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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The classical method of characteristic surfaces and bicharacteristic rays is used to study acceleration and higher order discontinuities in nonlinear simple elastic materials. No special material symmetry is assumed, and the analysis requires neither material homogeneity nor uniform conditions ahead of the wave in general, although many detailed results do require the latter two conditions. This paper draws heavily on known results, but at the same time many other results, believed to be new, have been included. Analysis of the motion of the singular surface precedes a discussion of the amplitude equations. It is shown that the Jacobian determinant of a certain coordinate transformation, induced by the motion of the surface, plays a dominant role in the equations for transport of amplitude. New results on the kinematics of singular surfaces are given for homogeneous and uniform materials, including a formula for the evolution of surface curvature in anisotropic materials and a complete description of the role of the curvatures of the initial singular surface and of the characteristic slowness surface in producing expansion or focusing of the singular surface. It is shown that the Jacobian determinant, mentioned above, produces a great simplification in the equations for transport of amplitude and bears significantly on the interpretation of solutions. Discontinuities of all higher orders are shown to be induced by a discontinuity of given order, and the implications of this result for transverse acceleration waves in isotropic materials are pointed out. Coupling of the modes of propagation for uniform multiplicity of slowness surfaces is described. Finally, it is shown that in directions of self intersection or conical intersection of slowness surfaces, the amplitude equations are not ordinary differential equations, but rather they are semilinear hyperbolic partial differential equations, and some of their properties are described. Hyperbolic transport equations have previously been shown to hold for some linear hyperbolic systems, but the kinematical description and reduction to a simple and readily interpretable form, as given here, are new. It seems clear that the methods employed here could be extended to materials with constitutive behavior far more elaborate than simple elastic.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Backman and Finnegan [1] have pointed out that shear bands initiate from a defect such as a second phase particle, microcrack, or a void. The defect has been modeled as a sinusoidal variation in the thickness of the tubular specimens tested in torsion by Chi [2] and Murphy [3]. Here we simulate their torsional tests numerically and consider different shapes and sizes of defects.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 55 (1897), S. 270-270 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] PROF. PERRY, in his review of my “Elements of Mechanics” in your issue of November 19, 1896, gives his method of explanation of mechanical units to engineering students. The method is almost as perplexing as the one he so severely condemns. The source of confusion in both cases is in ...
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of non-linear and coupled equations governing the thermomechanical deformations of a viscoplastic body undergoing simple shearing deformations is integrated in time by using the forward-difference Galerkin finite-element (FDGFE) method and the Crank-Nicolson-Galerkin finite-element (CNGFE) method. In the latter scheme the number of unknown functions is increased so that the governing equations contain only first-order spatial derivatives. It is shown that the solutions obtained by the two methods agree qualitatively; however, the CNGFE method seems to introduce some damping into the system for non-polar materials, but none for dipolar materials.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The regular pattern for shock reflection in a nonlinear hyperelastic solid is a centered array of shocks and simple wave fans. As the angle of incidence approaches grazing incidence or a critical angle, the reflection pattern overtakes the incident wave until finally the regular pattern can no longer be sustained. By expanding the reflection solution in powers of amplitude about the linear reflection solution, it is possible to develop a procedure to solve the reflection problem for weak but finite shocks for any material symmetry. Explicit solutions can be exhibited for isotropic materials, including relationships between amplitude and limiting angle for various boundary conditions and incident waves. Some problems require consideration of a nonlinear boundary condition even in the first approximation. Typically, these cases lead to considerable amplification in the leading reflected wave.
    Type of Medium: Electronic Resource
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