Generalized Parameter Identification for Finite Viscoelasticity

Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work we present an algorithm for the identification of material parameters for large strain viscoelasticity in which data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. A representative numerical example is referred to measured data based on short-time and long-time tests of a non-cellular polyurethane. As an advantage, the developed identification scheme renders solely one single set of material parameters.

[1]  Rolf Mahnken,et al.  Identification of Material Parameters for Constitutive Equations , 2004 .

[2]  Christian Miehe,et al.  Computation of isotropic tensor functions , 1993 .

[3]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

[4]  Christian Miehe,et al.  Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation , 2000 .

[5]  Giulio Maier,et al.  Stochastic calibration of local constitutive models through measurements at the macroscale in heterogeneous media , 2006 .

[6]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[7]  Ch. Tsakmakis,et al.  Finite deformation viscoelasticity laws , 2000 .

[8]  M. Ekh.  Thermo-Elastic-Viscoplastic Modeling of IN792 , 2001 .

[9]  Rolf Mahnken,et al.  A unified approach for parameter identification of inelastic material models in the frame of the finite element method , 1996 .

[10]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[11]  N. Huber,et al.  A neural network tool for identifying the material parameters of a finite deformation viscoplasticity model with static recovery , 2001 .

[12]  Stefanie Reese,et al.  A Presentation and Comparison of Two Large Deformation Viscoelasticity Models , 1997 .

[13]  Rolf Mahnken,et al.  Parameter identification for finite deformation elasto-plasticity in principal directions , 1997 .

[14]  Detlef Winter,et al.  Optische Verschiebungsmessung nach dem Objektrasterprinzip mit Hilfe eines flächenorientierten Ansatzes , 1993 .

[15]  Stefanie Reese,et al.  Theoretical and Numerical Aspects in the Thermo-Viscoelastic Material Behaviour of Rubber-Like Polymers , 1997 .

[16]  P. Haupt,et al.  Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling , 2001 .

[17]  S. Reese,et al.  A theory of finite viscoelasticity and numerical aspects , 1998 .

[18]  J. Ponthot,et al.  A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation , 2006 .

[19]  J. C. Simo,et al.  Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes , 1992 .

[20]  Rolf Mahnken,et al.  Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations , 1996 .

[21]  Rolf Mahnken,et al.  A comprehensive study of a multiplicative elastoplasticity model coupled to damage including parameter identification , 2000 .

[22]  Peter Haupt,et al.  Continuum Mechanics and Theory of Materials , 1999 .

[23]  S. Hartmann,et al.  Finite deformations of a carbon black-filled rubber. Experiment, optical measurement and material parameter identification using finite elements , 2003 .