A robust identification strategy for rate-dependent models in dynamics

The motivation of the paper is to develop a method allowing us to make use, in the context of identification, of highly perturbed tests leading to non-reliable measurements. Such tests are not seldom especially when dealing with structural fracture in dynamics. We follow here the concept of the modified constitutive relation error (MCRE) where error on the model and error on the experimental data are both introduced. A first paper was devoted to the extension of the MCRE method to transient elasticity. This paper is devoted to the extension to nonlinear constitutive relations, in particular viscoplasticity and damage. The MCRE formulation in transient dynamics leads to the solving of a coupled direct and adjoint nonlinear problem, which implies dedicated methods, which is the core of this paper. This has led us to define a particular MCRE formulation well suited for numerical treatment and to develop an extension of the LATIN method to ill-posed problems. Once the difficulties have been resolved and the formulation implemented in the one-dimensional case, the proposed identification strategy appears to be very robust with respect to perturbed measurements in the absence of a priori knowledge, even in the case of localization and rupture