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  • 1990-1994  (6)
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Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Shock conditions for hypoelastic materials (1993)
    Springer
    Theoretical and computational fluid dynamics 5 (1993), S. 49-55 
    Details
    ISSN: 1432-2250
    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 equations governing the motion of hypoelastic materials (and related models of non-Newtonian fluids) are not in conservation form. Hence there is no obvious formulation of Rankine-Hugoniot jump conditions across a shock. In this paper we demonstrate that a viscosity criterion can be used to obtain meaningful shock conditions. In particular, we discuss shocks of small amplitude. The shock conditions obtained will in general depend on the form of the viscosity term.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00418042
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on nonlocal interactions and hysteresis in phase transitions (1994)
    Springer
    Continuum mechanics and thermodynamics 8 (1994), S. 65-73 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper examines models of shape memory alloys in which the usual multiwell, nonconvex elastic energy is modified by the addition of a nonlocal interaction term. It is shown that minimizing such an energy over uniform Young-measures yields a good prediction of hysteresis in a material subjected to biaxial loading. In addition, the relationship between the nonlocal interaction energy and the coherency energy is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175752
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Nonlocal regularization of L. C. Young's tacking problem (1992)
    Springer
    Applied mathematics & optimization 25 (1992), S. 287-301 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract L. C. Young's tacking problem is a prototype of a nonconvex variational problem for which minimizing sequences for the energy do not attain a minimum. The “minimizer” of the energy is usually described as a Young-measure or generalized curve. In many studies, the tacking problem is regularized by adding a higher-order “viscosity term” to the energy. This regularized energy has classical minimizers. In this paper we regularize instead with a spatially nonlocal term. This weakly regularized problem still has measure-valued minimizers, but as the nonlocal term becomes stronger, the measure-valued solutions organize, coalesce, and eventually turn into classical solutions. The information on the measure-valued solutions is obtained by studying equivalent variational problems involving moments of the measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182325
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On a linear model of mechanical phase transitions (1990)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 728-733 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Existence and infinite speed of propagation are shown for the equation $$h_n \left( {x,t} \right) = \frac{1}{{\alpha \pi }}\int_{ - \infty }^\infty {\frac{{Ah_{xxx} \left( {\xi ,t} \right) - Bh_{xt} \left( {\xi ,t} \right)}}{{\left( {x - \xi } \right)}}d\xi } , - \infty〈 x〈 \infty ,0〈 t〈 T,$$ which is the linearization of a model equation for the mechanical phase transition phenomenon of melting-freezing waves. In addition, from the formal solution of the equation one can compute a decay rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946104
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  • 5
    Electronic Resource
    Electronic Resource
    Derivation of linear beam equations using nonlinear continuum mechanics (1993)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 732-754 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Familiar linear elastic and viscoelastic beam equations (Euler-Bernoulli, Rayleigh, Kelvin-Voigt, Timoshenko, and Shear Diffusion) and boundary conditions are derived from a nonlinear theory of large motions rather than the usual variational techniques. Also included is a fairly detailed derivation of the nonlinear theory and a careful discussion of the hypotheses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948486
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Nonlocal superconductivity (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 135-152 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00942851
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    Paper (German National Licenses)
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