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Digitale Medien

A weak approach to finite elasticity (1994)

Giaquinta, M. ; Modica, G. ; Souček, J.

Springer

Calculus of variations and partial differential equations 2 (1994), S. 65-100

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ISSN: 1432-0835

Schlagwort(e): 49Q20 ; 73C50

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract On the ground of four axioms we define thekinematics of perfectly elastic bodies and in particular the notion ofweak deformations of a perfectly elastic body. Weak deformations turn out to agree withweak diffeomorphisms introduced in [10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining thedynamics of perfectly elastic bodies in terms of twoconstitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01234316

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Digitale Medien

Energy functional depending on elastic strain and chemical composition (1994)

Fonseca, Irene ; Kinderlehrer, David ; Pedregal, Pablo

Springer

Calculus of variations and partial differential equations 2 (1994), S. 283-313

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ISSN: 1432-0835

Schlagwort(e): 26B25 ; 35J20 ; 46E27 ; 46E35 ; 73C50

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract In this paper we deal with energy functionals depending on elastic strain and chemical composition and we obtain lower semicontinuity results, existence theorems and relaxation in the spacesH 1,p(Ω; ℝn)×L q (Ω; ℝd) with respect to weak convergence. Our proofs use parametrized measures associated with weakly converging sequences.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01235532

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Digitale Medien

Representations for transversely hemitropic and transversely isotropic stress-strain relations (1959)

Pierce, John F.

Springer

Journal of elasticity 37 (1959), S. 243-280

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ISSN: 1573-2681

Schlagwort(e): 73CO5 ; 73C50

Quelle: Springer Online Journal Archives 1860-2000

Thema: Maschinenbau , Physik

Notizen: Abstract The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00041210

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