2020/08/31 by Cy Maor, Maria Giovanna Mora · 14 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Elasticity (physics) #Elasticity and Material Modeling #Linear elasticity #Linear system #Mathematics and Applications #Nonlinear elasticity #Nonlinear system #Nonlocal and gradient elasticity in micro/nano structures #Term (time) #Traction (geology) #math-ph #math.AP #math.MP #msc:74B20
paper · pdf · doi:10.1007/s00332-021-09716-2
published in Journal of Nonlinear Science 31(3) (Springer Science+Business Media) · v2: minor changes and clarification, Example 6.5 added
openalex created_date 2020/09/01 · arxiv created 2021/05/17 · openalex publication_date 2021/05/17 · arxiv updated 2021/05/18 · openalex updated_date 2026/08/06
Abstract We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full Γ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -convergence result. The analysis relies on identifying the correct reference configuration to linearize about, and studying its relation to the rotations preferred by the forces ( optimal rotations ). The Γ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -limit is the standard linear elasticity model, plus a term that penalizes for fluctuations of the reference configurations from the optimal rotations. However, on minimizers this additional term is zero and the limit energy reduces to standard linear elasticity.