The Euler-Bernoulli Limit of Thin Brittle Linearized Elastic Beams

被引：0

作者：

Ginster, Janusz ^{[1
]}

Gladbach, Peter ^{[2
]}

机构：

[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany

[2] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

JOURNAL OF ELASTICITY | 2024年 / 156卷 / 01期

关键词：

Dimension reduction; Brittle fracture; Gamma-Convergence; Euler-Bernoulli beam; NONLINEAR MEMBRANE ENERGY; VARIATIONAL DERIVATION; GAMMA-LIMIT; MODEL; FRACTURE; BLAKE; FILMS;

D O I：

10.1007/s10659-023-10040-x

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We show that the linear brittle Griffith energy on a thin rectangle Gamma-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.

引用

页码：125 / 155

页数：31

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