6533b872fe1ef96bd12d3a7f
RESEARCH PRODUCT
A new constructive method using the theory of invariants to obtain material behavior laws
Alain ThionnetAlain ThionnetC. MartinC. Martinsubject
PolynomialAnisotropic material[ PHYS.COND.CM-MS ] Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci]02 engineering and technologyTheory of invariants01 natural sciencesConstructiveSet (abstract data type)Constitutive behavior lawMaterials Science(all)0203 mechanical engineeringModelling and SimulationGeneral Materials Science0101 mathematicsMathematicsDegree (graph theory)Basis (linear algebra)Group (mathematics)Continuum (topology)Applied MathematicsMechanical EngineeringState (functional analysis)16. Peace & justiceCondensed Matter Physics010101 applied mathematics020303 mechanical engineering & transportsMechanics of MaterialsModeling and SimulationLaw[PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci]description
International audience; The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-01-01 | International Journal of Solids and Structures |