6 th World Congresses of Structural and Multidisciplinary Optimization Rio de Janeiro, 30 May - 03 June 2005, Brazil Modelling and Identification of Viscoelastic Materials by Means of a Time Domain Technique Daniel Alves Castello a Fernando Alves Rochinha a Ney Roitman b Carlos Magluta b a Solid Mechanics Laboratory, PEM/COPPE/UFRJ - P.O. Box 68506, Rio de Janeiro RJ 21945-970, Brazil castello@mecsol.ufrj.br and faro@serv.com.ufrj.br b Structures Laboratory, PEC/COPPE/UFRJ - P.O. Box 68503, Rio de Janeiro RJ 21945-970, Brazil roitman@labest.coc.ufrj.br and magluta@labest.coc.ufrj.br Abstract The present work is aimed at modelling and characterizing viscoelastic materials by means of a time domain technique. A constitutive equation containing internal variables is proposed. The parameter estimation problem is solved in time domain by means of the Levenberg-Marquadt technique. The ef- fectiveness of the time domain estimation is assessed experimentally for three different structres. Keywords: Viscoelastic material, constitutive equation, parameter estimation. 1. Introduction In the last years, System Identification [8] has emerged as an important discipline providing valuable tools within the Structural Dynamics Field. The applications are very diverse, ranging from active control of vibrations [2] to model updating [3], passing through damage detection [4] and [5]. Identification is intended to improve the robustness and performance of the involved systems by helping on building reliable models which provide the ground of modern engineering. Those models are used to understand, control involved phenomena and, probably their key feature, predict future behavior. Broadly speaking, identification consists on the process of developing a mathematical model for a real system by combining physical principles with experimental or field data. Therefore, identification uses a priori information, characterized by the model structure and characteristics, and a posteriori data, such as input-output observations. The main idea is to identify a set of parameters/functions which characterizes a chosen mathematical model. It is intended that, over a desired range of operating conditions, the model outputs are close to the system outputs when both are submitted to the same inputs. Therefore, identification plays a key role for different areas of applications. In general, the combination of identification techniques and the modelling of the dynamic behavior of some systems is of great interest. For the Structural Dynamics community, for example, the modelling and identification of viscoelastic materials are of great concern [10] and [11]. And such a problem will be addressed in the present work as well as other dissipative materials. The present work is aimed at modelling and characterizing viscoelastic materials by means of a time domain technique. A constitutive equation for viscoelastic materials, in time domain, is proposed based on the concepts of internal variables [12] and on the thermodynamics of irreversible processes [12]. The proposed constitutive equation is capable of dealing with common viscoelastic behaviour such as creep and relaxation phenomena. Nevertheless, this constitutive equation does not consider large deformation processes nor nonlinear viscoelastic effects such as Mullin’s [13] and Payne’s effect [14]. Once one has chosen the parsimony of the model, a finite element model of the system, which is parameterized by a set of constitutive functions or parameters, is built. The parameters and functions required to describe the dynamic behaviour of the dissipative materials are estimated by means of the solution of the inverse problem in time domain. The inverse problems have been solved by means of the Levenberg-Marquadt [15]. The Levenberg-Marquadt technique is applied, 1