Piecewise Homogeneous Body Model Research Articles

The influence of the finite initial strains on the axisymmetric wave dispersion in a circular cylinder embedded in a compressible elastic medium

The influence of the finite initial strains on the axisymmetric wave dispersion in a circular cylinder embedded in a compressible elastic medium is investigated within the scope of a piecewise homogeneous body model utilizing three-dimensional linearized theory of wave propagation in an initially stressed body. The material of the cylinder and the surrounding elastic medium are assumed to be compressible and the corresponding elasticity relations are described by the harmonic potential. The numerical results are presented and discussed. It is established that the dispersion curves are divided into four parts by the characteristic nondispersive wave velocities regarding the cylinder and the surrounding materials. As a result of the existence of the initial strains the lengths of these parts change and they move wholly up (down) under initial stretching (compressing) strain along the cylinder, i.e. along the wave propagation direction.

Energy release rate in a prestressed sandwich plate-strip containing interface cracks

Within the framework of a piecewise homogeneous body model, by utilizing the three-dimensional linearized theory of elasticity, the problem of opening of interface cracks in an initially stressed sandwich plate-strip is studied. To solve the corresponding boundary-contact problem, the FEM is employed. Numerical results for the influence of the initial stresses on the energy release rate (ERR) at various values of problem parameters are presented and discussed. In particular, it is established that the ERR in creases (de creases) with growing initial tension (compression) of the plate-strip.

Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder embedded in a finite prestrained compressible medium

Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder contained in a finite prestrained infinite body is investigated within the scope of the piecewise-homogeneous body model by employing the three-dimensional linearized theory of elastic waves in a prestressed body. It is assumed that the materials of the cylinder and infinite body are compressible and that their elastic relations are described by a harmonic potential. Numerical results are presented and discussed for the case where the elastic constants of the cylinder are greater than those of the surrounding infinite body

Time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane

The time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and orthotropic half-plane is studied within the scope of the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in an initially stressed body. The main focus is on the influence of the mechanical properties of the constituent materials and the initial stresses present on the “resonance” values of the normal stress acting on the interface plane and on the “resonance” values of the frequency of the external point-located force. The numerical results are presented and discussed. In particular, it is shown that the values of the normal stress decrease with a decrease in the modulus of elasticity of the materials along the thickness of the covering layer.

Axisymmetric longitudinal wave propagation in a finite prestretched compound circular cylinder made of incompressible materials

The propagation of an axisymmetric longitudinal wave in a finite prestrained compound (composite) cylinder is investigated using a piecewise-homogeneous body model and the three-dimensional linearized theory of wave propagation in prestressed body [13–15]. The inner and outer cylinders are assumed to be made of incompressible neo-Hookean materials. Numerical results on the influence of the prestrains in the inner and outer cylinders on wave dispersion are presented and discussed. These results are obtained for the case where the inner solid cylinder is stiffer than the outer hollow cylinder. In particular, it is established that the pretension of the cylinders increases the wave velocity

Near-surface failure of layered viscoelastic materials

Within the framework of a piecewise homogeneous body model, with the use of exact equations of the geometrically nonlinear theory of viscoelastic bodies, the distribution of near-surface self-balanced normal stresses in a body consisting of a viscoelastic half-plane, an elastic locally curved bond layer, and a viscoelastic covering layer is investigated. A method for solving the problem considered by employing the Laplace and Fourier transformations is developed. Numerical results for the self-balanced normal stresses caused by a local curving (imperfection) of an elastic bond layer upon tension and compression of the body mentioned along the free face plane are presented and analyzed. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operators. A macroscopic failure criterion is proposed, and the validity of this criterion is examined.

Dynamical response of a prestrained system comprising a substrate and bond and covering layers to a moving load

The dynamical response of a system consisting of a prestressed substrate and covering and bond layers to a moving load is investigated within the scope of a piecewise-homogeneous body model by using a three-dimensional linearized theory of wave propagation in initially stressed bodies. It is assumed that the materials of the constituents are isotropic and homogeneous, and the subsonic speed of the moving load acting on the covering layer is constant. The investigations are carried out for a plane strain state under complete and in complete contact conditions. For various values of problem parameters, numerical results for the critical speed are presented and discussed.

On the dynamics of a finite pre-strained bi-layered slab resting on a rigid foundation under the action of an oscillating moving load

This paper investigates the dynamic response of a finitely pre-strained bi-layered slab resting on a rigid foundation to a time-harmonic oscillating moving load, within the scope of the piecewise-homogeneous body model utilizing the 3D linearized wave propagation theory in the initially stressed body. It is assumed that the materials of the layers are highly elastic ones and their elasticity relations are given in terms of the harmonic potential. Moreover, it is also assumed that the velocity of the line-located time-harmonic oscillating moving load is constant as it acts on the free face of the upper layer of the slab. Our investigations were carried out for a 2D problem (plane-strain state) under subsonic velocity for a moving load in complete contact conditions. The corresponding numerical results were obtained for the stiff upper layer and soft lower layer system in which the constants of elasticity for the upper layer material are greater than those of the lower layer material. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it is established that with the oscillating frequency of the moving load, the values of the critical velocity decrease. Moreover, it is established that the initial stretching of the upper layer of the slab causes the critical velocity to increase and the absolute values of the normal stresses acting on the mid-planes of the layers of the slab to decrease.

