The Euler-Bernoulli limit of thin brittle linearized elastic beams

2021/11/18 by Gladbach, Peter, Ginster, Janusz · 1 citation
#49J45 #74B05 #74K10 #74R10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.09706

Abstract

We show that the linear brittle Griffith energy on a thin rectangle Γ-converges after rescaling to the linear one-dimensional brittle Euler-Bernoulli beam energy. In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy

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