On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity

Olive, Marc; Desmorat, Boris; Kolev, Boris; Desmorat, Rodrigue

doi:10.1007/s10659-020-09778-5

Cited by 2 publications

(2 citation statements)

References 20 publications

(22 reference statements)

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Order By: Relevance

“…Before detailing the classification obtained, let us explain how order two invariances are explicitly tested. Using results from [45,44], we provide in Theorems 4.1-4.3 the explicit equations to determine axes and/or directions related to such order two symmetries. 4.1.…”

Section: Symmetry Classes Characterisation Using Order Two Symmetriesmentioning

confidence: 99%

“…For any given piezoelectricity tensor P ∈ Piez, an order two symmetry is define to be some 𝑔 = r(𝑛 𝑛 𝑛, 𝜋) or 𝑔 = s(𝑛 𝑛 𝑛) such that with 𝑛 𝑛 𝑛 = (𝑛 1 , 𝑛 2 , 𝑛 3 ) a unit vector in R 3 as unknown, leading to 18 algebraic equations of homogeneous degree 6 in (𝑛 1 , 𝑛 2 , 𝑛 3 ). In fact, following [45,44], it is possible to obtain reduced algebraic equations of degree 3.…”

Section: Symmetry Classes Characterisation Using Order Two Symmetriesmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry classes in piezoelectricity from second-order symmetries

Olive,

Auffray

2020

Preprint

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The piezoelectricity law is a constitutive model that describes how mechanical and electric fields are coupled within a material. In its linear formulation this law comprises three constitutive tensors of increasing order: the second order permittivity tensor S, the third order piezoelectricity tensor P and the fourth-order elasticity tensor C. In a first part of the paper, the symmetry classes of the piezoelectricity tensor alone are investigated. Using a new approach based on the use of the so-called clips operations, we establish the 16 symmetry classes of this tensor and provide their associated normal forms. Second order orthogonal transformations (plane symmetries and 𝜋-angle rotations) are then used to characterize and classify directly 11 out of the 16 symmetry classes of the piezoelectricity tensor. An additional step to distinguish the remaining classes is proposed.

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Section: Symmetry Classes Characterisation Using Order Two Symmetriesmentioning

confidence: 99%

Section: Symmetry Classes Characterisation Using Order Two Symmetriesmentioning

confidence: 99%