Introduction of piecewise virtual fields method for solution of inverse problems - Syed Muhammad, Kashif (IIUM Press, 2011)
This chapter discusses the direct identification of bending rigidities of a thin anisotropic composite plate. The simultaneous identification of constitutive parameters from heterogeneous strain fields is an important issue in the experimental solid mechanics community.The idea is to determine the unknown parameters from a single test giving a unique heterogeneous strain field. It enables to retrieve greater number of parameters than in the case of mechanical tests resulting in homogeneous strain fields provided that full-field measurements are available. In the general case however, neither a closed-form solution nor a direct link between measurements and unknown parameters are available. The challenge is therefore to solve an inverse problem for which the specimen loading, the type of constitutive equations and the strain fields are known whereas the parameters governing these constitutive equations are to be found. Various techniques have been recently proposed for solving such inverse problem, among which the Virtual Fields Method (VFM) is presented here. Virtual fields method is based on the principle of virtual work. For the case of a thin composite plate bending problem, two aspects are discussed here in detail, namely piecewise construction of the virtual fields and noise minimization effect. Numerical simulations illustrate the relevance of the method and its stability with respect to noisy data.