Journal Article10.1007/BF00281221
Integrity Bases for a Symmetric Tensor and a Vector—The Crystal Classes
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TL;DR: In this paper, the integrity bases for symmetric second-order tensors and a vector for the transformation groups corresponding to each of the crystal classes are derived and the irreducibility of the integrity basis is proven.
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Abstract: Integrity bases are derived for a symmetric second-order tensor and a vector for the transformation groups corresponding to each of the crystal classes. In each case the irreducibility of the integrity basis is proven.
read more
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Citations
Mathematical homogenization theory for electroactive continuum
S. I. Kuznetsov,Jacob Fish +1 more
TL;DR: In this paper, two-scale continuum equations are derived for heterogeneous continua with full nonlinear electromechanical coupling using nonlinear mathematical homogenization theory, which can be applied to analyze the behavior of electroactive materials with heterogeneous fine-scale structure.
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Representation of Constitutive Equations in Creep Mechanics of Isotropic and Anisotropic Materials
Josef Betten
- 01 Jan 1981
TL;DR: In this article, the authors formulated constitutive equations for the secondary creep stage of isotropic and anisotropic materials, which can depend only on the basic or principal invariants of the stress tensor.
27
A unified approach to constitutive equations of inelasticity based on tensor function representations
S. Murakami,A. Sawczuk +1 more
TL;DR: In this paper, the applicability of the tensor function theory to the development of elaborate and rational constitutive equations of inelasticity is discussed to facilitate the description of the complicated in-elastic response of structural components.
24
Tensor representation of magnetostriction for all crystal classes
TL;DR: A systematic representation of the fourth-order magnetostriction tensor for all crystal classes is presented, based on the formalism proposed by Walpole, which allows the stress-free magnetostrictive strain tensor as well as the scalar strain in a given direction to be calculated.
23
Integrity bases, invariant operators and the state labelling problem for finite subgroups of SO3
R P Bickerstaff,B G Wybourne +1 more
TL;DR: In this article, the construction of integrity bases and invariant operators for finite subgroups of SO3 is discussed, where the integrity bases are realized in terms of rotationally invariant sets of kets and the invariant operator is realized by irreducible tensorial sets.
21
References
Ternary Quadratic Types
TL;DR: The first part of this paper deals with the determination of the complete system of concomitants of five or fewer ternary quadratic forms, and it is shown that this system is irreducible as discussed by the authors.
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Further results on the strain-energy function for anisotropic elastic materials
TL;DR: In this paper, it was shown that W is expressible in the form (t2) and there are no non-trivial relations of the form in this form.
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