Existence of minimizers for the pure displacement problem in nonlinear elasticity | Zendy

Cristinel Mardare | Zendy

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Existence of minimizers for the pure displacement problem in nonlinear elasticity

Author(s) -

Cristinel Mardare

Publication year - 2011

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.177

H-Index - 75

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.3546084

Subject(s) - hyperelastic material , elasticity (physics) , nonlinear elasticity , mathematical analysis , mathematics , nonlinear system , bounded function , elastic energy , norm (philosophy) , strain energy density function , linear elasticity , multiplicative function , boundary value problem , physics , finite element method , quantum mechanics , political science , law , thermodynamics

We show that the total energy of the pure displacement problem in nonlinear elasticity possesses a unique global minimizer for a large class of hyperelastic materials, including that of Saint Venant—Kirchhoff, provided the density of the applied forces are small in Lp‐norm. We also establish a nonlinear Korn inequality with boundary showing that the H1‐distance between two deformation fields is bounded, up to a multiplicative constant, by the L2‐distance between their Cauchy‐Green strain tensors.

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