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Calibration of a class of non‐linear viscoelasticity models with sensitivity assessment based on duality
Author(s) -
Johansson Håkan,
Runesson Kenneth
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1856
Subject(s) - sensitivity (control systems) , viscoelasticity , calibration , mathematics , duality (order theory) , mathematical optimization , galerkin method , finite element method , physics , engineering , statistics , discrete mathematics , electronic engineering , thermodynamics
The calibration of constitutive models is based on the solution of an optimization problem, whereby the sought parameter values minimize an objective function that measures the discrepancy between experimental observations and the corresponding simulated response. By the introduction of an appropriate adjoint problem, the resulting formulation becomes well suited for a gradient‐based optimization scheme. A class of viscoelastic models is studied, where a discontinuous Galerkin method is used to integrate the governing evolution equation in time. A practical solution algorithm, which utilizes the time‐flow structure of the underlying evolution equation, is presented. Based on the proposed formulation it is convenient to estimate the sensitivity of the calibrated parameters with respect to measurement noise. The sensitivity is computed using a dual method, which compares favourably with the conventional primal method. The strategy is applied to a viscoelasticity model using experimental data from a uniaxial compression test. Copyright © 2006 John Wiley & Sons, Ltd.