Thesis Defense by Huicheng HUANG

During the numerical modeling of thin-sheet metal forming, numerous highly nonlinear phenomena can occur, resulting from large deformations, contact with friction, viscoplasticity, damage, and fracture.

The finite element method is often confronted with problems of mesh distortion, costly remeshing, and the management of discontinuities during necking.

In this thesis, we propose a robust and efficient mesh-free simulation technique based on the SSPH (Shell Smoothed Particle Hydrodynamics) method, specifically developed for thin shells and dedicated to the simulation of sheet metal forming under large deformations.

First, we will analyze a 2D elastoplastic SPH model based on a total Lagrangian formulation, enhanced by the CSPM (Corrective Smoothed Particle Method) for boundary consistency and by an artificial viscosity for numerical stability. An explicit integration scheme was developed to solve the strong-form equilibrium PDEs and coupled with the cutting-plane algorithm to ensure consistent stress and plastic strain states in each particle.

Subsequently, this framework was extended to shell structures by adopting the Reissner-Mindlin theory, with the mean surface discretized using a single layer of particles. Integration through the thickness allows for the consideration of membrane, bending, and shear effects. For a robust update of large rotations, we use quaternions to avoid singularities.  The properties of materials with a functional gradient vary spatially within the model, following the Tamura-Tomota-Ozawa model. Both the MCK and GTN micromechanical damage models have been integrated at each integration point within the thickness, allowing us to capture any initiation of striction during forming. We adopted a pragmatic approach to rigid particle-tool contact, using a Hertz-type normal law coupled with Coulomb friction, to ensure the stability of tool-sheet interactions.

The proposed approach was validated by comparison with analytical solutions and ABAQUS finite element simulations on a series of benchmarks. The results show that the SSPH method accurately reproduces the global responses, local stress/strain fields, and damage localization, while avoiding issues associated with EF meshing.

This work thus establishes a reliable, mesh-free numerical method—an alternative to EF—for predicting defects during the deep drawing process.

• Mr. Hakim NACEUR, University Professor, INSA Hauts-de-France, Thesis Advisor
• Mr. Yabo JIA, Associate Professor, INSA Hauts-de-France, Co-advisor
• Mr. Xiangyu HU, Professor, Technical University of Munich, Examiner
• Mr. Mohamed GUESSASMA, University Professor, Université de Picardie Jules-Verne, Reviewer
• Ms. Isabelle TITEUX, University Professor, Université de Reims Champagne Ardenne, Examiner
• Ms. Valentina LOPRESTO, Professor, University of Naples Federico II, Examiner
• Ms. Lisa SCHEUNEMANN, Professor, Institut für Angewandte Mechanik, Examiner
• Mr. Daniel COUTELLIER, University Professor, Université Polytechnique Hauts-de-France, Examiner

SPH shell, Micromechanics, FGM, Damage, Forming processes, Numerical modeling.