16 citations · 85 across the 17 of their papers we have counts for
21 papers
Classical and relativistic balance of configurational forces
Rodrigue Desmorat, Anthony Gravouil, Boris Kolev
This article develops a unified variational framework for configurational (or material) forces in both Classical (3D, non-relativistic) and Relativistic (4D) Continuum Mechanics. C…
Relativistic second gradient theory of continuous media
Mina Chapon, Lionel Darondeau, Rodrigue Desmorat +2
Variational Relativity is a framework developed by Souriau in the sixties to better formulate General Relativity and its classical limit\,: Classical Continuum Mechanics. It has be…
Souriau's Relativistic general covariant formulation of hyperelasticity revisited
Boris Kolev, Rodrigue Desmorat
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 m…
On the isotropy stratification of a real representation of a compact Lie group
Perla Azzi, Rodrigue Desmorat, Julien Grivaux +1
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some resul…
Distance to a constitutive tensor isotropy stratum by Lasserre polynomial optimization method
Perla Azzi, Rodrigue Desmorat, Boris Kolev +1
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 t…
Upper bounds estimates of the distance to cubic or orthotropic elasticity
Rodrigue Desmorat, Boris Kolev
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…
The distance to cubic symmetry class as a polynomial optimization problem
Perla Azzi, Rodrigue Desmorat, Boris Kolev +1
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 Nickel…
Reduced polynomial invariant integrity basis for in-plane magneto-mechanical loading
Julien Taurines, Boris Kolev, Rodrigue Desmorat +1
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…
Distance to plane elasticity orthotropy by Euler-Lagrange method
Adrien Antonelli, Boris Desmorat, Boris Kolev +1
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 re…
Objective rates as covariant derivatives on the manifold of Riemannian metrics
Boris Kolev, Rodrigue Desmorat
The subject of so-called objective derivatives in Continuum Mechanics has along history and has generated varying views concerning their true mathematical interpretation. Several a…
Minimal functional bases for elasticity tensor symmetry classes
Rodrigue Desmorat, N Auffray, B Desmorat +2
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 functio…
An intrinsic geometric formulation of Hyper-elasticity, pressure potential and non-holonomic constraints
Boris Kolev, Rodrigue Desmorat
Isotropic hyper-elasticity, altogether with the equilibrium equation and the usual boundary conditions, are formulated directly on the body B, a three-dimensional compact and orien…
Integrity bases for cubic nonlinear magnetostriction
Julien Taurines, Marc Olive, Rodrigue Desmorat +2
A so-called smart material is a material that is the seat of one or more multiphysical coupling. One of the key points in the development of the constitutive laws of these material…
Continuous anisotropic damage as a twin modelling of discrete bi-dimensional fracture
C Oliver-Leblond, R Desmorat, Boris Kolev
In this contribution, the use of discrete simulations to formulate an anisotropic damage model is investigated. It is proposed to use a beam-particle model to perform numerical cha…
Computation of minimal covariants bases for 2D coupled constitutive laws
Boris Desmorat, Marc Olive, Nicolas Auffray +2
We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors an…
On the determination of plane and axial symmetries in linear Elasticity and Piezo-electricity
Marc Olive, Boris Desmorat, Boris Kolev +1
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 con…
Recovering the normal form of an elasticity tensor
Sophie Abramian, Boris Desmorat, Rodrigue Desmorat +2
We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which b…
Reduced algebraic conditions for plane/axial tensorial symmetries
Marc Olive, Boris Desmorat, Boris Kolev +1
In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of o…
Generic separating sets for 3D elasticity tensors
Rodrigue Desmorat, Nicolas Auffray, Boris Desmorat +2
We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants…
Characterization of the symmetry class of an Elasticity tensor using polynomial covariants
Marc Olive, Boris Kolev, R. Desmorat +1
We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of e…
Micromechanics based framework with second-order damage tensors
Rodrigue Desmorat, Boris Desmorat, Marc Olive +1
The harmonic product of tensors---leading to the concept of harmonic factorization---has been defined in a previous work (Olive et al, 2017). In the practical case of 3D crack dens…