Dissipative Materials Research Articles

Laminate-based modelling of single and polycrystalline ferroelectric materials – application to tetragonal barium titanate

The present contribution deals with the development of a laminate-based model designed to study the single and polycrystalline tetragonal ferroelectric material behaviour. Laminate-based models are micromechanically motivated and consider the volume fraction of the distinct ferroelectric variants directly in their formulation. At first, a single crystal laminate-based model is established by considering the average strain and polarisation compatibility conditions. A suitable thermodynamic electric Gibbs energy and a rate-dependent dissipation equation are postulated to capture the dissipative hysteretic material response. The update of the inequality constrained volume fractions is solved by adopting a Fischer–Burmeister-type algorithm in combination with a Newton–Raphson scheme. Following the single crystal formulation, a homogenisation procedure based on random orientation of the individual grains in a polycrystalline aggregate is considered. The material properties and the polarisation switching response of the randomly oriented individual grains are averaged using a finite element framework in order to study the macroscopic polycrystalline behaviour. A parameter fitting procedure based on experimental data for single crystalline response, taken from the literature, is detailed and the material model as well as the algorithmic scheme are verified by solving representative boundary value problems. Moreover, the finite element based simulation results are compared with newly generated experimental hysteresis data for a barium titanate piezoceramic.

On the experimental analysis of dissipative processes under cyclic loading of metals

The article is devoted to the experimental study of dissipative material properties tested under homogeneous stress-strain conditions, which realized on the gage part of a smooth sample subjected to cyclic loading with increasing amplitude. A new method to estimate inelastic material properties under strain lower than the nominal strength is proposed. At the initial stages of loading, the method makes it possible to find out irreversible changes in sample characteristics and define material elastic limit under cyclic loading. Strain, longitudinal and lateral stress, as well as temperature of the gage part of a sample are the sample characteristics measured simultaneously. They make it possible to distinguish the components connected with reversible and irreversible strain processes associated with fatigue damage of material.

Numerical modeling of sound and vibration reduction using viscoelastic materials and shunted piezoelectric patches

In this paper, a reduced order coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by viscoelastic and passive piezoelectric treatments is presented. The system consists of a sandwich structure composed of elastic faces and a viscoelastic core (with surface mounted piezoelectric patches) and coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low-frequency range while dissipative viscoelastic materials are used for the higher-frequency domain. The originality of the present paper lies (i) in evaluating the classically used FEM/BEM methods for structural-acoustics problems when taking account smart systems at the fluid-structure interfaces and viscoelastic interlayers and (ii) in development of a reduced-order model, based on a normal mode expansion, able to capture the main characteristics of the system dynamical behavior.

A constitutive multiphysics modeling for nearly incompressible dissipative materials: application to thermo–chemo-mechanical aging of rubbers

In this paper we investigate the modeling of chemo-physical evolution due to thermo-mechanical loadings at finite strain in soft materials. In particular we discuss the question of a proper and consistent thermodynamical formulation in the case of nearly incompressible materials. The objective of this phenomenological modeling is to represent the thermo–chemo-mechanical aging that occurs in filled rubbers during high-cycle fatigue for some specific loading conditions.

High-phase-speed Dyakonov–Tamm surface waves

Two numerical studies, one based on a canonical boundary-value problem and the other based on a reflection-transmission problem, revealed that the propagation of high-phase-speed Dyakonov-Tamm (HPSDT) surface waves may be supported by the planar interface of a chiral sculptured thin film and a dissipative isotropic dielectric material. Furthermore, many distinct HPSDT surface waves may propagate in a specific direction, each with a phase speed exceeding the phase speed of plane waves that can propagate in the isotropic partnering material. Indeed, for the particular numerical example considered, the phase speed of an HPSDT surface wave could exceed the phase speed in bulk isotropic dielectric material by a factor of as much as 10.

Temperature-mediated transition from Dyakonov–Tamm surface waves to surface-plasmon-polariton waves

The effect of changing the temperature on the propagation of electromagnetic surface waves (ESWs), guided by the planar interface of a homogeneous isotropic temperature-sensitive material (namely, InSb) and a temperature-insensitive structurally chiral material (SCM) was numerically investigated in the terahertz frequency regime. As the temperature rises, InSb transforms from a dissipative dielectric material to a dissipative plasmonic material. Correspondingly, the ESWs transmute from Dyakonov–Tamm surface waves into surface-plasmon-polariton waves. The effects of the temperature change are clearly observed in the phase speeds, propagation distances, angular existence domains, multiplicity, and spatial profiles of energy flow of the ESWs. Remarkably large propagation distances can be achieved; in such instances the energy of an ESW is confined almost entirely within the SCM. For certain propagation directions, simultaneous excitation of two ESWs with (i) the same phase speeds but different propagation distances or (ii) the same propagation distances but different phase speeds are also indicated by our results.

