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) [1] 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 [2]. 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 [3] 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.