Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior

1993 ◽  
Vol 60 (2) ◽  
pp. 265-269 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Spontaneous Polarization ◽  
Electric Field Intensity ◽  
Local Fields ◽  
Composite Media ◽  
Piezoelectric Composites ◽  
Arbitrary Phase ◽  
Electromechanical Loading ◽  
Piezoelectric Behavior ◽  
Binary Composite ◽  
Effective Constants

Binary composite media of arbitrary phase geometry are considered. The constituent phases have general anisotropic piezoelectric behavior and contain constant eigenstress and spontaneous polarization fields. An electromechanical loading of the composite aggregate is found which results in uniform strain and electric field intensity throughout the solid. The existence of these uniform fields is used to derive exact universal relations between the local fields as well as between the effective constants of the composite aggregate.

Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity

1993 ◽  
Vol 441 (1911) ◽  
pp. 59-81 ◽  
Keyword(s):  
Transversely Isotropic ◽  
Dielectric Constants ◽  
Local Fields ◽  
Piezoelectric Composite ◽  
Uniform Temperature ◽  
Piezoelectric Composites ◽  
Three Phase ◽  
Phase Systems ◽  
Electromechanical Loading ◽  
Exact Relations

Piezoelectric fibrous composites of two, three and four phases are considered. The phase boundaries are cylindrical but otherwise the microgeometry is totally arbitrary. The constituents are transversely isotropic, and exhibit pyroelectricity. Exact relations are derived between the local fields arising under a uniform electromechanical loading and a uniform temperature change in the piezoelectric composite. For given overall material symmetry, exact connections are obtained among the effective elastic, piezoelectric and dielectric constants of two- and three- phase systems. It is also shown that the effective thermal stress and pyroelectric coefficients can be expressed in terms of the effective elastic, piezoelectric, dielectric constants and constituent properties in two-, three- and four-phase composites.

Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part II: Multiphase Media—Effective Behavior

1993 ◽  
Vol 60 (2) ◽  
pp. 270-275 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Spontaneous Polarization ◽  
Binary Systems ◽  
Virtual Work ◽  
Companion Paper ◽  
Piezoelectric Composites ◽  
Piezoelectric Media ◽  
Electromechanical Loading ◽  
Dielectric Tensors ◽  
The Individual ◽  
Special Case

We consider heterogeneous piezoelectric media in general and multiphase piezoelectric composites in particular. A distribution of statistically homogeneous eigenstress and spontaneous polarization fields is admitted in the solid which is itself statistically homogeneous, and the effective eigenstress and spontaneous polarization is sought. The method here is based on the use of virtual work theorems in piezoelectric media and therefore differs from the approach used in the companion paper (Benveniste, 1993). We show that the effective eigenstress and polarization follow from a knowledge of the influence functions related to an electromechanical loading of the composite aggregate in which no eigenstresses and polarizations are present. When applied to the special case of binary systems with constant eigenstress and polarization fields in the phases, the above result implies that the effective eigenstress and polarization can be determined in terms of the effective elastic, piezoelectric, dielectric tensors of the medium, the constituent properties, and the individual eigenstresses and polarizations.

Exact Results Concerning the Local Fields and Effective Properties in Piezoelectric Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 260-267 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Effective Properties ◽  
Transversely Isotropic ◽  
Local Fields ◽  
The Other ◽  
Effective Moduli ◽  
Piezoelectric Composites ◽  
Arbitrary Phase ◽  
New Findings ◽  
Piezoelectric Solids ◽  
Underlying Theme

This paper consists of two parts: (a) a concise summary and discussion is given of the recent contributions of the author in the micromechanics of piezoelectric composites. The underlying theme here is the derivation of exact connections for the local fields and effective moduli of heterogeneous piezoelectric solids. Composites of arbitrary phase geometry as well as fibrous systems are considered. (b) New results are presented on the effective behavior of fibrous piezoelectric systems. Fibrous composites with transversely isotropic constituents and cylindrical microgeometry are considered. The exact connections of the author (Benveniste (1993), Proc. R. Soc., Series A, Vol. 441, pp. 59-81) are extended to include the most generally possible overall symmetry of the composite aggregate. The other category of the new findings concerns exact expressions for the effective thermal terms of fibrous systems which possess the same shear modulus GT.

