Isotropic realizability of a strain field for the two−dimensional incompressible elasticity system
نویسندگان
چکیده
منابع مشابه
Isotropic realizability of a strain field for the two-dimensional incompressible elasticity system
In the paper we study the problem of the isotropic realizability in R2 of a regular strain field e(U) = 12 ( DU +DU ) for the incompressible Stokes equation, namely the existence of a positive viscosity μ > 0 solving the Stokes equation in R2 with the prescribed field e(U). We show that if e(U) does not vanish at some point, then the isotropic realizability holds in the neighborhood of that poi...
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Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of pa...
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This paper deals with the isotropic realizability of a given regular divergence free field j in R3 as a current field, namely to know when j can be written as σ∇u for some isotropic conductivity σ > 0, and some gradient field ∇u. The local isotropic realizability in R3 is obtained by Frobenius’ theorem provided that j and curl j are orthogonal in R3. A counter-example shows that Frobenius’ cond...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 2016
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/32/6/065002