型.模型的主要特点是:1)节理材料的软化塑性和扩容特性直接与断裂失效过程相联系,所采用的材料参数比已有的弹塑性软化模型所用的参数少;2)模型可以描述混合断裂失效及相应的摩擦滑动,具有较广的适用性.     

A FLUID-PARTICLE MODEL WITH ELECTRIC FIELDS NEAR A LOCAL MAXWELLIAN WITH RAREFACTION WAVE

The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and inviscid fluid by Euler-Poisson equations through the relaxation drag frictions, Vlasov forces between the macroscopic and microscopic momentums and the electrostatic potential forces. Precisely, based on a new micro-macro decomposition around the local Maxwellian to the kinetic part of the fluid-particle coupled system, which was first developed in [16], we show the time-asymptotically nonlinear stability of rarefaction wave to the one-dimensional compressible inviscid Euler equations coupled with both the Vlasov-Fokker-Planck equation and Poisson equation.     

Micro-mechanical study of interactions between polymers and filler aggregates

Filled rubber-like materials exhibit a complex, history-dependent hysteretic behavior which is mostly due to damage of micro-structures inside the rubber matrix. In this paper, we study the contribution of filler aggregates inside the elastomer to this damage behavior. To this end, a recently proposed multi-scale model of single aggregates [1] is applied. The network decomposition concept adopted there is further extended here to an additional network [1] which takes into account elasticity of filler aggregates and polymer chains in their vicinity. This network is described by means of a 3D statistical volume element (SVE) obtained by homogenization over the aggregate size distribution within the rubber matrix. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Day-to-Day Buying Policy for Commodities — A Study of Purchasing Maize

The majority of the imported raw materials used by European industry have to be purchased in commodity markets where prices fluctuate over time. The overall purchasing decision contains several component stages. The work described in this paper concentrates on the final stage of this process, the tactical buying policy. A major difficulty lies in the definition of a proper measure of performance, so as to assess the merits of any proposed buying policy. The measures previously suggested by Kingsman and Taylor are discussed, and a new measure, thought to be more appropriate, is put forward. The paper describes a new heuristic buying policy, which is applied to the purchasing of maize. The policy uses Taylor's price-trend forecasting model and leads to purchasing costs which are shown to be significantly lower than the average market prices and better than those obtained from Kingsman's pricebreak policy.     

Numerical techniques for ice masses dyamics simulation by using a complete shallow ice approximation

In this work a complex coupled shallow ice model which governs the thermal, hydrodynamic and mechanical processes in the dynamics of large ice masses is proposed and solved by means of efficient numerical techniques. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isotropic continuum damage/repair model for alveolar bone remodeling

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an adaptative elasticity behavior or an update of the elasticity constants with density evolution. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear reversible elasticity. It leads to permanent deformations due to biochemical actions. The proposed biomechanical constitutive law, inspired from Doblaré and García (2002) [30], is based on a elasto-viscoplastic material coupled with Continuum isotropic Damage Mechanics (Doblaré and García (2002) [30] considered only the case of a linear elastic material coupled with damage). The considered damage variable is not actual damage of the tissue but a measure of bone density. The damage evolution law therefore implies a density evolution. It is here formulated as to be used explicitly for alveolar bone, whose remodeling cells are considered to be triggered by the pressure state applied to the bone matrix. A 2D model of a tooth submitted to a tipping movement, is presented. Results show a reliable qualitative prediction of bone density variation around a tooth submitted to orthodontic forces.     

Numerical solution of a thermomechanical coupled model governing glacier evolution

In this paper the numerical solution of a highly nonlinear model for the thermomechanical behavior of polythermal glaciers is presented. The modeling follows the shallow ice approximation (SIA) for glaciers introduced in Fowler (1997) [13]. The model has been extended to incorporate additional moving boundaries and other nonlinear features. Moreover, a fixed domain formulation is proposed to avoid the computational drawbacks of a time-dependent domain in the numerical simulation with front tracking methods. In this setting, the coupled problem is decomposed into different nonlinear problems which allow one to obtain sequentially the profile evolution, the velocity field, the glacier surface and atmospheric temperatures, basal magnitudes and the temperature distribution inside the ice mass. A fixed point iteration algorithm converges to the solution of the nonlinear coupled problem. Among different numerical methods involved in the solution of the subproblems, characteristic schemes for time discretization, finite elements for spatial discretization, duality methods for the nonlinearities associated to maximal monotone operators and a Newton scheme for the nonlinear viscous term are proposed. Several numerical simulation examples illustrate the performance of the numerical methods and the behavior of the involved physical magnitudes.     

