Nonlinear viscoelastic constitutive model identification for a polyurethane adhesive in a bonded joint using structural dynamic model updating

Modification and evaluation of a FRF-based model updating method for identification of viscoelastic constitutive models for a nonlinear polyurethane adhesive in a bonded joint

“…The reader is referred to Najib and Nobari [2] for a brief introduction and to Imregun et al [9] and Visser [10] for more details and computational aspects. The updating equation that was used in this study is [2]: (1) where is the circular frequency in (rad/sec), is the element in i-th row and j-th column of the analytical receptance matrix ( ), is the element in i-th row and j-th column of the experimental inertance matrix ( ), is the transpose of i-th column of the analytical receptance matrix and is the j-th column of the experimental inertance matrix. is the dynamic stiffness error matrix, , where and are the dynamic stiffness matrices of the analytical and experimental models of structure, respectively.…”

“…In the frequency domain, the Fourier transforms of stress and strain ( and ) are related by: (2) where and , and are referred to as dynamic (or complex) modulus, storage modulus and loss modulus, respectively.…”

“…Recently, Najib and Nobari [2] classified these methods into two categories, namely, direct and inverse identification methods, that is repeated here briefly with some instances.…”

“…A recent instance of the methods based on the FE mode updating is the work of Najib and Nobari [2] in which they modified a model updating method based on Frequency Response Function (FRF), referred to as the Response Function Method (RFM), for identification of the parameters of the viscoelastic constitutive model. For a steel beam bonded to a heavy rigid steel block by a layer of adhesive, they measured the accelerance FRFs at different excitation levels, using the concept of Optimum Equivalent Linear FRF (OELF) [14] and identified the parameters of the nonlinear viscoelastic constitutive model.…”

“…In this paper, the method developed in [2] will be implemented on 5 different viscoelastic models, in order to identify their parameters and to see which one of the models gives the best prediction of the behavior of the adhesive in question. In this respect, for a beam bonded to a rigid support via a layer of elastic adhesive, the accelerance FRFs were measured experimentally, using the concept of Optimum Equivalent Linear FRF (OELF).…”