On one-dimensional shock waves in composite materials modelled as interpenetrating solid continua

A one dimensional version of a theory of composite materials modelled as interpenetrating solid continua is used to study the propagation of shock waves in composites with two identifiable constituents. It is found that two distinct types of shock waves may propagate except when one of the constituents is a chopped fiber. The speeds at which the shock waves propagate are determined as are the differential equations which govern the evolutionary behaviour of the amplitudes of the waves. The implications of these results are studied in detail in a number of particular situations. Finally, the special results which hold when the amplitudes of the shock waves are infinitesimal are also presented.     

On one-dimensional acceleration waves in composite materials modeled as interpenetrating solid continua

A one-dimensional version of a theory of composite materials modeled as interpenetrating solid continua is applied in the analysis of acceleration waves in composites containing two identifiable constituents. As expected, two distinct acceleration waves always propagate except when one of the constituents consists of a chopped fiber. The influence of viscous type damping is included in only the volumetric interaction between the constituents in portions of the treatment. Equations are derived both for the propagation velocities and the varying amplitudes of the disturbance as a function of the state of the material immediately ahead of the wavefront. These rather general results are specialized to the case of a homogeneous steady-state ahead of the fast wave. The various types of behavior possible and the order of the discontinuities occurring across the wavefront are discussed in detail for a number of special cases.     

Transient waves in composite materials

A continuum theory for transient wave propagation in three-dimensional composite materials is given. The derived model provides a set of governing equations for the prediction of dynamic response of elastic composites to impulsive loadings. Pulse propagation normal to the direction of layering in periodically bilaminated media, and normal to the fiber direction in unidirectional long-fiber composites are obtained as special cases. The dynamic response of the composite is determined solely from the materials properties of the constituents (assumed in general to be orthotropic) and their geometrical dimensions. The predicted propagating transient waves are checked with exact solutions for impacted laminated composites, and with measured data for a fiber-reinforced material. Applications are given for pulse propagation in particulate composites and in tri-othogonally fiber-reinforced materials.     

Propagation of quasishear waves in prestressed materials with unbonded layers

The propagation of quasi-shear waves along the layers of a prestressed composite material is described using the three-dimensional linearized theory of elasticity. The composite consists of two alternating layers that are free to slip relative each other. The dispersion equation is analyzed numerically. The effect of the prestresses on the wave velocity is studied     

Some remarks on the growth behavior of one-dimensional shock waves in non-linear materials

The growth behavior of both compressive and expansive one-dimensional shock waves which propagate into an unstrained region of a non-linear material exhibiting anelastic response, in the sense of Eckart, is analyzed. In each case, a differential equation governing the growth of the amplitude of the shock is derived and it is shown that a critical strain gradient may be defined. The growth behavior of the waves closely resembles the growth behavior of compressive and expansive shock waves propagating in sufficiently smooth non-linear materials with fading memory, i.e., in materials which can be approximated by linear viscoelastic materials for small relative strains.     

Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

We explore the utility of strain-controlled large amplitude oscillatory shear (LAOS) deformation for identifying and characterizing apparent yield stress responses in elastoviscoplastic materials. Our approach emphasizes the visual representation of the LAOS stress response within the framework of Lissajous curves with strain, strain rate, and stress as the coordinate axes, in conjunction with quantitative analysis of the corresponding limit cycle behavior. This approach enables us to explore how the material properties characterizing the yielding response depend on both strain amplitude and frequency of deformation. Canonical constitutive models (including the purely viscous Carreau model and the elastic Bingham model) are used to illustrate the characteristic features of pseudoplastic and elastoplastic material responses under large amplitude oscillatory shear. A new parameter, the perfect plastic dissipation ratio, is introduced for uniquely identifying plastic behavior. Experimental results are presented for two complex fluids, a pseudoplastic shear-thinning xanthan gum solution and an elastoviscoplastic invert-emulsion drilling fluid. The LAOS test protocols and the associated material measures provide a rheological fingerprint of the yielding behavior of a complex fluid that can be compactly represented within the domain of a Pipkin diagram defined by the amplitude and timescale of deformation.     

Propagation behavior of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with line defects

Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.     

Interaction of a one-dimensional unloading wave with an elastoplastic boundary in an elastoviscoplastic medium

This paper presents a solution of the boundary-value problem of the theory of large elastoviscoplastic strains for the development of viscoplastic flow in a heavy layer of material located on an inclined plane and subjected to loading at the free surface with subsequent instantaneous removal of the load. This discontinuous change in the boundary conditions gives rise to a surface of strain discontinuity propagating in the medium and called an unloading wave. The reflection of the wave from the elastoviscoplastic boundary and its motion after reflection from the fixed plane and the free surface are considered.     

Modelling shock waves in composite materials using generalised orthotropic pressure

Continuum Mechanics and Thermodynamics - Excellent mechanical properties of composite materials have numerous engineering applications, especially in aerospace structures. The main characteristics...     

On one-dimensional shock waves

In this paper uniform asymptotic expansions for the solutions of a system of differential equations are obtained in the domain containing a shock wave. It is shown, in particular, that the function θ(t,x)/ε contained in the expansions and describing the behavior of the solution in the neighborhood of the wave front has, generally speaking, a discontinuity of derivatives at the front. The results are applicable to one-dimensional problems in gas dynamics with low viscosity and heat-conductivity.     

Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials

Summary Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B. To approximate the integral equation, the self-consistent scheme is followed. In order to obtain consistent approximation conditions, we introduce fluctuations of elastic and viscoplastic strain rate fields with respect to known kinematically compatible fields. It results in a strain rate concentration relation connecting the strain rate at each point to the macroscopic loading conditions and the local stress field. The results are presented and compared with other models and with experimental data in the case of a two-phase material. Received 26 August 1997; accepted for publication 2 July 1998