共查询到20条相似文献,搜索用时 15 毫秒
1.
J. J. Rushchitsky 《International Applied Mechanics》2005,41(11):1288-1298
General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly
elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying
the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial
velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted
theoretically. One of such effects is blocking of certain types of plane waves by initial stresses
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 96–107, November 2005. 相似文献
2.
The nonlinear wave equation is solved analytically in cylindrical coordinates using the third-order approximation of the Hankel
function. The second-order and third-order solutions are compared. The evolution of the initial wave profile is simulated
numerically for different initial frequencies
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 36–45, April 2007. 相似文献
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Nonlinear torsional waves propagating along an infinite transversely isotropic cylinder are considered. The hyperelasticity
of the cylinder is described by Guz’s generalization of the Murnaghan potential to quasi-isotropic materials. The evolution
of the initial waveprofile in cylinders made of composite materials reinforced with micro-and nanoscale fibers is modeled
numerically. It is shown that the transverse isotropy of this class of composites has a weak effect on the wave phenomena
accompanying the propagation of a torsional wave. Three-dimensional plots of evolution are presented
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 32–44, May 2008. 相似文献
7.
E. I. Romenskii 《Journal of Applied Mechanics and Technical Physics》2007,48(3):437-444
Constitutive equations that describe the experimentally observed failure waves are proposed to model inelastic strains of
brittle materials. The complete system of equations is hyperbolic, each equation of this system has divergent form. The model
is based on the assumption that continual failure is the process of transition from an intact state to a “fully damaged” state
described by the kinetics of the order parameter. The structure of stationary traveling compressive waves is analyzed using
a simplified model. It is shown that in a certain range of amplitudes, the wave splits into an elastic precursor and a failure
wave.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 164–172, May–June, 2007. 相似文献
8.
W?odzimierz Domański 《International Journal of Non》2009,44(5):494-498
Using the perturbation method of weakly non-linear asymptotics we analyze the propagation and interaction of elastic plane waves in a model of a soft solid proposed by Hamilton et al. [Separation of compressibility and shear deformation in the elastic energy density, J. Acoust. Soc. Am. 116 (2004) 41-44]. We derive the evolution equations for the wave amplitudes and find analytical formulas for all interaction coefficients of quadratically non-linear interacting waves. We show that in spite of the assumption of almost incompressibility used in Hamilton et al. [Separation of compressibility and shear deformation in the elastic energy density, J. Acoust. Soc. Am. 116 (2004) 41-44], the model behaves essentially like that of a compressible isotropic material. Both the structure of the equations and the interaction patterns are similar. The models differ, however, in the elastic constants that characterize them, and hence the values of the coefficients in the evolution equations and the values of the interaction coefficients differ. 相似文献
9.
The exact solutions of the equations of motion derived under refined theories of shells and ribs based on the Timoshenko model
are used to plot dispersion curves for harmonic waves propagating along a cylindrical shell reinforced with discrete longitudinal
ribs
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 37–41, May 2006. 相似文献
10.
In this paper, a dynamical problem is considered for an incompressible hyperelastic solid sphere composed of the classical isotropic neo-Hookean material, where the sphere is subjected to a class of periodic step radial tensile loads on its surface. A second-order non-linear ordinary differential equation that describes cavity formation and motion is proposed. The qualitative properties of the solutions of the equation are examined. Correspondingly, under a prescribed constant dead-load, it is proved that a cavity forms in the sphere as the dead-load exceeds a certain critical value and the motion of the formed cavity presents a class of singular periodic oscillations. Under periodic step loads, the existence conditions for periodic oscillation of the formed cavity are determined by using the phase diagrams of the motion equation of cavity. In each section, numerical examples are also carried out. 相似文献
11.
The solution of a model differential equation for the three-dimensional perturbations of the interface between two immiscible fluids of different densities lying between a stationary nondeformable bottom and cover is presented. It is assumed that the waves have an arbitrary length and small, though finite, amplitude. The shapes of stationary traveling internal waves, both periodic in the two horizontal coordinates and soliton-like, are presented. These shapes depend on different parameters of the problem: the direction of the perturbation wave vector and the fluid layer depth and density ratios. 相似文献
12.
