Elastic composite materials having a negative stiffness phase can be stable

We prove that composite materials containing an isotropic phase having negative bulk and Young's moduli (hence being unstable by itself) can be stable overall, under merely applied traction boundary conditions, if the stable encapsulating phase is sufficiently stiff. We derive specific quantitative requirements on the elastic moduli of the constituent materials that ensure composite stability for two fundamental composite geometries. These results legitimize the concept of negative-stiffness-phase composites, thus dramatically expanding the parameter landscape in which novel and optimal overall material properties may be sought.     

Negative stiffness-induced extreme viscoelastic mechanical properties: stability and dynamics

Use of negative stiffness inclusions allows one to exceed the classic bounds upon overall mechanical properties of composite materials. We here analyse discrete viscoelastic ‘spring’ systems with negative stiffness elements to demonstrate the origin of extreme properties, and analyse the stability and dynamics of the systems. Two different models are analysed: one requires geometrical nonlinear analysis with pre-load as a negative stiffness source and the other is a linearized model with a direct application of negative stiffness. Material linearity is assumed for both models. The metastability is controlled by a viscous element. In the stable regime, extreme high mechanical damping tan?δ can be obtained at low frequency. In the metastable regime, singular resonance-like responses occur in tan?δ. The pre-stressed viscoelastic system is stable at the equilibrium point with maximal overall compliance and is metastable when tuned for maximal overall stiffness. A reversal in the relationship between the magnitude of complex modulus and frequency is also observed. The experimental observability of the singularities in tan?δ is discussed in the context of designed composites and polycrystalline solids with metastable grain boundaries.     

Micromechanical modelling of an arbitrary ellipsoidal multi-coated inclusion

The present work aims to provide a general framework to deal with an elementary heterogeneous problem, where the inhomogeneity consists of an n-layered inclusion composed of n concentric ellipsoids made of anisotropic elastic materials. The methodology is based on a combination of Green's function techniques with interface operators, illustrating the stress and strain jump conditions at the interfaces between two adjacent coatings, which are considered perfectly bonded. The model is validated in the case of double-coated spherical inclusions made of isotropic materials, where the obtained analytical results cover the exact solution of Hervé and Zaoui. The model can be applied, after adequate choice of scale-transition methods, to describe the overall behaviour of real composite materials with complex microstructures that are significantly influenced by the presence of interphase layers between constituents (fillers and matrix). Such composites are widely employed in automotive and aerospace industries. As a typical example one can consider a composite with an epoxy matrix reinforced by glass beads coated using a thin soft polymeric phase or syntactic foams particulate composites obtained by filling a polymeric matrix with hollow solid inclusions.     

Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.     

Elastic interaction and the phase transition in coherent metal-hydrogen systems

We study the statistical mechanics of hydrogen dissolved in metals. The underlying model is based on the assumption that the dominant attractive interaction between the protons in the metal is of an elastic nature.

In the first part of the paper we review some general properties of the elastic interaction. We then discuss the importance of boundary conditions for the form of the elastic interaction, which turns out to be of the Curie-Weiss type with macroscopic range.

In the second part we investigate the a-a' (‘gas-liquid’) phase transition in the hydrogen lattice fluid. The long-range part of the elastic interaction is treated in mean field approximation. In the canonical ensemble as opposed to the grand canonical ensemble one finds no co-existing phases near the critical point. Instead there is a continuous transition which changes into a first-order transition at tricritical points. In the temperature-density region which normally corresponds to the two-phase co-existence region the hydrogen density is inhomogeneous and varies on a macroscopic scale.

The peculiar nature of the a-a' phase transition is due to the long-range character of the elastic interaction, which ultimately results from the requirement of coherency of the host crystal. We argue that coherent metal-hydrogen systems offer examples of real systems where the classical theory of phase transitions applies.     

Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain,a boundary integral method

We consider numerical algorithms for the simulation of hydrodynamics of two-dimensional vesicles suspended in a viscous Stokesian fluid. The motion of vesicles is governed by the interplay between hydrodynamic and elastic forces. Continuum models of vesicles use a two-phase fluid system with interfacial forces that include tension (to maintain local “surface” inextensibility) and bending. Vesicle flows are challenging to simulate. On the one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives in the bending term. On the other hand, implicit time-stepping schemes can be expensive because they require the solution of a set of nonlinear equations at each time step.     

A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a level set to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the level set function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.     

Tunable two-phase coexistence in half-doped manganites

We discuss our very interesting experimental observation that the low-temperature two-phase coexistence in half-doped manganites is multi-valued (at any field) in that we can tune the coexisting antiferromagnetic-insulating (AF-I) and the ferromagnetic-metallic (FM-M) phase fractions by following different paths in (H, T) space. We have shown experimentally that the phase fraction, in this two-phase coexistence, can take continuous infinity of values. All but one of these are metastable, and two-phase coexistence is not an equilibrium state.      

