Related papers: An Irreducible Polynomial Functional Basis of Two-…

The elasticity tensor is one of the most important fourth order tensors in mechanics. Fourth order three-dimensional symmetric and traceless tensors play a crucial role in the study of the elasticity tensors. In this paper, we present two…

Tensor function representation theory is an essential topic in both theoretical and applied mechanics. For the elasticity tensor, Olive, Kolev and Auffray (2017) proposed a minimal integrity basis of 297 isotropic invariants, which is also…

Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four…

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity…

For piezoelectric tensors, Olive (2014) proposed a minimal integrity basis of 495 hemitropic invariants, which is also a functional basis. In this article, we construct a new functional basis of hemitropic invariants of piezoelectric…

In this paper, we address the open problem (stated in Pennisi and Trovato, 1987. Int. J. Engng Sci., 25(8), 1059-1065) associated with the irreducibility of representations for isotropic functions. In particular, we prove that for isotropic…

In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity…

We present a straightforward analytical-numerical methodology for determining polynomially complete and irreducible scalar-valued invariant sets for anisotropic hyperelasticity. By applying the proposed technique, we obtain irreducible…

In this paper, we study invariants of second order tensors in an $n$-dimensional flat Riemannian space. We define eigenvalues, eigenvectors and characteristic polynomials for second order tensors in such an $n$-dimensional Riemannian space…

We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor C. Decomposing C into its SO(3)-irreducible components we reduce this problem to finding joint…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…

Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativity theory. The singular values and spectral norm of a…

Eshelby's inclusion problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically…

Functional bases, synonymous with separating sets, are usually formulated for an entire vector space, such as the space Ela of elasticity tensors. We propose here to define functional bases limited to symmetry strata, i.e. sets of tensors…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

Fourth-order tensor-valued functions appear in numerous fields of study. The formulation of practical models for these complex functions often requires their representation in terms of tensors of order two. In this paper, we develop an…

In 1957 Eshelby showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in a homogeneous isotropic host would feel uniform strains and stresses when uniform strains or stresses are applied in the far-field. Of specific…

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…

We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all…