PGD-Based Modeling of Materials, Structures and Processes

• 1 Introduction.- 1.1 Recurrent issues in numerical simulation.- 1.2 Model reduction: information versus relevant information.- 1.3 PGD at a glance.- 1.4 Revisiting the simulation challenges.- 1.5 A brief state of the art on PGD-based model order reduction.- 2 Multiscale modelling.- 2.1 From quantum mechanics to kinetic theory.- 2.2 Advanced solvers for multi-dimensional models.- 2.3 Numerical examples.- 2.4 Conclusions.- 3 Homogenization.- 3.1 Homogenization of linear heterogenous models.- 3.2 Non-concurrent nonlinear homogenization.- 3.3 Numerical examples.- 3.4 Conclusions.- 4 Coupled models.- 4.1 Efficient coupling of global and local models.- 4.2 Fully globalized local models.- 4.3 Heterogeneous time integration.- 4.4 Numerical example.- 4.5 Discussion.- 5 Parametric models in evolving domains.- 5.1 Evolving domains issues.- 5.2 PGD in evolving domains.- 5.3 Separated representation constructor.- 5.4 Numerical test.- 5.5 Towards parametric modeling in evolving domains.- 5.6 Numerical test involving parametric modeling.- 5.7 Conclusions.- 6 Space separation.- 6.1 In-plane/out-of-plane separated representation.- 6.2 Laminates.- 6.3 Conclusions.- 7 Process optimization.- 7.1 Parametric boundary conditions.- 7.2 Parametric modeling of pultrusion.- 7.3 Optimization strategy.- 7.4 Conclusion 8 Shape optimization.- 8.1 Introduction.- 8.2 Geometrical parameters as extra-coordinates.- 8.3 Numerical results.- 8.4 Conclusions.- 9 DDDAS.- 9.1 Introduction to DDDAS.- 9.2 PGD solution of a flowing process.- 9.3 Simulating a breakdown scenario.- 9.4 Post-processing in a smartphone.- 9.5 Conclusions.- 10 Inverse analysis.- 10.1 PGD based parameter identification.- 10.2 PGD based Cauchy’s problem.- 10.3 Parameter identification examples.- 10.4 Cauchy’s problem example.- 10.5 Conclusions.- 11 Tape placement.- 11.1 Parametric modeling.- 11.2 ATP thermal model.- 11.3 ATP mechanical modeling.- 11.4 Numerical results.- 11.5 Conclusions.- 12 Augmented learning.- 12.1 Towards augmented learning.- 12.2 Examples of augmented learning.- 12.3 Conclusions.- References.- Index.

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