Finite Strain Shape Memory Alloys Modeling - Scuola di Dottorato in ...

γ• R,Ct=12EEtt(5.28)• R γ , Δ ζ= 0(5.29)• R γ = , γ0(5.30)The three-dimensional model herein proposed has been implemented into a standard2D four-node quadrilateral finite element. In the following, the weak formulation ofmomentum balance equations is developed as the first step toward the numericalimplementation of the model in the framework of the finite-element method (Ciarlet,1978; Bathe, 1982; Crisfield, 1986, 1991, 1997; Reddy, 1993).5.2 Principle of Virtual Worki. Spatial description.Generally, the finite element formulation is established in terms of a weak form ofthe differential equation (Reddy, 1984; Bonet and Wood, 1997). In the context ofsolid mechanics this implies the use of the virtual work equation. For this purpose,let η=η( x ) denote an arbitrary vector-valued function defined on the currentposition of the body. Using equation (3.73) for the static problem( )divσ + ρ0 b=0, inφB (5.31)and integrating it over the volume of the body it can be derived a weak statement ofthe static equilibrium of the body as:85