Mathematical homogenization of inelastic dissipative materials: a survey and recent progress

In this paper, a review of papers on mathematical homogenization of dissipative composites under small strains and on the interplay between homogenization procedure and dissipation due to mechanical work is presented. Moreover, a critical survey on the links between mathematical homogenization and computational homogenization is attempted.

On Thermodynamic Consistency of Homogenization-Based Multiscale Theories

In this paper, the necessary and sufficient conditions for fulfilling the thermodynamic consistency of computational homogenization schemes in the framework of hierarchical multiscale theories are defined. The proposal is valid for arbitrary homogenization based multiscale procedures, including continuum and discontinuum methods in either scale. It is demonstrated that the well-known Hill–Mandel variational criterion for homogenization scheme is a necessary, but not a sufficient condition for the micro–macro thermodynamic consistency when dissipative material responses are involved at any scale. In this sense, the additional condition to be fulfilled considering that the multiscale thermodynamic consistency is established. The general case of temperature-dependent, higher order elastoplasticity is considered as theoretical framework to account for the material dissipation at micro and macro scales of observation. It is shown that the thermodynamic consistency enforces the homogenization of the nonlocal terms of the finer scale's free energy density; however, this does not lead to nonlocal gradient effects on the coarse scale. Then, the particular cases of local isothermal elastoplasticity and continuum damage are considered for the purpose of the proposed thermodynamically consistent approach for multiscale homogenizations.

A novel essential work of fracture experimental methodology for highly dissipative materials

Determining fracture toughness for soft, highly dissipative, solids has been a challenge for several decades. Amongst the limited experimental options for such materials is the essential work of fracture (EWF) method. However, EWF data are known to be strongly influenced by specimen size and test speed. In contrast to time-consuming imaging techniques that have been suggested to address such issues, a simple and reproducible method is proposed. The method accounts for diffuse dissipation in the specimen while ensuring consistent strain rates by scaling both the sample size and testing speed with ligament length. We compare this new method to current practice for two polymers: a starch based food and a polyethylene (PE) tape. Our new method gives a size independent and more conservative fracture toughness. It provides key-data, essential in numerical models of the evolution of structure breakdown in soft solids as seen for example during oral processing of foods.

Plasma-Enhanced Atomic Layer Deposition of Two-Dimensional WS2 from WF6, H2 Plasma, and H2S

Two-dimensional (2D) transition metal dichalcogenides are potential low dissipative semiconductor materials for nanoelectronic devices. Such applications require the deposition of these materials in their crystalline form and with controlled number of monolayers on large area substrates, preferably using deposition temperatures compatible with temperature sensitive structures. This paper presents a low temperature plasma-enhanced atomic layer deposition (PEALD) process for 2D WS2 based on a ternary reaction cycle consisting of consecutive WF6, H2 plasma, and H2S reactions. Strongly textured, nanocrystalline WS2 is grown at 300 °C. The composition and crystallinity of these layers depends on the PEALD process conditions, as understood by a model for the redox chemistry of this process. The H2 plasma is essential for the deposition of WS2 as it enables the reduction of −W6+Fx surface species. Nevertheless, the impact of subsurface reduction reactions needs to be minimized to obtain WS2 with well-controlled ...

SmEdA vibro-acoustic modelling in the mid-frequency range including the effect of dissipative treatments

Vibro-acoustic simulation in the mid-frequency range is of interest for automotive and truck constructors. The dissipative treatments used for noise and vibration control such as viscoelastic patches and acoustic absorbing materials must be taken into account in the problem. The Statistical modal Energy distribution Analysis (SmEdA) model consists in extending Statistical Energy Analysis (SEA) to the mid-frequency range by establishing power balance equations between the modes of the different subsystems. The modal basis of uncoupled-subsystems that can be estimated by the finite element method in the mid-frequency range is used as input data. SmEdA was originally developed by considering constant modal damping factors for each subsystem. However, this means that it cannot describe the local distribution of dissipative materials. To overcome this issue, a methodology is proposed here to take into account the effect of these materials. This methodology is based on the finite element models of the subsystems that include well-known homogenized material models of dissipative treatments. The Galerkin method with subsystem normal modes is used to estimate the modal damping loss factors. Cross-modal coupling terms which appear in the formulation due to the dissipative materials are assumed to be negligible. An approximation of the energy sharing between the subsystems damped by dissipative materials is then described by SmEdA. The different steps of the method are validated experimentally by applying it to a laboratory test case composed of a plate-cavity system with different configurations of dissipative treatments. The comparison between the experimental and the simulation results shows good agreement in the mid-frequency range.

