Distance to plane elasticity orthotropy by Euler–Lagrange method

Antonelli, Adrien; Desmorat, Boris; Kolev, Boris; Desmorat, Rodrigue

doi:10.5802/crmeca.122

Cited by 8 publications

(6 citation statements)

References 33 publications

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“…Moreover, in the 3D case there are more material classes. Depending on the symmetry class, the associated distances are-to our knowledge-not yet ana-lytically given and thus have to be computed numerically [39,63]. Thus, the theoretical adaption is feasible, but we expect the computational challenges of the 3D case to be significantly larger.…”

Section: Discussionmentioning

confidence: 99%

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

et al. 2022

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A fuzzy arithmetic framework for the efficient possibilistic propagation of shape uncertainties based on a novel fuzzy edge detection method is introduced. The shape uncertainties stem from a blurred image that encodes the distribution of two phases in a composite material. The proposed framework employs computational homogenisation to upscale the shape uncertainty to a effective material with fuzzy material properties. For this, many samples of a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying mapping from shape parametrisation to the upscaled material behaviour, a diffeomorphism is constructed by generating an appropriate family of meshes via transformation of a reference mesh. The shape uncertainty is then propagated to measure the distance of the upscaled material to the isotropic and orthotropic material class. Finally, the fuzzy effective material is used to compute bounds for the average displacement of a non-homogenized material with uncertain star-shaped inclusion shapes.

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Section: Discussionmentioning

confidence: 99%

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

et al. 2022

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“…This approach, developed further by Vannucci, is useful for the design of composite materials [41]. Another point of view consists in evaluating the distance to a given symmetry class [42]. In recent years, a new trend appears, the study of the coupling of the elasticity with other phenomena, in particular the piezoelectricity (appearance of a polarization in a dielectric material when it is subjected to an uniform mechanical strain) and the flexoelectricity (linear response of a polarization to a non-uniform strain or a strain-gradient) [43].…”

Section: Symmetry Group Of Constitutive Lawsmentioning

confidence: 99%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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“…Since elements within a stratum have conjugate symmetry groups, the stability with regard to linear combination is not automatic. It can be proved that for 2D linear elasticity, all closed strata, except the orthotropy one, are vector spaces (Vianello, 1997;Antonelli, Desmorat, Kolev and Desmorat, 2022).…”

Section: For Orthotropic Elasticity Tensorsmentioning

confidence: 99%