Interfacial reactions and microstructure control in metal and intermetallic matrix composite processing

The achievement of the potential of composites for demanding applications where high specific strength and stiffness are required together with useful toughness is often limited by the available materials processing capabilities to develop specific reinforcement-matrix interface characteristics. Similarly, the elevated temperature stability of advanced composites is dominated by the behavior of internal interfaces. In order to develop effective processing strategies and stable composite designs, it is essential to consider the relevant phase diagrams which for most composites are at least of ternary order. On the basis of these diagrams, it is possible to select compositions of phases which possess desirable properties. In addition to phase diagram data, kinetic data such as the interdiffusion pathway and rates are required to understand and to control the possible interfacial chemical reactions in a composite system. From this basis, reinforcement coatings and barrier layers can be developed to control reactions and allow for in-service lifetime analysis. With solidification processing of composites, melt-reinforcement interactions involved in wetting, solidification reactions, and matrix microstructure evolution can also be evaluated in terms of the phase equilibria and kinetic pathways. Some applications of this approach have been demonstrated in the development of Ti- and A1-based composite systems.     

Ab initio study of anisotropic mechanical and electronic properties of strained carbon-nitride nanosheet with interlayer bonding

Due to the noticeable structural similarity and being neighborhood in periodic table of group-IV and-V elemental monolayers, whether the combination of group-IV and-V elements could have stable nanosheet structures with optimistic properties has attracted great research interest. In this work, we performed first-principles simulations to investigate the elastic, vibrational and electronic properties of the carbon nitride (CN) nanosheet in the puckered honeycomb structure with covalent interlayer bonding. It has been demonstrated that the structural stability of CN nanosheet is essentially maintained by the strong interlayer σ bonding between adjacent carbon atoms in the opposite atomic layers. A negative Poisson’s ratio in the out-of-plane direction under biaxial deformation, and the extreme in-plane stiffness of CN nanosheet, only slightly inferior to the monolayer graphene, are revealed. Moreover, the highly anisotropic mechanical and electronic response of CN nanosheet to tensile strain have been explored.     

How quantum bound states bounce and the structure it reveals

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.     

Towards a nonlinear elastic representation of finite compression and instability of boron carbide ceramic

A nonlinear constitutive model invoking third-order anisotropic elasticity is developed for boron carbide single crystals subjected to potentially large compressive stresses. The model makes use of limited available published data from various experimental and theoretical (i.e., quantum or ab initio) studies. The model captures variations in second-order tangent elastic moduli and loss of elastic mechanical stability with increasing compression. In particular, reduced stability of boron carbide single crystals compressed normal to the c-axis (i.e., [0001]-direction) relative to higher stability in spherical compression is represented. Different stability criteria proposed in the literature are examined for boron carbide under spherical and uniaxial compression; model predictions show that the most critical criterion corresponds to a vanishing eigenvalue of a particular tangent stiffness matrix (i.e., incremental modulus) derived exactly in the present work. Model constants are proposed for CCC (less elastically stable) and polar CBC (more elastically stable) polytypes of boron carbide. Application of the model to a homogeneously strained polycrystal provides support for the hypothesis that failure (e.g., amorphization) follows a loss of elastic stability of favorably oriented grains at shock pressures on the order of 18–20?GPa. Additional experiments or atomic simulations are suggested that would resolve currently indeterminate features of the nonlinear elastic model.     

The elastic stiffness constants of β-NH4LiSO4 around its phase transition at 460 K

The complete tensor of the elastic stiffness constantsC _ij (i,j=1 to 6) of -NH₄LiSO₄ has been measured in the temperature range 290 K to 540 K including the ferroelectric phase transition at 460 K, by the ultrasonic pulse echo overlap method.Some ultrasonic attenuation coefficients were determined.The elastic stiffness constants were calculated using Landau Theory. The elastic stiffness constants are all well described within this theory with the exception ofC ₆₆, which can not be reproduced with coupling terms allowed by group theoretical arguments. This together with double peaks observed in the specific heat and in sound attenuation in some directions leads one to suspect an intermediate phase between the paraelectric and the ferroelectric phases.     

Identification of gradient elasticity parameters based on interatomic interaction potentials accounting for modified Lorentz-Berthelot rules

