However, engineered structures are usually designed so that the maximum expected stresses are well within the range of linear elasticity ( the generalization of Hooke s law for continuous media ); that is, the deformations caused by internal stresses are linearly related to them.
22.
Thus, the equivalent Young's modulus of a neo-Hookean solid in uniaxial extension is 3 \ mu, which is in concordance with linear elasticity ( E = 2 \ mu ( 1 + \ nu ) with \ nu = 0.5 for incompressibility ).
23.
He is known for his work on rigid body mechanics, on the mathematical theory of elasticity ( including both linear elasticity and finite strain theory ), on the history of mathematics and on cosmology and extragalactic celestial mechanics : in particular he is considered one of the founders of the latter branch of cosmology.
24.
For instance, a Fermi estimate might indicate whether the internal stresses of a structure are low enough that it can be accurately described by linear elasticity; or if the estimate already bears significant relationship in scale relative to some other value, for example, if a structure will be over-engineered to withstand loads several times greater than the estimate.
25.
Her research deals with a wide range of topics in PDEs and numerical analysis : " isogeometric analysis, fully compatible discretization of PDEs, linear and non linear elasticity, contact mechanics, integral equations on non-smooth manifolds, functional theory for Maxwell equations in non-smooth domains, finite element techniques for Maxwell equations, non-conforming domain decomposition methods, asymptotic analysis, stabilization techniques for finite element discretizations ."
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