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【期刊论文】Two-dimensional tensor function representation for all kinds of material symmetry
郑泉水, BY Q.-S. ZHENG
Proc. R. Soc. Lond. A (1993) 443, 127-138,-0001,():
-1年11月30日
All kinds of physically possible material symmetry in two-dimensional space were investigated in a recent work of Q.-S. Zheng and J. P. Boehler. In this paper, we establish the complete and irreducible representations with respect to every kind of material symmetry for scalar-, vector-, and second-order tensor-valued functions in two-dimensional space of any finite number of vectors and second-order tensors. These representations allow general invariant forms of physical and constitutive laws of anisotropic materials to be developed in plane problems.
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郑泉水, BY Q.-S. ZHENG AND K.C. HWANG
Proc. R. Soc. Lond. A (1996) 452, 2493-2507 ,-0001,():
-1年11月30日
In our another recent work (Zheng & Hwang 1996), we established the explicit relationsbetween the effective and the matrix elastic properties in two-dimensional (2D) elasticity, as the effective medium is comprised of an isotropic and homogeous matrix, microcracks,and holes of various shapes. The present paper extends the above result to the case for acomposite material comprising either isotropic or anisotropic matrix and inclusions whichhave respectively continuously varying compliances, and for a variety of interfaceconditions. It is shown that the effective compliance depends upon a reduced list of thematrix and inclusion material constants. In particular, when the matrix and inclusions areall isotropic and respectively homogeneous, then Em, H (i.e., the defect compliance H whichis the difference S-Sm, between the effective compliance S and the matrix compliance S, multiplied by the matrix Young's modulus Em) has a reduced dependence upon the Em/EIand vm-viEm/EI for the inclusion Young's moduli E1 and Poisson's ratios v1 and the MatrixPoisson's ratio vu, rather than the full material constant list of EI, vI, Em, vm. Applicationsto various important types of matrix and inclusion materials are given. We also show thatthe generalized self-consistent method (Christenson & Lo, 1979) provides solutions of theeffective moduli for unidirectional fibre composites in compatible forms with the generaldependence relations proved in the present paper.
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【期刊论文】The description, classification, and reality of material and physical symmetries
郑泉水, Q.-S. Zheng
Acta Mechanica 102, 73-89 (1994),-0001,():
-1年11月30日
We reconsider the definitions of both material symmetries and physical symmetries which aredescribed in terms of point groups, i.e. subgroups of the full orthogonal group, because these two conceptsare often confused and the classical descriptions of physical symmetry for inelastic behaviour of materials areimpracticable. All two-and three-dimensional point groups are classified into two types: compact andnon-compact. The reality of every compact point group in the description of a material or a physicalsymmetry is justified in four aspects, that is: (i) point groups characterized by a finite set of tensors, (ii)Hilbert's theorem for integrity bases, (iii) correlation between integrity bases and function bases (generalization of Wineman and Pipkin's theorem), and (iv) physical reality. The unreality of anynon-compact point group in the description of a material or a physical symmetry is proposed as a newprinciple of continuum physics. As applications, the complete sets of all classes of two-and three-dimensional point groups which describe physical symmetries for linear physical properties (such as thermalexpansion, piezoelectricity, elasticity, etc.) and for more general mechanical constitutive laws are given.
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郑泉水, Q.-S. ZHENG, A. J. M. SPENCER
Printed in Great Britain. All rights rcserved Voi. 31, No.4, pp. (1993) 617-635,-0001,():
-1年11月30日
The material symmetry of the constitutive law of a continuum material is described by the Kronecker powers of the orthogonal tensors which belong to the so-called material symmetry group, a subgroup of the full orthogonal tensor group, of the material. The properties, especially the canonical representations, of Kronecker powers of orthogonal tensors may be applied to deal with material symmetry problems. In this paper, we obtain the basic recurrence formulae in order to determine the canonical representations for finite order Kronecker powers of any given orthogonal tensor; and by usingthe recurrence formulae we derive the canonical representations for first, second, third and fourth order Kronecker powers of any two or three-dimensional orthogonai tensor. Finally, we apply these results to construct the micropolar elasticity matrices for micropolar elastic tensors under the 13 anisotropic mechanics symmetry groups Cn=1, 2....,13 as well as the isotropic symmetry group Co; and we also explain how to find an appropriate orthogonal tensor subgroup which may be regarded as the idealized material symmetry group for a given tensor.
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【期刊论文】TENSORS WHICH CHARACTERIZE ANISOTROPIES
郑泉水, Q.-S. ZHENG, A. J. M. SPENCER
Printed in Great Britain. All rights reserved Vol. 31, No.5, pp. (1993) 679-693,-0001,():
-1年11月30日
The theory of tensor function representations constitutes a rational basis for a consistentma them atical modelling of complex mechanical behaviour of anisotropic materials. The so-ca Uedstructural tensors, which characterize the symmetry group of anisotropy of concern, play a key role inobtaining irreducible and coordinate-free representations for anisotropic tensor functions. In thispaper, based on available properties of Kronecker products of orthogonal transformations, a simplemethod of determining the structural tensors with respect to any given symmetry group is developed.As its application, the structural tensors corresponding to the five transverse isotropy groups, all oftheir finite subgroups, and the symmetry group of the 32 crystal classes, which present the most usualand worthwhile anisotropic symmetry groups, are constructed. In particular, we also show that each ofthese anisotropic symmetry groups can be characterized by only one simple structural tensor.
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