Computational homogenization of mesoscale gradient viscoplasticity

Variationally consistent selective homogenization is applied to a class of gradient-enhanced dissipative materials which is adopted for the mesoscale modeling. The adopted standard first order homogenization assumption results in the classical equilibrium equation for a local continuum on the macroscale, while the internal variables “live” on the mesoscale only. Among the issues considered in the paper, we note (i) the variationally consistent setting of homogenization of gradient theory on the mesoscale, (ii) the variational basis of the SVE-problem (SVE = Statistical Volume Element) in the time-incremental setting. The SVE-problem is formulated for the classical boundary conditions (Dirichlet and Neumann) pertinent to the standard momentum balance as well as the “micro-momentum” balance. The weak format of the SVE-problem constitutes the stationarity condition of an incremental SVE-potential, which represents an extension of the situation for a single-phase continuum model. The macroscale stress in a given time-increment is derivable from an incremental “macroscale pseudo-elastic strain energy”. Moreover, the saddle-point properties of the SVE-potential are shown to form the basis for establishing upper and lower bounds on the pseudo-elastic strain energy. Bingham viscoplasticity with gradient-enhanced hardening is chosen as the prototype model problem for the numerical evaluation. The computed stress–strain response relations confirm the theoretical predictions of the influence of different combinations of boundary conditions on the SVE.

Granular compaction and the topology of pore deformation

The mechanism of crystallisation in highly dissipative materials such as foams or granular materials is still widely unknown. In macroscopic granular materials high levels of energy need to be injected to overcome the natural propensity of these dissipative materials to form amorphous structures [1, 2]. The transition from disordered to ordered packings in such systems triggers a wide range of geometrical, topological and mechanical changes at multi length scales [3]. Formation of cavities and patterns by aggregates of grains and their evolution during this transition requires a complete topological description of the system. Here, crystallisation of three-dimensional packings of frictional spheres is studied at the grain scale with x-ray tomography. Using a novel and powerful topological tool, Persistent Homology, we describe the complete formation process of perfect tetrahedral and octahedral patterns: the two building blocks of FCC and HCP crystalline arrangements. Additionally we present possible and allowable deformations of these components that accurately reproduce the main topological features of the system. These results give new insights into the crystallisation of these highly dissipative materials.

Dissipative out-of-equilibrium assembly of man-made supramolecular materials.

The use of dissipative self-assembly driven by chemical reaction networks for the creation of unique structures is gaining in popularity. In dissipative self-assembly, precursors are converted into self-assembling building blocks by the conversion of a source of energy, typically a photon or a fuel molecule. The self-assembling building block is intrinsically unstable and spontaneously reverts to its original precursor, thus giving the building block a limited lifetime. As a result, its presence is kinetically controlled, which gives the associated supramolecular material unique properties. For instance, formation and properties of these materials can be controlled over space and time by the kinetics of the coupled reaction network, they are autonomously self-healing and they are highly adaptive to small changes in their environment. By means of an example of a biological dissipative self-assembled material, the unique concepts at the basis of these supramolecular materials will be discussed. We then review recent efforts towards man-made dissipative assembly of structures and how their unique material properties have been characterized. In order to help further the field, we close with loosely defined design rules that are at the basis of the discussed examples.

Analysis of a system related to a model for phase transitions in dissipative isochoric thermoviscoelastic materials

We analyze a highly nonlinear system of partial differential equations related to a model solidification and/or melting of thermoviscoelastic isochoric materials with the possibility of motion of the material during the process. This system consists of an internal energy balance equation governing the evolution of temperature, coupled with an evolution equation for a phase field whose values describe the state of material and a balance equation for the linear moments governing the material displacements. For this system, under suitable dissipation conditions, we prove global existence and uniqueness of weak solutions. Copyright © 2016 John Wiley & Sons, Ltd.

Real-space Hopfield diagonalization of inhomogeneous dispersive media

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields, and we invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory can be naturally extended to the case of dissipative materials.

