Abstract
The linearization of response mappings for elastic materials with internal constraints is discussed with a geometric perspective. It is shown that, when the active residual stress is not zero, the Weingarten map of the constraint manifold plays an important role in the deduction of linearized constitutive equations. As an example, the Weingarten map is computed for a material which is incompressible and inextensible in a given direction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W.Noll, Lectures on the foundations of continuum mechanics and thermodynamics.Arch. Rational Mech. Anal. 52 (1973) 62–92.
M. E.Gurtin and P.Podio-Guidugli, The thermodynamics of constrained materials.Arch. Rational Mech. Anal. 51 (1973) 192–208.
P.Podio-Guidugli and M.Vianello, Constraint manifolds for isotropic solids.Arch. Rational Mech. Anal. 105 (1989) 105–121.
H.Cohen and C. C.Wang, On the response and symmetry of elastic materials with internal constraints.Arch. Rational Mech. Anal. 99 (1987) 1–36.
P.Podio-Guidugli, Constrained elasticity.Rend. Mat. Acc. Lincei 1 (1990) 341–350.
R. S.Marlow, On the stress in an internally constrained elastic material.J. Elasticity 27 (1992) 97–131.
M.Spivak,A Comprehensive Treatise on Differential Geometry (five vols.). Publish or Perish, Boston, Mass. (1974).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Podio-Guidugli, P., Vianello, M. Linearization of response mappings in constrained elasticity. J Elasticity 34, 185–189 (1994). https://doi.org/10.1007/BF00041192
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00041192