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CAD and virtual reality tools are useful to simulate the manipulation of rigid parts, and particularly their collisions. Real time simulation need to take into account the deformation of flexible part; this suppose the computation of the deformation of parts in real time, with mechanical contact. The finite-element method can not allow a real-time response for a non-linear mechanical model (geometry, material, mechanical contact). A methodology divided into two phases is proposed. First, the learning phase consists on a calculation campaign of characteristic load cases, in respect of the requirements of the real time simulation. Then, the real time phase, used the results of the first phase by interpolation. Only the first one is exposed in this paper. The aim is to obtain quickly a reduced response. In order to attempt this goal, model reduction methods are used. We focus on three reduction levels : adaptive method, POD approach, and hyper reduction. A crush of a cylinder in rubber is used to expose the performance of the model reduction methods. [ABSTRACT FROM AUTHOR]

In this paper, the mechanical behaviour of a titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al. (Orthotropic yield criterion for hexagonal closed packed metals, Tnt. J. Plasticity 22 (2006) 1171-1194), to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switches between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows to define all the parameters needed to model the elasto-plastic behaviour. Simulation of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis. [ABSTRACT FROM AUTHOR]