Waves in Constrained Linear Elastic Materials |
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Authors: | Maria Luisa Tonon |
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Institution: | (1) Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy |
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Abstract: | This paper deals with the propagation of acceleration waves in constrained linear elastic materials, within the framework
of the so-called linearized finite theory of elasticity, as defined by Hoger and Johnson in 12, 13]. In this theory, the
constitutive equations are obtained by linearization of the corresponding finite constitutive equations with respect to the
displacement gradient and significantly differ from those of the classical linear theory of elasticity. First, following the
same procedure used for the constitutive equations, the amplitude condition for a general constraint is obtained. Explicit
results for the amplitude condition for incompressible and inextensible materials are also given and compared with those of
the classical linear theory of elasticity. In particular, it is shown that for the constraint of incompressibility the classical
linear elasticity provides an amplitude condition that, coincidently, is correct, while for the constraint of inextensibility
the disagreement is first order in the displacement gradient. Then, the propagation condition for the constraints of incompressibility
and inextensibility is studied. For incompressible materials the propagation condition is solved and explicit values for the
squares of the speeds of propagation are obtained. For inextensible materials the propagation condition is solved for plane
acceleration waves propagating into a homogeneously strained material. For both constraints, it is shown that the squares
of the speeds of propagation depend by terms that are first order in the displacement gradient, while in classical linear
elasticity they are constant.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | acceleration waves constrained elastic materials linearized finite elasticity |
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