Calculus of Variations and Geometric Measure Theory
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E. Mainini - D. Percivale

Sharp conditions for the linearization of finite elasticity

created by mainini on 28 Dec 2020
modified on 12 Oct 2021

[BibTeX]

Published Paper

Inserted: 28 dec 2020
Last Updated: 12 oct 2021

Journal: Calc. Var. Partial Differential Equations
Volume: 60
Number: 164
Year: 2021
Doi: 10.1007/s00526-021-02037-y

ArXiv: 2012.10666 PDF

Abstract:

We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can be strictly lower than the minimal value of the standard linear elastic energy if a strict compatibility condition for external loads does not hold. The results are provided for both the compressible and the incompressible case.

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