The energy functional of linear elasticity is obtained as Gamma-limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density W(del upsilon) for large values of the deformation gradient del upsilon is replaced here by the weaker condition W(del upsilon) >= vertical bar del upsilon vertical bar(p), for some p > 1. Energies of this type are commonly used in the study of a large class of compressible rubber-like materials. (c) 2012 Elsevier Masson SAS. All rights reserved.
Linear elasticity obtained from finite elasticity by Γ -convergence under weak coerciveness conditions
Agostiniani, Virginia;
2012-01-01
Abstract
The energy functional of linear elasticity is obtained as Gamma-limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density W(del upsilon) for large values of the deformation gradient del upsilon is replaced here by the weaker condition W(del upsilon) >= vertical bar del upsilon vertical bar(p), for some p > 1. Energies of this type are commonly used in the study of a large class of compressible rubber-like materials. (c) 2012 Elsevier Masson SAS. All rights reserved.
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