In this note we discuss the strong ellipticity condition within the nonlinear strain gradient elasticity. Considering a one-dimensional case, i.e. an elastic bar loaded by a tensile force, we analyze the correspondence of violation of the strong ellipticity condition and compare the results with classic nonlinear elasticity. The correspondence of ellipticity loss to the non-uniqueness of solutions are discussed in more detail.

Strong Ellipticity Within the Strain Gradient Elasticity: Elastic Bar Case

Eremeyev V. A.
;
Reccia E.
2022-01-01

Abstract

In this note we discuss the strong ellipticity condition within the nonlinear strain gradient elasticity. Considering a one-dimensional case, i.e. an elastic bar loaded by a tensile force, we analyze the correspondence of violation of the strong ellipticity condition and compare the results with classic nonlinear elasticity. The correspondence of ellipticity loss to the non-uniqueness of solutions are discussed in more detail.
2022
978-3-031-04547-9
978-3-031-04548-6
Strong ellipticity; Strain gradient elasticity; Nonlinear elasticity; Elastic bar; Non-uniqueness
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/335873
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