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Azzi, Perla; Desmorat, Rodrigue; Kolev, Boris; Priziac, Fabien

Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method. (English) Zbl 1527.90149

Math. Mech. Complex Syst. 11, No. 3, 393-428 (2023).
Summary: We give a detailed description of a polynomial optimization method allowing one 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 experimental tensor, and the calculation of the distance to the given tensor from the considered isotropy stratum. We take advantage of the fact that the isotropy strata are semialgebraic sets to show that the method, developed by Lasserre and coworkers which consists in solving polynomial optimization problems with semialgebraic constraints, successfully applies.

MSC:

90C23 Polynomial optimization
14P10 Semialgebraic sets and related spaces
74B05 Classical linear elasticity
74E10 Anisotropy in solid mechanics
90C22 Semidefinite programming

Keywords:

polynomial optimization; Lasserre’s method; semidefinite programming; distance to a symmetry class; cubic symmetry; elasticity; piezoelectricity; semialgebraic and real algebraic geometry
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