The identification algorithm developed here for scale parameters of gradient elasticity combines solutions for a deformed heterogeneous composite fragment in a continuous one-dimensional model and for a diatomic chain in a discrete atomistic model. For the identification, the models are taken equivalent and the effective stiffnesses of equivalent composite fragments are compared. In the discrete model, only the nearest neighbor atoms interact and the interaction between dissimilar atoms are determined by a modified Lorentz-Berthelot rule. As a result, the effective stiffness of the discrete composite represented as a nonuniform atomic chain is found. The continuous model is a gradient one and takes into account nonlocal effects in the volume and adhesive properties of phase boundaries. The problem of determining the effective stiffness of a composite fragment is solved analytically in the one-dimensional approximation. The study is aimed to develop a procedure of identifying the scale parameters of gradient theories such that the parameters would be independent of the choice of potentials used in discrete modeling. On the example of modeling using the Morse and Lennard-Jones potentials, we propose an identification methodology invariant with respect to the choice of potentials. It is shown that the invariance is provided if the potentials in discrete modeling are coincided in the vicinity of equilibrium points. It is demonstrated that for unambiguous determination of the scale parameters of gradient elasticity, it suffices to use the simplest two-parameter potentials approximating any other potentials subject to equal equilibrium bond distances and equal second derivatives at the equilibrium point (i.e., force constants). An example of identifying the gradient elasticity parameters is presented for a two-phase W-Si composite.     

LDPE phase composition in LDPE/Cu composites using thermal analysis and FTIR spectroscopy

Low-density polyethylene (LDPE) films with different copper contents were prepared from solu-tion. The TGA (thermogravimetric analysis) results show that the presence of copper particles can im-prove the thermal stability of the composite since a maximum increment of 14°C is obtained compared with the pure LDPE in this experiment. The results of DSC (differential scanning calorimetry) in stan-dard conditions show that the Cu content has little influence on the crystallinity, X _c , of LDPE. But a trace of DSC under non-standard conditions suggests that the presence of the copper microparticles has a greater effect on the network phase than on the crystalline long-range-order phase. FTIR spectroscopy was used to study the phase content of LDPE in LDPE/Cu non-oriented composite films prepared from solution with different copper contents by analysis of CH₂ rocking vibrations. A spectral simulation of transmission spectra performed using a two-phase model does not show any variation into the phase composition of the LDPE matrix for all copper contents. When a three-phase model was taken into account, the amount of the orthorhombic phase was found to be constant. However, the fraction of the amorphous and that of the network phase were found to increase and decrease respectively with increase in the copper particle load in the film.     

Bounds on size-dependent behaviour of composites

Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical first-order computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the size-dependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected ‘smaller is stronger’ trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.     

Equivalent-inclusion approach and effective medium estimates for elastic moduli of two-dimensional suspensions of compound inclusions

An effective medium scheme is developed to estimate the elastic moduli of two-dimensional macroscopically isotropic suspensions of compound inclusions in a continuous matrix material. The two-phase (coated) compound inclusions are substituted by equivalent one-phase inclusions, using dilute solution results. Then, the available effective medium approximations and bounds are applied to the equivalent medium with homogeneous inclusions. Numerical fast Fourier transform simulations in some benchmark examples are compared favourably with the predictions of the scheme.     

Elasticity,fracture and thermoreversible gelation of highly filled physical gels<Superscript>⋆</Superscript>

We describe a physically associating triblock copolymer-based gel that exhibits a reversible transition between solid and liquid states at a temperature of approximately 55^°C. The thermal transition of the gel enables us to compare the properties of liquid suspensions and elastic composites with identical particle loadings, with particle volume fractions as large as 0.55. The suspension viscosity and the composite elasticity scale in a similar manner with the overall particle volume fraction, a result that is rationalized in terms of an effective strain amplification factor that depends only on the particle loading. Measured values of the strain amplification factor are in good agreement with the expected form for well-dispersed spheres. We also find that the elastic composites are exceptionally strong, with fracture strengths that exceed the modulus of the base gel by a factor of 100 or more. Deviations from purely elastic behavior became important for high particle volume fractions, and were probed by stress relaxation experiments.     

Characterization of the tensile behaviour of a co-woven-knitted composite in the continuous and discrete frequency domain

Laplace-transform and Z-transform theories have been applied to analyze the tensile stress–strain curves of a co-woven-knitted (CWK) composite under quasi-static (0.001/s) and high strain rates (up to 2586/s) tension. The transform results were extended to characterize the tension failure and dynamic responses of the CWK composite in the frequency domain. Specifically, the Laplace-transform theory was employed to analyze the stress–strain curves of the CWK composite along 0°, 45° and 90° directions when the composite is assumed to be a continuous system, while the Z-transform theory was used for the discrete system for the composite. From the transformed results, it was found that the stress–strain curves of the CWK composite specimen under different strain rates tension have similar stability behaviours for the Laplace- and Z-transform. For the continuous system, few pole plots are distributed on the left side of the imaginary axis, which means the system is unstable. Nevertheless, the pole-plot distribution is stable before the post-critical deformation of the CWK composite. For the discrete system, most of the poles are located inside the unit circle before post-critical deformation, indicating the system is stable. From the stiffness–time history and fracture morphology, the stability of the pole-plot distribution corresponds to the stiffness stability and fracture uniformity. From continuous and discrete system analyses, it is found that the stress–time and strain-time histories of the CWK composite can be regarded as a digital signal system. Digital signal processing (DSP) methods can be extended to the investigation of the mechanical behaviour of composites.