The bifurcation instability problem for cylindrical shells made of particulate composites with nonlinear elastic matrix and
damaged inclusions is formulated and solved
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 80–91, August 2007. 相似文献
13.
The structural theory of short-term microdamage is generalized to a fibrous composite with a microdamageable matrix and physically
nonlinear fibers. The basis for the generalization is the stochastic elasticity equations of a fibrous composite with a porous
matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation
for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a fibrous composite
with porous matrix and physically nonlinear fibers constitute a closed-form system of equations. This system describes the
coupled processes of physically nonlinear deformation and microdamage occurring in different components of the composite.
Algorithms for computing the microdamage-macrostrain and macrostress-macrostrain relationships are developed. Uniaxial tension
curves are plotted for a fibrous composite with linearly hardening fibers
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 38–47, January 2006. 相似文献
14.
The bifurcation instability problem for cylindrical shells made of particulate composites with nonlinear elastic inclusions
and damageable matrix is formulated and solved
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 68–79, October 2007. 相似文献
15.
E. Rodrigues Ferreira 《International Journal of Non》2009,44(5):450-455
In this paper, waves propagating in Mooney-Rivlin and neo-Hookean non-linear elastic materials subjected to a homogeneous pre-strain are considered. In a previous paper, Boulanger and Hayes [Finite-amplitude waves in deformed Mooney-Rivlin materials, Q. J. Mech. Appl. Math. 45 (1992) 575-593] showed, for deformed Mooney-Rivlin materials, that the superposition of two finite-amplitude shear waves polarized in different directions (orthogonal to each other) and propagating along the same direction is an exact solution of the equations of motion. The two waves do not interact. Here, we are interested in superpositions of waves propagating in different directions. Two types of superpositions are considered: superpositions of waves polarized in the same direction, and also superposition of waves polarized in different directions. It is shown that such superpositions are exact solutions of the equations of motion with appropriate choices of the propagation and polarization directions. 相似文献
16.
A structural theory of short-term microdamage is proposed for a fibrous composite with physically nonlinear matrix and microdamaged
reinforcement. The theory is based on the stochastic elasticity equations of a fibrous composite with porous fibers. Microvolumes
of the fiber material are damaged in accordance with the Huber-Mises failure criterion. A balance equation for damaged microvolumes
in the reinforcement is derived. This equation together with the equations relating macrostresses and macrostrains of a fibrous
composite with porous reinforcement and physically nonlinear matrix constitute a closed-form system. This system describes
the coupled processes of physically nonlinear deformation and microdamage that occur in different components of the composite.
Algorithms are proposed for computing the dependences of microdamage on macrostrains and macrostresses on macrostrains. Uniaxial
tension curves are plotted for a fibrous composite with a linearly hardening matrix
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 3–13, February 2006. 相似文献
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ANALYSISOFINTERPHASEMECHANICALBEHAVIORWITHINTERFACEELEMENTINTHECOMPOSITEMATERIALSANALYSISOFINTERPHASEMECHANICALBEHAVIORWITHIN... 相似文献
19.
Sets of physical constants are tabulated for three structural models of fibrous composites with fibers of four types: Thornel-300
carbon microfibers, graphite whiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. The matrix for all the types
of composites is always éPON-828 epoxy rosin (in some cases with polystyrene or pyrex additive). The values of the physical
constants are commented on and used to study the distinctions in the evolution of three types of waves (plane longitudinal,
plane transverse, and cylindrical) propagating in materials with soft and hard nonlinearities
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 47–60, December 2005. 相似文献
20.
A method is proposed for studying the evolution of plane waves in micro- and nanocomposite materials. This method permits comparing the evolutions of harmonic waves and produces results that are in agreement with data obtained earlier and with the metaphysical reasoning on the nanomechanics of composite materials 相似文献