Torsional wave dispersion relations in a pre‐stressed bi‐material compounded cylinder

AbstractWithin the framework of the piecewise homogeneous body model and through the application of the three‐dimensional linearized theory of elastic waves in an initially stressed body, the torsional wave dispersion in pre‐stretched bi‐material compounded cylinders is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinders are given through the Murnaghan potential. The numerical investigations are made for steel (St) (as a material for the solid cylinder) and bronze (Br) (as a material for a hollow covering cylinder). According to the numerical results obtained, the influence of the problem parameters such as the initial stresses in the components of the bi‐material compounded cylinder, the values of the mechanical and physical constants of the components, and the geometrical parameters (such as the relation of the thickness of the covering cylinder with the radius of the inner solid cylinder on the dispersion curves) are analyzed.

Dynamics of a system comprising an orthotropic layer and orthotropic half-plane under the action of an oscillating moving load

This paper investigates the dynamic response to a time-harmonic oscillating moving load of a system comprising a covering layer and half-plane, within the scope of the piecewise-homogeneous body model utilizing of the exact equations of the linear theory of elastodynamics. It is assumed that the materials of the layer and half-plane are anisotropic (orthotropic), and that the velocity of the line-located time-harmonic oscillating moving load is constant as it acts on the free face of the covering layer. Our investigations were carried out for a two-dimensional problem (plane-strain state) under subsonic velocity for a moving load in complete and incomplete contact conditions. The corresponding numerical results were obtained for the stiffer layer and soft half-plane system in which the modulus of elasticity of the covering layer material (for the moving direction of the load) is greater than that of the half-plane material. Numerical results are presented and discussed for the critical velocity, displacement and stress distribution for various values of the problem parameters. In particular, it is established that the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the existence of the oscillation of the moving load causes two types of critical velocity to appear: one of which is less, but the other one is greater than that attained for the case where the mentioned oscillation is absent.

Stress distribution in an infinite elastic body containing two neighboring locally curved fibers

A method is developed for analyzing the stresses in an infinite elastic body containing two neighboring inphase locally curved fibers located along two parallel lines. The body is loaded at infinity by uniformly distributed nor mal forces in the direction of fibers. The investigation is carried out within the frame work of a piecewise homogeneous body model with the use of the three-dimensional ex act equations of the elasticity theory. Numerical results for stress distributions in the body and for the influence of interaction between fibers on these distributions are given.

Stress distribution in an infinite elastic body with a covered periodically curved fiber

Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed.

Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium

Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.

Propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder imbedded in a finitely prestrained infinite elastic body

Within the framework of a piecewise homogeneous body model and with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), the propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder (fiber) imbedded in a finitely prestrained infinite elastic body (matrix) is investigated. It is assumed that the fiber and matrix materials have the same density and are in compressible. The stress-strain relations for them are given through the Treloar potential. Numerical results regarding the influence of initial strains in the fiber and matrix on wave dispersion are presented and discussed. These results are obtained for the following cases: the fiber and matrix are both without initial strains; only the fiber is prestretched; only the matrix is prestretched; the fiber and matrix are both prestretched simultaneously; the fiber and matrix are both precompressed simultaneously.

Stress distribution in multilayered composites near loaded edges

The edge effect in layered composite material is studied using the piecewise-homogeneous body model and the exact equations of the theory of elasticity. It is assumed that continuously distributed normal forces act at the edges of the reinforcing layers. A plain strain state is considered and the stresses are expressed in terms of the solutions of a system of dual singular integral equations. The singularity of the stresses is determined by the solution procedure. The concentration of the reinforcing layers is assumed low and the interaction between them is not taken into account. A numerical algorithm is developed and numerical results on the stress distribution are presented

Dynamics of a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane under the action of a moving load

This paper investigates the dynamic response to a moving load of a system comprising an initially stressed covering layer and initially stressed half-plane, within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It was assumed that the materials of the layer and half-plane are anisotropic (orthotropic), and that the velocity of the line-located moving load is constant as it acts on the free face of the covering layer. The investigations were made for a two-dimensional problem (plane-strain state) under subsonic velocity of the moving load for complete and incomplete contact conditions. Corresponding numerical results were obtained for the stiffer layer and soft half-plane system in which the modulus of elasticity of the covering layer material (for the moving direction of the load) is greater than that of the half-plane material, which was assumed to be isotropic. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it was established that, the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the initial stretching of the covering layer causes to increase these values.

On the propagation of Lamb waves in a sandwich plate made of compressible materials with finite initial strains

The propagation of flexural Lamb waves in a prestrained sandwich plate made from compressible highly elastic materials is investigated within the scope of a piecewise homogeneous body model by utilizing TLTEWISB. The mechanical relations of layer materials are described by a harmonic-type potential, and numerical results are obtained for the first and second vibration modes. According to the results, the influence of problem parameters and of the initial stretching strain along the layers on the wave propagation speed is examined. The asymptotic values of the speed are considered in the cases of short and long wavelengths, and the influence of the initial strains on these asymptotic (limit) values are also analyzed.

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed.

Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review)

Recent investigations of dynamic problems for bodies with initial stresses are reviewed. These are investigations carried out over the last six years using the piecewise-homogeneous body model and the three-dimensional linearized theory of elastic waves in initially stressed bodies. Emphasis is on the investigations performed by the author and his students. The research studies on the wave propagation and dynamic time-harmonic stress-state problems are reviewed separately. The areas for further investigations are pointed out

The critical speed of a moving load on a prestressed plate resting on a prestressed half-plane

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the dynamical response of a system consisting of a prestressed covering layer and a prestressed half-plane to a moving load applied to the free face of the covering layer is investigated. Two types (complete and incomplete) of contact conditions on the interface are considered. The subsonic state is considered, and numerical results for the critical speed of the moving load are presented. The influence of problem parameters on the critical speed is analyzed. In particular, it is established that the prestressing of the covering layer and half-plane increases the critical speed.