Exact Relations for Effective Tensors of Polycrystals. II. Applications to Elasticity and Piezoelectricity
نویسندگان
چکیده
منابع مشابه
Exact relations for effective tensors of polycrystals. II: Applications to elasticity and piezoelectricity
An important necessary condition for an exact relation for effective moduli of polycrystals to hold is stability of that relation under lamination. This requirement is so restrictive that it is possible (if not always feasible) to find all such relations explicitly. In order to do that one needs to combine the results developed in Part I of this paper and the representation theory of the rotati...
متن کاملExact relations for effective tensors of polycrystals. I: Necessary conditions
The set of all effective moduli of a polycrystal usually has a nonempty interior. When it does not, we say that there is an exact relation for effective moduli. This can indeed happen as evidenced by recent results [4, 10, 12] on polycrystals. In this paper we describe a general method for finding such relations for effective moduli of laminates. The method is applicable to any physical setting...
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Composite materials play an increasingly important role in our everyday life and technology from skis and golf clubs to sensors and actuators in high tech components. By “composite” we mean a perfectly bonded homogeneous mixture of two or more materials on a length scale much smaller than human size and much larger than interatomic distances. The physical properties of a composite (conducting, ...
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Typically, the elastic and electrical properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for effective moduli that are universally valid no matter what the microstructure. Such exact formulae provide useful benchmarks for testing numerical and actual experimental data, and for evaluating the merit of various appr...
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In this paper we will review and extend the results of [21], which covered the case of 3D thermo-piezoelectric polycrystals. In that context the settings of conductivity, elasticity, pyroelectricity, piezoelectricity, thermo-electricity and thermo-elasticity can be viewed as particular cases. We will consider a class of composites more general than polycrystals, where the set of allowable mater...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 1998
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s002050050108