4. Elastic Materials. Change of Observer
Morton E. Gurtin · Society for Industrial and Applied Mathematics eBooks · 1981
An elastic material is defined by a constitutive equation giving the stress at each place x=u(p) when the deformation gradient at p is known:T(x)=T^(F(p),p).(4.1)HereT^:Lin+×ℬ→{symmetrictensors},Lin+=thesetofalltensorswithdet>0,with T^ a smooth function. For convenience, we will generally not indicate the dependence of the above functions on p and x, and write, in place of (4.1),T=T^(F).LetOrth+=theproperorthogonalgroup.