Costanti di Lamé

Nella meccanica del continuo, le costanti di Lamé sono una coppia di parametri dipendenti dal materiale, denotati rispettivamente con le lettere greche λ e μ, che compaiono nella relazione tra deformazione e tensione interna.[1] Prendono il nome da Gabriel Lamé e in generale sono note come prima e seconda costante di Lamé, ma a seconda del contesto differenti nomi possono essere usati. Ad esempio, in meccanica dei fluidi μ è nota come viscosità dinamica, mentre nel contesto delle deformazioni elastiche è nota come modulo di taglio,[2] che è a volte indicato con G (tipicamente la notazione con G è usata insieme al modulo di Young E, quella con μ insieme a λ).

Per i materiali isotropi e omogenei, le costanti di Lamé definiscono la legge di Hooke nel caso tridimensionale

dove σ è la tensione interna, ε il tensore di deformazione, la matrice identità e la traccia.

Le due costanti formano una parametrizzazione del modulo elastico per materiali omogenei isotropi, usata in genere per esprimere altri moduli elastici, ad esempio il modulo di compressibilità può essere scritto come .

Mentre la seconda costante è sempre positiva, la prima costante può assumere valori negativi, sebbene sia positiva per la maggior parte dei materiali.

Le costanti hanno la stessa dimensione di una tensione, e tipicamente hanno assegnata un'unità di pressione in analisi dimensionale.

Note

  1. ^ "Lamé Constants". Weisstein, Eric. Eric Weisstein's World of Science, A Wolfram Web Resource. Retrieved 2015-02-22.
  2. ^ Jean Salencon (2001), "Handbook of Continuum Mechanics: General Concepts, Thermoelasticity". Springer Science & Business Media ISBN 3-540-41443-6

Bibliografia

  • K. Feng, Z.-C. Shi, Mathematical Theory of Elastic Structures, Springer New York, ISBN 0-387-51326-4, (1981)
  • G. Mavko, T. Mukerji, J. Dvorkin, The Rock Physics Handbook, Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)
  • W.S. Slaughter, The Linearized Theory of Elasticity, Birkhäuser, ISBN 0-8176-4117-3, (2002)

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