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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i3.70
pages 363-378

Calibration of a Nonlinear Elastic Composite With Goal-Oriented Error Control

Hakan Johansson
Department of Applied Mechanics, Chalmers University of Technology S-412 96 Goteborg, Sweden
Kenneth Runesson
Department of Structural Mechanics Chalmers, University of Technology S-41296 Goteborg, Sweden
Fredrik Larsson
Department of Applied Mechanics, Chalmers University of Technology, S-412 96 Gothenburg

ABSTRACT

In order to determine the parameter values for the constituents of a nonlinear elastic composite on the mesoscale, while experimental data are available on the macroscale only, a meso-macro-transition approach is adopted. A representative volume element (RVE) with piecewise linear Dirichlet boundary conditions, is analyzed using a recently proposed technique for the calibration of constitutive models. The strategy is based on an optimization problem expressed such that the state equation is incorporated via an additional costate field, which has the distinct advantage that error control in an arbitrary “goal” quantity is formally straightforward. The practical solution of the optimization problem is essentially based on Newton's method, which is feasible since it is possible to decompose each Newton step in a number of linear problems using the conventional finite element structure for the RVE problem. The same problem character is pertinent to the solution of the dual problem for a given choice of error measure, which is the key ingredient in the a posteriori error computation. The numerical results show the effectivity of the error prediction for the special case when the material parameters are constant within the subdomains of mesostructural constituents.


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