0588490 20250317090234.220240814235959.9 85193696710 000986340000001 10.1017/prm.2023.36 24 s. P cav_un_epca*02575020308-21051543 (2024)769-792Royal Society of Edinburgh Two-well problems nonlinear elasticity rigidity estimates cav_un_auth*0471276 Akramov I. DE cav_un_auth*0471277 Knuepfer H. DE 25 cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR 25 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0471278 Rueland A. DE 25 https://library.utia.cas.cz/separaty/2024/MTR/kruzik-0588490.pdf https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/minimal-energy-for-geometrically-nonlinear-elastic-inclusions-in-two-dimensions/8E4138F662DB9421EEF5E96FB8A95D34 GF21-06569K GA ČR cav_un_auth*0412957 We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from Conti and Schweizer (Commun. Pure Appl. Math. 59 (2006), 830–868) and Knüpfer and Kohn (Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 467 (2011), 695–717), we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion. WOS BA 10000 10100 10102 2025 4 RVO:67985556 https://hdl.handle.net/11104/0355756 S C MATHEMATICS.APPLIED|MATHEMATICS 1.2 0.2 16.8 0.00389 0.884 2807 64 1.076 33.04 0.98 375 Q1 0.800 131 Q2 53 0.8 Q2 67.6 2024 85193696710 SCOPUS PUBMED 000986340000001 WOS cav_un_epca*0257502 Proceedings of the Royal Society of Edinburgh. A - Mathematics Roč. 154 č. 3 2024 769 792 0308-2105 1473-7124 Royal Society of Edinburgh