The Euler–Bernoulli Limit of Thin Brittle Linearized Elastic Beams

Abstract

AbstractWe show that the linear brittle Griffith energy on a thin rectangle $\varGamma $ 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.