Sommario
Si prova che la restrizione forte di Baker & Ericksen sulla funzione di risposta di un materiale elastico compressibile isotropo costituisce condizione necessaria e sufficiente perchè ad uno sforzo uniassiale corrisponda una deformazione di semplice estensione.
Si mostra come la stessa restrizione assicuri, più in generale, uguale molteplicità per gli autovalori del tensore degli sforzi e della misura di deformazione. Si ottiene infine una nuova restrizione a priori che coinvolge soltanto due dei coefficienti di risposta.
Summary
We prove that the strong restriction of Baker & Ericksen on the response function of a compressible elastic material is equivalent to require that a simple extension corresponds to simple tension.
We also show that under the same restriction, corresponding eigenvalues of the stress tensor and the measure of deformation have the same multiplicity. Finally, a new restriction involving only two response coefficients is proposed.
References
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Marzano, S. An interpretation of Baker-Ericksen inequalities in uniaxial deformation and stress. Meccanica 18, 233–235 (1983). https://doi.org/10.1007/BF02128248
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DOI: https://doi.org/10.1007/BF02128248