Novel nanofibrillated cellulose/polyvinylpyrrolidone/silver nanoparticles films with electrical conductivity properties

Nanofibrillated cellulose (NFC) isolated from rice straw pulp was used with polyvinylpyrrolidone (PVP) and silver nanoparticles (AgNPs) to prepare nanocomposites in the form of flexible films. The later films have promising mechanical and electrical conductivity properties. The isolated cellulose nanofibers were characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). Silver nanoparticles prepared via in-situ reduction in PVP were characterized using TEM and UV–vis spectroscopy. Tensile properties, microscopic structure, and electrical properties of nanocomposites films were studied. TEM and UV–vis spectroscopy proved the in-situ formation of AgNPs in PVP matrix. Films with good flexibility and tensile strength properties could be obtained from NFC/PVP/AgNPs as revealed from the (SEM) images and tensile properties testing. The electrical conductivity of NFC/PVP/AgNPs supports this system to be an excellent choice for sensitive electronic components packing as it can be used as antistatic and electrostatic dissipative materials.

On the propagation of Voigt waves in energetically active materials

If Voigt-wave propagation is possible in a dissipative anisotropic dielectric material characterised by the permittivity dyadic , then it is also possible in the analogous energetically active material characterised by the permittivity dyadic , where is the hermitian conjugate of . This symmetry follows directly from a theoretical analysis of the necessary and sufficient conditions for Voigt-wave propagation in anisotropic materials. As a consequence of this symmetry, a porous dissipative material that exhibits Voigt-wave propagation can be used to construct a material that allows the propagation of Voigt waves with attendant linear gain in amplitude with propagation distance, by means of infiltration with an electrically or optically activated dye, for example. This phenomenon is captured by the Bruggeman formalism for homogenised composite materials based on isotropic dielectric component materials that are randomly distributed as oriented spheroidal particles.

Multiple scales of shock waves in dissipative laminate materials.

The shock waves generated by a plate impact are numerically investigated in Al-W laminates with different mesostructures. The main characteristic time scales (and the corresponding spatial scales) related to the formation of the stationary shock are identified: the duration (width) of the leading front, the time (distance) from the impact required to establish a stationary profile, and the shock front width, identified as a time span (distance) from the initial state to the final quasiequilibrium state. It is demonstrated that the width of the leading front and the maximum strain rates are determined by the dispersive and the nonlinear parameters of the laminate and not by the dissipation, as is the case for uniform solids. The characteristic spatial scale of the leading front is related to the spatial scale observed on solitarylike waves, which are satisfactorily described by the Korteweg-de Vries (KdV) approximation, as well as the speed of the wave and the ratio of maximum to final strain. The dissipation affects the width of the transition distance (shock front width) where multiple loading-unloading cycles bring the laminate into the final quasiequilibrium state. This spatial scale is of the same order of magnitude as the distance to form stationary shock wave. The period of fast decaying oscillations is well described by the KdV approach and scales linearly with the cell size. The rate of the decay of the oscillations in the numerical calculations does not scale with the square of the cell size as expected from the dissipative KdV approach that assumes a constant viscosity. This is due to the different mechanisms of dissipation in high-amplitude compression pulses.

Nonlinear Microstructured Material to Reduce Noise and Vibrations at Low Frequencies

At low frequencies, for which the wavelengths are wide, the acoustic waves and the mechanical vibrations cannot easily be reduced in the structures at macroscale by using dissipative materials, contrarily to the middle- and high-frequency ranges. The final objective of this work is to reduce the vibrations and the induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix. The dynamical regimes of the inclusions will be imposed in the nonlinear domain in order that the energy be effectively pumped over a broad frequency band around the resonance frequency, due to the nonlinearity. The first step of this work is to design and to analyze the efficiency of an inclusion, which is made up of a hollow frame including a point mass centered on a beam. This inclusion is designed in order to exhibit nonlinear geometric effects in the low-frequency band that is observed. For this first step, the objective is to develop the simplest mechanical model that has the capability to roughly predict the experimental results that are measured. The second step, which is not presented in the paper, will consist in developing a more sophisticated nonlinear dynamical model of the inclusion. In this paper, devoted to the first step, it is proved that the nonlinearity induces an attenuation on a broad frequency band around the resonance, contrarily to its linear behavior for which the attenuation is only active in a narrow frequency band around the resonance. We will present the design in terms of geometry, dimension and materials for the inclusion, the experimental manufacturing of this system realized with a 3D printing system, and the experimental measures that have been performed. We compare the prevision given by the stochastic computational model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, which were expected.