Dielectric and piezoelectric behavior of PVDF-modified 3-3 type cement-based piezoelectric composites

2021 ◽  
Author(s):  
Wei Liu ◽  
Jianneng Yin ◽  
Jianhong Wang ◽  
Yingge Dong ◽  
Zhi Cheng ◽  
...  
Keyword(s):  
Piezoelectric Composites ◽  
Piezoelectric Behavior

Exact connections between polycrystal and crystal properties in two-dimensional polycrystalline aggregates

1994 ◽  
Vol 447 (1929) ◽  
pp. 1-22 ◽  
Keyword(s):  
Three Dimensional ◽  
Local Fields ◽  
Field Analysis ◽  
Uniform Field ◽  
Two Dimensional ◽  
Special Cases ◽  
Crystal Properties ◽  
Polycrystalline Aggregates ◽  
Special Case ◽  
Effective Constants

Exact connections are shown to exist between the properties of two-dimensional polycrystalline aggregates and those of its constituent elongated crystals. The analysis is given for piezoelectric crystals and polycrystals. Both the crystal and the polycrystal are assumed to belong to the 2 mm class of the orthorhombic system. Classes that are special cases of 2 mm crystals are also admitted. The corresponding results for purely elastic aggregates, hitherto unknown, are obtained as a special case. The majority of the derived results are an outcome of uniform fields in the polycrystals considered, whose existence is established in this paper. In addition, these fields allow the derivation of certain correspondence relations between the pointwise local fields in the polycrystal, when it is subjected to certain electromechanical loadings. Exact connections for a subclass of the effective constants which are not amenable to the uniform field analysis are obtained by a matrix diagonalization formalism. It is shown that uniform fields and local correspondence relations exist also in three-dimensional elastic polycrystalline aggregates with tetragonal, hexagonal or trigonal crystals.

Effective Behavior of Piezoelectric Composites

1994 ◽  
Vol 47 (1S) ◽  
pp. S112-S121 ◽  
Author(s):  
Biao Wang
Keyword(s):  
Electric Field ◽  
Piezoelectric Material ◽  
Transversely Isotropic ◽  
Piezoelectric Composite ◽  
Algebraic Equations ◽  
Piezoelectric Composites ◽  
Spheroidal Inclusion ◽  
Linear Algebraic Equations ◽  
General Relations ◽  
Effective Constants

In this paper, general relations between the overall properties of piezoelectric composites and the properties of their constituents are derived. Based on the solution for an ellipsoidal inclusion in a piezoelectric material developed by Wang (Int. J. Solids and Structures, 29, 293, 1992), it is found that the coupled elastic and electric field inside a spheroidal inclusion in a transversely isotropic, piezoelectric matrix can be expressed in terms of a system of the linear algebraic equations which contains only some simple integrals. These internal fields are then used to obtain the effective constants of a piezoelectric composite.

Thermal Expansion of Elastic-Plastic Composite Materials

1986 ◽  
Vol 53 (4) ◽  
pp. 737-743 ◽  
Author(s):  
G. J. Dvorak
Keyword(s):  
Composite Materials ◽  
Heterogeneous Media ◽  
Moisture Absorption ◽  
Thermal Strain ◽  
Local Fields ◽  
Mechanical Stiffness ◽  
Plastic Composite ◽  
Decomposition Procedure ◽  
Concentration Factors ◽  
Binary Composite

Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stiffness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also, the local instantaneous thermal strain and stress concentration factors are related in an exact way to the corresponding mechanical concentration factors. The results depend on instantaneous thermoelastic constants and volume fractions of the phases. They are found for fibrous composites with two distinct elastically isotropic or transversely isotropic phases, and for any binary composite with elastically isotropic phases. The results indicate that in the plastic range the thermal and mechanical loading effects are coupled even if the phase properties do not depend on changes in temperature. The derivation is based on a novel decomposition procedure which shows that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase eigenstrains with local strains, caused by piecewise uniform stress fields which are in equilibrium with prescribed surface tractions. The method is extended to discretized microstructures, and also to the analysis of moisture absorption and phase transformation effects on overall response and on local fields in the two composite materials.

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