An Extended Technique for Computation of Laplace Transformed Dynamic Fundamental Solutions for 3d Anisotropic Elastic Solids

We study three “incompressibility flavors” of linearly elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric, and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

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The Eigenvectors of the S Matrix and Their Relations with Line Dislocations and Forces in Anisotropic Elastic Solids

Micromechanics and Inhomogeneity ◽

10.1007/978-1-4613-8919-4_29 ◽

1990 ◽

pp. 449-467 ◽

Cited By ~ 2

Author(s):

T. C. T. Ting

Keyword(s):

Elastic Solids ◽

S Matrix ◽

Anisotropic Elastic

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Finite strains in an anisotropic elastic continuum

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1950.0105 ◽

1950 ◽

Vol 202 (1070) ◽

pp. 345-358 ◽

Cited By ~ 19

Keyword(s):

Equations Of State ◽

Elastic Solid ◽

Finite Strains ◽

Free Energy Function ◽

Elastic Solids ◽

Elastic Continuum ◽

Invariance Properties ◽

Anisotropic Elastic ◽

Necessary And Sufficient ◽

Thermodynamic Restrictions

The discussion in a previous paper (Oldroyd 1950), on the invariance properties required of the equations of state of a homogeneous continuum, is extended by taking into account thermodynamic restrictions on the form of the equations, in the case of an elastic solid deformed from an unstressed equilibrium configuration. The general form of the finite strainstress-temperature relations, expressed in terms of a free-energy function, is deduced without assuming that the material is isotropic. The results of other authors based on the assumption of isotropy are shown to follow as particular cases. The equations of state are derived by considering quasi-static changes in an elastic solid continuum; the results then apply to non-ideally elastic solids in equilibrium, or subjected to quasi-static changes only, and to ideally elastic solids in general motion. A necessary and sufficient compatibility condition for the finite strains at different points of a continuum is also derived. As a simple illustration of the derivation and use of equations of state involving anisotropic physical constants, the torsion of an anisotropic cylinder is discussed briefly.

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