Translated from the French: "Modélisation numérique en science et génie des matériaux". Contents: Preface.- Continuous Media.- The Finite Different Method.- Elements of Numerical Algorithms.- Phase Transformations.- Deformation of Solids.- Incompressible Fluid Flow.- Inverse Methods.- Stochastic Methods.- Appendices.- Index.This book introduces the concepts and methodologies related to the modelling of the complex phenomena occurring in materials processing. After a short reminder of conservation laws and constitutive relationships, the authors introduce the main numerical methods: finite differences, finite volumes and finite elements. These techniques are developed in three main chapters of the book that tackle more specific problems: phase transformation, solid mechanics and fluid flow. The two last chapters treat inverse methods to obtain the boundary conditions or the material properties and stochastic methods for microstructural simulation. This book is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics and for engineering professionals or researchers who want to get acquainted with numerical simulation to model and compute materials processing

International audienceThe injection stretch/blow molding process of PET bottles is a complex process, in which the performance of the bottles depends on various processing parameters. Experimental work has been conducted on a properly instrumented stretch/blow molding machine in order to characterize these processing parameters. The objective being a better understanding of the pressure evolution, preform free inflation has been processed and compared with a simple thermodynamic model. In addition, a numerical model for the thermomechanical simulation of the stretch/blow molding process has been developed. At each time step, mechanical and temperature balance equations are solved separately on the current deformed configuration. Then, the geometry is updated. The dynamic equilibrium and the Oldroyd B constitutive equations are solved separately using an iterative procedure based on a fixed-point method. The heat transfer equation is discretized using the Galerkin method and approximated by a Crank-Nicholson's scheme over the time increment. Successful free blowing simulations as well as stretch/blow molding simulations have been performed and compared with experiments

This paper addresses the two-dimensional finite element simulation of steel continuous casting using a global non steady-state approach. The method aims at the calculation of the thermomechanical state (temperature, deformation, stresses) of steel all along the continuous casting machine. Both plane deformation and axisymmetric versions have been developed. The first one addresses the simulation of continuous casting of slabs, taking into account the possible curvature of the machine, whereas the second one applies to cylindrical billets. The implementation of the method is validated by comparison with results from the literature. It is applied to the study of a slab continuous caster for which successive depressive and compressive stress states are revealed in the secondary cooling region.KEY WORDS: continuous casting; finite elements; thermomechanics; stress-strain calculation.which Grill et al., 2) Kristiansson, 3) Thomas et al.,4) Boehmer et al.5) It consists in conveying throughout the machine a transverse section of the product: either a plane section or a volumic domain having a small thickness in the casting direction. Regarding heat transfer, top and bottom surfaces are adiabatic, the heat being extracted through the lateral boundary. As thermal gradients are very low along the casting direction in steel CC, this method yields good thermal results. However, it has major drawbacks regarding the mechanical analysis. Generally, a plane strain deformation state is assumed in the slice. Some authors, like Pascon 6) have extended this concept by assuming a state of generalized plane strain in order to cope with the bending and unbending. In spite of this, the slice approach does not take into account any shear effect and then cannot be representative of complex deformation states such as those associated with bulging. Global Steady-state MethodAn alternative consists of a Eulerian steady-state formulation, which operates on a quasi static computational domain covering the whole machine. This requires the integration of highly non linear constitutive equations (elasticviscoplasticity) along streamlines, which needs specific advection methods, such as those proposed by Huespe et al. 7)In addition, such a problem is a free surface problem, since the location of the mesh boundary is unknown, because of bulging. Therefore specific algorithms must be used in order to move boundary nodes so that the velocity field be tangent to the surface. This has been done by Dalin and Chenot 8) but only on short isolated sections of the secondary cooling. In order to overcome this difficulty, Fachinotti and Huespe have proposed to keep the mesh identical in the analysis and to deduce the bulging a posteriori, 7,9) which makes yet the steady-state formulation not fully consistent. In the authors' opinion, it would be extremely challenging to develop a fully consistent free surface steady-state model, especially because of the contact conditions to be satisfied with a great number of rolls (typically more than 100). The converge...