Aspects of the simulation of the ferroelectric hysteresis

In this paper we present a thermodynamically consistent phenomenological model for an assumed transversely isotropic ferroelectric crystal. Such materials become spontaneously polarized within a certain range of temperature. On the macro scale a remanent polarization and remanent strains, due to the reorientation of the polarization vectors, are observed, if an electric field above the so-called coercive field is applied. The goal of this work is to construct a thermodynamically consistent formulation of the electro-mechanically coupled ceramic on a meso scale, that takes into account the orientation of the assumed transversely isotropic unit cell, see [4]. The anisotropic behavior is governed by isotropic tensor functions, which are formulated in terms of a finite set of invariants, see [3]. Considering a simple model problem we discuss the linearization of discrete weak forms, resulting from the electromechanical boundary value problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Phase Field Modeling of Laminate Deformation Microstructure in Finite Gradient Crystal Plasticity

The macroscopic mechanical behavior of many materials crucially depends on the formation and evolution of their microstructure. In this work, we consider the formation and evolution of laminate deformation microstructure in plasticity. Inspired by work on the variational modeling of phase transformation [5] and building on related work on multislip gradient crystal plasticity [9], we present a new finite strain model for the formation and evolution of laminate deformation microstructure in double slip gradient crystal plasticity. Basic ingredients of our model are a nonconvex hardening potential and two gradient terms accounting for geometrically necessary dislocations (GNDs) by use of the dislocation density tensor and regularizing the sharp interfaces between different kinematically coherent plastic slip states. The plastic evolution is described by means of a nonsmooth dissipation potential for which we propose a new regularization. We formulate a continuous gradient-extended rate-variational framework and discretize it in time to obtain an incremental-variational formulation. Discretization in space yields a finite element formulation which is used to demonstrate the capability of our model to predict the formation and evolution of laminate deformation microstructure in f.c.c. Copper with two active slip systems in the same slip plane. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A thermodynamical consistent model for modeling of ionic electroactive polymers (EAPs) within the framework of the Theory of Porous Media

Ionic electroactive polymers are widely used in many engineering fields. These kind of materials can be stimulated to change their shape and size, see [1]. Since, the material under consideration has a complex multiphasic microstructure, such multiphasic materials are best described by a continuum mechanical approach. Thus, the presented model is based on the Theory of Porous Media (TPM), cf. [2]. In this contribution, we consider the Ionic Polymer Metal Composites (IPMCs). Stimulating by an electrical voltage, a structural deformation will be caused. Responsible for this deformation are the mobile ions. The focus of the presented model is to capture this material behavior, e.g. the distribution of the mobile cations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A modified coupled map car following model and its traffic congestion analysis

Based on the coupled map car following model which was presented by Konishi et al. [Konishi KJ, Kokame H, Hirate K. Phys Rev E 1999;60:4000-7.] (for short, KKH), a modified coupled map car following model is proposed. In this model two successive vehicles’ headway distances in front of the considered one are incorporated in the optimal velocity (for short, OV) function. The stability condition is given for the change of the speed of the preceding vehicle on the base of the control theory. The control scheme in KKH model is applied to the modified model and the feedback gains are determined. Comparison between the modified model and KKH model is carried out. And the corresponding numerical simulation results show that the temporal behavior obtained by our model is better than that by KKH model. The simulation results are in good agreement with the theoretical analysis.     

Existence of a solution for a thermoelectric model with several phase changes and a Carathéodory thermal conductivity

We present an existence result for the time domain eddy current model for electromagnetic field, coupled with a Stefan problem for temperature. We have extended the existence result proved by Bermúdez et al. (2005) [40] to the case of materials with several phase changes and thermal conductivity depending on both position and temperature.The new proof starts from a totally implicit time discretization of a truncated system. The thermal part can be rewritten as a variational inequality of the second kind. Then, a priori estimates independent of the truncation parameter are obtained for the solution of the truncated problem, using a technique that adapts the method of Boccardo and Gallouët (1989)  [28] to the case of materials with several phase changes.     

Convergence of Clock Processes and Aging in Metropolis Dynamics of a Truncated REM

We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law distribution function, almost surely in the random environment and in the full range of time scales and temperatures for which such a result can be expected to hold. This establishes that the dynamics ages in the same way as Bouchaud’s REM-like trap model, thus extending the universality class of the latter model. The proof relies on a clock process convergence result of a new type where the number of summands is itself a clock process. This reflects the fact that the exploration process of Metropolis dynamics is itself an aging process, governed by its own clock. Both clock processes are shown to converge to stable subordinators below certain critical lines in their time-scale and temperature domains, almost surely in the random environment.     

Irregular modulation of non-linear Alfvén/Beltrami wave coupled with an ion-sound wave

A singularity of a system of differential equations may produce “intrinsic” solutions that are independent of initial or boundary conditions—such solutions represent “irregular behavior” uncontrolled by external conditions. In the recently formulated non-linear model of Alfvén/Beltrami waves [Commum Nonlinear Sci Numer Simulat 17 (2012) 2223], we find a singularity occurring at the resonance of the Alfvén velocity and sound velocity, from which pulses bifurcate irregularly. By assuming a stationary waveform, we obtain a sufficient number of constants of motion to reduce the system of coupled ordinary differential equations (ODEs) into a single separable ODE that is readily integrated. However, there is a singularity in the separable equation that breaks the Lipschitz continuity, allowing irregular solutions to bifurcate. Apart from the singularity, we obtain solitary wave solutions and oscillatory solutions depending on control parameters (constants of motion).