A Computational Shell SPH–MCK Damage Framework for Failure Prediction in Sheet Metal Forming

  • Huang, Huicheng (Université Polytechnique Hauts-de-France)
  • Jia, Yabo (INSA Hauts-de-France)
  • Naceur, Hakim (INSA Hauts-de-France)

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The numerical prediction of ductile fracture in thin-walled metallic structures remains a persistent challenge in computational mechanics. While shell formulations are essential for computational efficiency in industrial stamping applications, Standard Finite Element Methods (FEM) suffer from pathological mesh dependence and element distortion during severe localization and rupture. Conversely, Smoothed Particle Hydrodynamics (SPH) offers a robust Lagrangian framework for large deformations [1] but often lacks the rigorous micromechanical damage descriptions required to predict complex failure modes accurately. This work proposes a novel computational framework that bridges this gap by integrating a Mindlin-Reissner Shell-SPH formulation [2] with the MCK (Monchiet-Charkaluk-Kondo) micromechanical damage model [3]. We extend a previously developed shell-based SPH method [1, 2], which utilizes a single layer of particles at the mid-surface and corrects for shear locking via Assumed Natural Strain concepts, to account for deformation-induced porosity. Unlike phenomenological damage models, the incorporated MCK criterion is derived from limit analysis theory using Eshelby-like trial velocity fields for the void-matrix aggregate. This formulation provides a superior yield surface description for porous ductile media compared to standard Gurson-type models [3], particularly in capturing the effects of void shape evolution and coalescence under complex stress states typical of deep drawing. The numerical implementation involves a specific coupling where the MCK plastic-damage internal variables are updated at integration points through the shell thickness. The cutting plane algorithm was used within the explicit SPH time-integration scheme, ensuring thermodynamic consistency. The proposed approach has been validated through the simulation of several deep drawing benchmarks. Preliminary results showed that this meshfree micromechanical approach successfully predicts the onset of localized necking and subsequent rupture without the need for ad-hoc element deletion or remeshing as used in FEM.