This paper deals with the identification of constitutive parameters of materials from whole-field strain data. The inverse identification procedure used is the virtual fields method. It is based on the principle of virtual work written with particular virtual fields. A keypoint of the method is the determination of the virtual fields since they directly extract the unknown parameters from the measured fields. The main improvement of the present paper is to show the feasibility of piecewise virtual fields. These piecewise virtual fields are defined by virtual nodal displacements. The headlines of the virtual fields method are recalled in the first part of the paper. The procedure leading to the definition of piecewise virtual fields is then described. Numerical simulations finally illustrate the relevance of the approach and its sensitivity to noisy data.