We introduce a new class of isotropic elastic solids is which is characterized by the constraint λ1λ2+λ1λ3+λ2λ3=3, where the λi, i=1,2,3, stand for the principal stretches. We point out that there is not yet a physical justification for considering this new class of constrained materials' but, as in many other circumstances, it is interesting to see what the theory predicts. We discuss the geometry of the constraintand and derive the stress-strain relation for this class of materials. We also show certain non-homogeneous deformations (such as the bending and stretching of a rectangular block, straightening of an annular cylindrical sector, etc.) to be possible in these materials, subject to boundary tractions alone.
Some nonhomogeneous deformations for a special class of isotropic constrained materials.
SALVATORI, Maria Cesarina
1996
Abstract
We introduce a new class of isotropic elastic solids is which is characterized by the constraint λ1λ2+λ1λ3+λ2λ3=3, where the λi, i=1,2,3, stand for the principal stretches. We point out that there is not yet a physical justification for considering this new class of constrained materials' but, as in many other circumstances, it is interesting to see what the theory predicts. We discuss the geometry of the constraintand and derive the stress-strain relation for this class of materials. We also show certain non-homogeneous deformations (such as the bending and stretching of a rectangular block, straightening of an annular cylindrical sector, etc.) to be possible in these materials, subject to boundary tractions alone.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
