11/20 Recursive algorithm: At the beginning, σ=0 Then, from one step to another: Elastic properties identified during elastic regime with the virtual fields method Irreversible strains: need a model Implicit definition of constitutive equations
12/20 Associated plasticity Von Mises criterion: Prandtl-Reuss rule with isotropic hardening: Implicit definition of constitutive equations N is the tensor of yield flow directions: if σ eq < Y(p) if σ eq = Y(p)
13/20 Introduction of constitutive parameters in the hardening law Bilinear model: Y(p) = Y 0 + H p Power model (JohnsonCook): Y(p) = Y 0 + α p n If the parameters are chosen, it is possible reconstruct the stress fields and to test their validity. Iterative up to the minimization of the cost function.
14/20 Application onto experimental data Standard with strain gageStatically undetermined
16/20 Complexity of loading path has been handled
17/20 Application on a heterogeneous specimen (with Prof. M. Sutton, USC) Zone of FSW
18/20 Measured strain fields subimages = different time steps
19/20 Experimental results on a homogeneous specimen
20/20 Identification of model with up to 21 parameters in one single test. Possibility of handling complex specimen geometry and strain localization. Prospects: 1.Viscoplasticity with high-speed cameras (S53, p156) 2.Kinematic hardening, more complex loading paths 3.Software implementation with Camfit Summary
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