39 citations · 82 across the 11 of their papers we have counts for
13 papers
Geometric theory of generalised continua using moving frames
Boris Kolev, Cl{é}ment Ecker
Generalised continuum theories couple the macroscopic deformation and the micro-/meso-scopic deformation of an underlying micro-structure. They can account for internal length-scal…
Weyl's Polarization in Classical Invariant Theory: A Primer, with Worked Examples
L. Darondeau, M. Florence, B. Kolev
Hermann Weyl's The Classical Groups is a landmark work connecting classical invariant theory with modern representation theory. It shows how polynomial invariants of the general li…
Minimal surfaces: A Lagrangian derivation of first and second variations
Romain Lloria, Boris Kolev
This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. It is shown, i…
The linear Elasticity complex: a natural formulation
Romain Lloria, Boris Kolev
We reformulate the Elasticity complex and Saint-Venant's compatibility condition using the generalized differential complex of Dubois-Violette-Henneaux. This is just a slight and n…
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…
The Haar measure in solid mechanics
Clément Ecker, Boris Kolev
This article addresses the overlooked but crucial role of the Haar measure in solid mechanics, a concept well-established in mathematical literature but frequently misunderstood by…
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…
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…
Harmonic factorization and reconstruction of the elasticity tensor
Marc Olive, Boris Kolev, Boris Desmorat +1
In this paper, we propose a factorization of a fourth-order harmonic tensor into second-order tensors. We obtain moreover explicit equivariant reconstruction formulas, using second…
A minimal integrity basis for the elasticity tensor
Nicolas Auffray, Marc Olive, Boris Kolev
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)-irreducibl…