Explicit material point method for fracture analysis of nearly incompressible materials involving large deformation

  • Zhang, Shun (dalian university of technology)
  • Yang, Weilong (dalian university of technology)
  • Sun, Wei (Dalian University of Technology Department of)
  • Qiu, Yisong (Dalian University of Technology Department of)
  • Zheng, Yonggang (dalian university of technology)

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Numerical simulation of fracture in soft materials plays a crucial role in structural design, safety assessment and advanced manufacturing. However, the nonlinear mechanical response of large deformations presents significant challenges for efficient fracture behavior simulation. This work develops an explicit total Lagrangian material point method (MPM) for simulating large deformation and fracture behavior of nearly incompressible materials. The phase-field model combined with strain energy decomposition is used to describe the nucleation and propagation of cracks in the material. Within the total Lagrangian MPM framework, an adaptive mesh refinement (AMR) algorithm is developed to refine the background grid and particles adaptively at the crack tip, enhancing the solution efficiency of the phase-field governing equations. To address the volumetric locking issue caused by the incompressible nature of soft materials, a hybrid F-bar formulation is proposed to effectively alleviate pressure oscillations. A volume decomposition based on pressure field differentiation is introduced to coordinate the coupling contradiction between incompressible constraints and the diffuse crack model. Finally, several classical numerical examples are presented to demonstrate the effectiveness and applicability of the proposed method in simulating large deformation and fracture behavior of nearly incompressible materials.