Zobrazeno 1 - 10
of 193
pro vyhledávání: '"Desmorat, P."'
Autor:
Kolev, Boris, Desmorat, Rodrigue
We present and modernize Souriau's 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since, focusing as much as possible on the Continuum Mechanics point of view. We describe
Externí odkaz:
http://arxiv.org/abs/2301.09437
In this article we study the isotropy stratification of a linear representation $V$ of a compact Lie group $G$. We prove that the closed isotropy strata are real algebraic manifolds and that for each isotropy subgroup $H$, every rational invariant of
Externí odkaz:
http://arxiv.org/abs/2301.08599
Publikováno v:
Math. Mech. Compl. Sys. 11 (2023) 393-428
We give a detailed description of a polynomial optimization method allowing to solve a problem in continuum mechanics: the determination of the elasticity or the piezoelectricity tensor of a specific isotropy stratum the closest to a given experiment
Externí odkaz:
http://arxiv.org/abs/2207.04729
Autor:
Desmorat, Rodrigue, Kolev, Boris
We address the problem, not of the determination -- which usually needs numerical methods -- but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there are not one
Externí odkaz:
http://arxiv.org/abs/2206.03063
Constitutive tensors are of common use in mechanics of materials. To determine the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We address h
Externí odkaz:
http://arxiv.org/abs/2107.14456
Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickelbased CMSX-4, cubic symmetry is nevertheless expected. It is in practi
Externí odkaz:
http://arxiv.org/abs/2203.14562
The description of the behavior of a material subjected to multi-physics loadings requires the formulation of constitutive laws that usually derive from Gibbs free energies, using invariant quantities depending on the considered physics and material
Externí odkaz:
http://arxiv.org/abs/2202.01883
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 of the same
Externí odkaz:
http://arxiv.org/abs/2105.14930
Publikováno v:
International Journal of Engineering Science, 2023, 191, pp.103880
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 law, photoel
Externí odkaz:
http://arxiv.org/abs/2007.01576
We formulate necessary and sufficient conditions for a unit vector n to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the comp
Externí odkaz:
http://arxiv.org/abs/2003.11272