Complements

Abstract

Various issues raised by the Virtual Fields Method in some particular cases are addressed in this chapter. It is first shown that the characterization of heterogeneous materials can be carried out using constitutive parameters defined by subregions or modeled with functions varying continuously. The principle of virtual work is then recalled in the case of large deformations, thus opening the way for the characterization of parameters governing hyperelastic laws for instance. The case of thick plates is then introduced as a logical follow-up of the case of thin plates addressed in the previous sections. In particular, it is shown that the through-thickness shear moduli can be identified if suitable full-field measurements are available on the top surface of bent plate specimens. Dynamic loads are then addressed and two particular cases are examined: harmonic and nonharmonic loads. It is shown than complex moduli can be identified in the first case. Concerning the second case, it is shown that it is also possible to use the virtual work of inertial forces in the identification procedure, thus potentially avoiding the need for external force measurements. Finally, even though the Virtual Fields Method was introduced to solve problem 2 presented in the first chapter, it is shown that problem 3 dealing with force reconstruction can also be solved if full-fields measurements are available and if the constitutive equations are completely characterized a priori.