Publications

2024

• The T-coercivity approach for mixed problems
  
  • Barré Mathieu
  • Ciarlet Patrick
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2024, 362, pp.1051-1088. Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the T-coercivity approach to derive a global inf-sup condition. Generally speaking, this is a constructive approach that, in addition, drives the design of suitable approximations. As a matter of fact, the derivation of the uniform discrete inf-sup condition for the approximate problems follows easily from the study of the original problem. To support our view, we solve a series of classical mixed problems with the T-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems. (10.5802/crmath.590)
  DOI : 10.5802/crmath.590
• Three‐dimensional multiscale assembly of phyllosilicates, organics, and carbonates in small Ryugu fragments
  
  • Dionnet Zelia
  • Rubino Stefano
  • Aléon-Toppani Alice
  • Brunetto Rosario
  • Tsuchiyama Akira
  • Lantz Cateline
  • Djouadi Zahia
  • Baklouti Donia
  • Nakamura Tomoki
  • Borondics Ferenc
  • Sandt Christophe
  • Héripré Eva
  • Troadec David
  • Mivumbi Obadias
  • Aléon Jérome
  • Ternier Theo
  • Matsumoto Megumi
  • Amano Kana
  • Morita Tomoyo
  • Yurimoto Hisayoshi
  • Noguchi Takaaki
  • Okazaki Ryuji
  • Yabuta Hikaru
  • Naraoka Hiroshi
  • Sakamoto Kanako
  • Tachibana Shogo
  • Yada Toru
  • Nishimura Masahiro
  • Nakato Aiko
  • Miyazaki Akiko
  • Yogata Kasumi
  • Abe Masanao
  • Okada Tatsuaki
  • Usui Tomohiro
  • Yoshikawa Makoto
  • Saiki Takanao
  • Tanaka Satoshi
  • Terui Fuyuto
  • Nakazawa Satoru
  • Watanabe Seiichiro
  • Tsuda Yuichi
  Meteoritics and Planetary Science, Wiley, 2024, 59 (8), pp.1859-1876. We report μm‐scale nondestructive infrared (IR) hyperspectral results (IR computed tomography, IR‐CT) in 3‐D and IR surface imaging, IR‐S) in 2‐D, at SOLEIL) combined with X‐ray nano‐computed tomography analyses (at SPring‐8) performed on eight small Ryugu fragments extracted from mm‐sized grains coming both from touchdown first and second sites. We describe the multiscale assembly of phyllosilicates, carbonates, sulfides, oxides, and organics. Two types of silicates, as well as diverse kinds of organic matter, were detected inside Ryugu material. Their spatial correlations are described to discuss the role of the mineralogical microenvironments in the formation/evolution of organic matter. In particular, we have shown that there is a redistribution of the organic matter diffuse component during aqueous alteration on the parent body, with a preferential circulation among fine‐grained phyllosilicates. (10.1111/maps.14068)
  DOI : 10.1111/maps.14068
• Asymptotic, second-order homogenization of linear elastic beam networks
  
  • Ye Yang
  • Audoly Basile
  • Lestringant Claire
  Journal of the Mechanics and Physics of Solids, Elsevier, 2024, 188, pp.105637. We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and geometric properties are allowed to vary slowly in space, in addition to being periodic at the scale of the unit cell. The reference configuration may be prestressed. A homogenized strain energy depending on both the macroscopic strain ɛ and its gradient ∇ɛ is obtained by means of a two-scale expansion. The homogenized energy is asymptotically exact two orders beyond that obtained by classical homogenization. The homogenization method is implemented in a symbolic calculation language and applied to various types of networks, such as a 2D honeycomb, a 2D Kagome lattice, a 3D truss and a 1D pantograph. It is validated by comparing the predictions of the microscopic displacement to that obtained by full, discrete simulations. This second-order method remains highly accurate even when the strain gradient effects are significant, such as near the lips of a crack tip or in regions where a gradient of pre-strain is imposed. (10.1016/j.jmps.2024.105637)
  DOI : 10.1016/j.jmps.2024.105637