Shear modulus analysis of a modied Jeffreys model
Thales Augusto Barbosa Pinto Silva1; Hilbeth Parente Azikri de Deus1
1 Universidade Tecnológica Federal do Paraná
doi:10.20906/CPS/CILAMCE2017-0002
Resumo
Thixotropic materials have economically important industrial applications. Recently proposed models describing its behavior are formulated by means of a two coupled equations system: the constitutive equation (based on viscoelastic classic models) and the rate equation (in which the microstructural evolution is described). The shear modulus and the viscosity coefficient(s) are considered, in such a class of models, as functions of the structural parameter. The expressions used for the formulation of such functions are defined by satisfying some asymptotic limits, such that the model is physically consistent. However, there is no agreement as to the form in which the expressions are constructured. The Tikhonov regularization method together with the L-curve parameter-choice criterion is applied to determine the form of shear modulus function, using some experimental data from rheological tests. The function is obtained using a model that formally considers the microstrutural dependence of the shear modulus and viscosity coefficients in the dynamic principle that origins the constitutive equation. The model, presented in a recent work, is deduced from the Smoluchowski coagulation theory and a modified Jeffreys model. It is considered the use of a multi-objective framework, for a more general solution of the problem. The algorithm is implemented through a MATLAB developed code. It is evidenced the necessity of regularization methods and the feasibility of the Tikhonov/ L-curve method and a new function for the shear modulus is proposed.
Palavras-chave: Shear modulus; Thixotropic materials; Tikhonov regularization method; L-curve criterion; Multi-objective framework