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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 150 (1999), S. 153-177 
    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
    Archive for rational mechanics and analysis 151 (2000), S. 311-337 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: The effective elastic properties of a polycrystalline material depend on the single crystal elastic constants of the crystallites comprising the polycrystal and on the manner in which the crystallites are arranged. In this paper we apply the techniques of homogenization to put the problem of determining effective elastic constants in a precise mathematical framework that permits us to derive an expression for the effective elasticity tensor. We also study how the homogenized elasticity tensor changes as the probability characterizing the ensemble changes. Under the assumption that the field of orientations of the crystallographic axes of the crystallites is an independent random field, we show that our theory is compatible with the formulation used in texture analysis. In particular, we are able to prove that the physical assumption made by [10] in his study of weakly-textured polycrystals holds true. In addition, we establish some elementary bounds on the material constants that characterize the effective elasticity tensor of weakly-textured orthorhombic aggregates of cubic crystallites.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 155 (2000), S. 215-235 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: Structured deformations provide a multi-scale geometrical setting for resolving the fields occurring in continuum mechanics into two parts: the part arising from smooth changes at smaller lengths scales and the part due to slips and separations (disarrangements) at smaller length scales. The portion without disarrangements is known to be associated with limits of gradients of approximating deformations, and the portion due to disarrangements corresponds to the effects of jumps in the approximating deformations. This paper extends the principal concepts and results on structured deformations to include the effects of limits of second gradients and jumps in the first gradients of approximating deformations and provides examples illustrating these effects. The resulting second-order structured deformations provide a setting for a complete description of structured motions and for the systematic treatment of mesolevel phase transitions, including the effects of jumps in first gradients on the bulk density of the Helmholtz free energy.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of elasticity 60 (2000), S. 19-34 
    ISSN: 1573-2681
    Keywords: texture ; orientation measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Let w be the orientation distribution function of a polycrystalline aggregate of crystallites with symmetry G cr and with group of texture symmetry G tex. In this paper we obtain a “recipe” on how to derive optimal bounds on the texture coefficients W lmn associated with w. In particular, we find explicit bounds in the case in which G tex is a group with orthorhombic symmetry and G cr is either a group with cubic symmetry or a group with hexagonal symmetry.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of elasticity 45 (1996), S. 91-116 
    ISSN: 1573-2681
    Keywords: 73B40 ; 73C99 ; 73S10 ; stress ; texture ; acoustoelastic birefringence ; ultrasonics ; nondestructive evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper we develop a simple micromechanical model of a prestressed polycrystalline aggregate, in which the texture-induced and stress-induced anisotropies of the aggregate are precisely defined; here the word ‘texture’ always refers to the texture of the aggregate at the given prestressed configuration, not to that of a perhaps fictitious natural state of the aggregate. We use this model to derive, for a prestressed orthotropic aggregate of cubic crystallites, a birefringence formula which shows explicitly the effects of the orthotropic texture on the acoustoelastic coefficients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one reflecting purely the influence of stress on the birefringence, and the other encompassing all the effects of texture. The same formula, on the other hand, provides for each material specific quantitative criteria under which the ‘separation of stress-induced and texture-induced birefringence’ would become meaningful in an approximate sense.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of elasticity 59 (2000), S. 145-173 
    ISSN: 1573-2681
    Keywords: residual stress ; crystallographic texture ; acoustoelasticity ; micromechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Herein we derive, under the micromechanical model we proposed earlier, Man and Paroni [14], a complete set of formulae for the twelve material constants in the acoustoelastic constitutive equation for orthorhombic aggregates of cubic crystallites. We present also a second model and compare its predictions on the material constants with those of the first model. Both these models lead to constitutive equations which are indifferent to rotation of reference placement. This allows us to appeal to a new representation theorem (Paroni and Man [15]), which greatly facilitates our derivation of the formulae for the material constants. The second model introduced in this paper is intimately related to some previous averaging theories in the literature. We explain why and in what sense our second model could be taken as a generalization of its predecessors.
    Type of Medium: Electronic Resource
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