Two-field variational formulations for a class of nonlinear mechanical models
Keyword(s):
A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential [Formula: see text], related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential [Formula: see text], a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed.
1993 ◽
Vol 24
(1)
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pp. 77-91
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2005 ◽
Vol 2005
(4)
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pp. 437-453
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1996 ◽
Vol 198
(1)
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pp. 35-48
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2000 ◽
Vol 13
(3)
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pp. 207-238
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