A Lagrangian/semi-Lagrangian coupling approach for accelerated meshfree modelling of extreme deformation problems

Pasetto, Marco; Baek, Jaewook; Chen, Jiun‐Shyan; Wei, Haoyan; Sherburn, Jesse A.; Roth, Michael

doi:10.1016/j.cma.2021.113827

Cited by 14 publications

(5 citation statements)

References 62 publications

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“…Further, the gradient smoothing cell update algorithm combined with the adaptive VC correction ensures better solution convergence with refinement. Although the calculation of the semi-Lagrangian RK shape functions at every time consumes additional CPU, this disadvantage can be improved by coupled Lagrangian and semi-Lagrangian RKPM techniques recently proposed in [53] and will be included in the future work.…”

Section: Discussionmentioning

confidence: 99%

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A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

Baek¹,

Chen²,

Zhou

et al. 2021

Comput Mech

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The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the volumetric strain energy to accurately embed the key shock physics in the absence of a mesh or grid, which is shown to also ensure the conservation of linear momentum. For kernel stability, a deformation-dependent anisotropic kernel support update algorithm is proposed, which is shown to capture excessive plastic flow and material separation. A quasi-conforming nodal integration is adopted to avoid the need of updating conforming cells which is tedious in extreme deformations. It is shown that the proposed formulation effectively captures shocks, jet formation, and smooth-to-wavy interface morphology transition with good agreement with experimental results.

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Section: Discussionmentioning

confidence: 99%

“…Also, the run-times per time step of each model were 0.406 s, 0.692 s, and 1.753 s, respectively. Note that the computational efficiency can be enhanced by dynamic load balancing and the employment of coupling of Lagrangian and semi-Lagrangian RKPM [53].…”

Section: High Velocity Impact Weldingmentioning

confidence: 99%

A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

Baek¹,

Chen²,

Zhou

et al. 2021

Comput Mech

Self Cite

View full text Add to dashboard Cite

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“…To address the aforementioned issue concerning the failure of the VC correction under material fragmentation, we propose a VC and Non-VC blending strategy based on local deformation intensity. This method draws inspiration from the blending approach utilized in the Lagrangian/semi-Lagrangian reproducing kernel particle method discussed by Baek et al [44] and Pasetto et al [42], where the blending is employed to reduce computational costs when employing semi-Lagrangian methods for material fragmentations.…”

Section: Vc and Non-vc Blending Schemementioning

confidence: 99%

“…Lian et al [40,41] implemented a similar idea for the coupling of FEM and MPM to solve extreme deformation problems. Recently, Pasetto et al [42] introduced Lagrangian and semi-Lagrangian configurations blending for the meshfree reproducing kernel particle method (RKPM), where semi-Lagrangian RK [43] is suitable for fragmentation problems and Lagrangian RK can handle continuous regions. However, the blending zone was predefined in this approach.…”

Section: Introductionmentioning

confidence: 99%

A Blended Variationally Consistent Phase Field Material Point Method for Material Fragmentation Problems

Tangade,

Huang,

Rodriguez

2024

Preprint

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The material point method (MPM) can effectively addresses material fragmentation issues over mesh-based method due to its meshfree nature but faces numerical inaccuracies such as cell-crossing instability and Galerkin inexactness inherent in its numerical framework. The utilization of previously developed variational consistent (VC) corrections with smooth reproducing kernel (RK) approximations has proven effective in preventing cell-crossing and ensuring Galerkin exactness, albeit limited to continuum bodies. In this study, we present a blended variationally consistent phase field material point method for modeling material fragmentation process. The phase field damage method is integrated into MPM to facilitate the tracking of damage/cracks during the fragmentation process. The incorporation of VC correction alongside smooth RK approximation offers benefits not only for non-oscillatory stress modes but also for robust phase field evolution. To address the complexities of VC in handling domain boundary tracking during fragmentation, we introduce a deformation-driven blending scheme to seamlessly blend non-VC for fragmented regions and VC for continuous domains with a smooth transition zone in the Galerkin MPM. This approach enhances the stability and robustness of the formulation for simulating fragmentation problems. Benchmark examples involving extreme deformation scenarios illustrate the effectiveness of the proposed MPM framework, confirming its consistency and stability.

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“…Numerical simulation and discontinuity problems still do not agree, since researchers are always looking to improve numerical solutions to be able to reflect reality. In this sense, various numerical methods are developed that cite the classical finite element method (CFEM) [1,2], element-free Galerkin methods (EFG) [3], the extended finite element method (X-FEM) [4][5][6], the phase field numerical manifold method (PFNMM) [7], the boundary element method [8], and the thermo-mechanical peridynamic model (TMPM) [9]. Despite the huge use of the CFEM, however, it suffers from a certain lack of treatment of the cracking problems; it imposes that the mesh conforms with the crack or to a surface defect, and adopting a specific mesh creates difficulties at the simulation stage.…”

Section: Introductionmentioning

confidence: 99%

Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

et al. 2021

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In this study, a NURBS basis function-based extended iso-geometric analysis (X-IGA) has been implemented to simulate a two-dimensional crack in a pipe under uniform pressure using MATLAB code. Heaviside jump and asymptotic crack-tip enrichment functions are used to model the crack’s behaviour. The accuracy of this investigation was ensured with the stress intensity factors (SIFs) and the J-integral. The X-IGA—based SIFs of a 2-D pipe are compared using MATLAB code with the conventional finite element method available in ABAQUS FEA, and the extended finite element method is compared with a user-defined element. Therefore, the results demonstrate the possibility of using this technique as an alternative to other existing approaches to modeling cracked pipelines.

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A Lagrangian/semi-Lagrangian coupling approach for accelerated meshfree modelling of extreme deformation problems

Cited by 14 publications

References 62 publications

A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

A Blended Variationally Consistent Phase Field Material Point Method for Material Fragmentation Problems

Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

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