Explicit phase-field total Lagrangian material point method for the dynamic fracture of hyperelastic materials

A mixed three‐field total Lagrangian material point method for phase‐field fracture modeling of nearly incompressible rubber‐like solids

“…where 𝜌 0 is the initial mass density. For the explicit PFM, a viscosity coefficient 𝜂 of the phase-field variable is introduced to the dynamic system, 35,55 whose corresponding dissipation energy D v reads…”

“…To solve the coupled three‐field problem by the TLMPM, the explicit time integration and staggered solution scheme are adopted. According to our previous work, 35 the phase field should be solved after the displacement field. Noting that the pressure is related to both displacement and phase‐field variables while updating the phase field do not require the pressure, the pressure field can be solved after the displacement and phase fields.…”

“…The results indicate the good mesh convergence property of the proposed method and reasonable results can be obtained with $$$ h={l}_0/2 $$$ and a relatively small amount of calculations. In Figure 8B, $$$ {l}_0 $$$ is changed with the mesh size to keep $$$ h={l}_0/2 $$$ and the results of the original PF‐TLMPM 35 are also presented for comparison. The results show that the proposed method in this work performs better than the original one when dealing with the nearly incompressible materials.…”

“…Hu et al developed a coupled PFM‐MPM for the fracture in geomaterials involving finite deformation 33,34 . In our previous work, a coupled total Lagrangian material point method (TLMPM) and PFM was proposed to solve the dynamic fracture of rubber‐like hyperelastic solids involving extreme deformation and impact 35 . By solving the governing equations of phase and displacement fields through the MPM, the mesh distortion caused by large deformation during crack initiation and propagation can be prevented, and the contact and impact modeling can also be easily implemented.…”

Distance minimizing based data‐driven computational method for the finite deformation of hyperelastic materials

“…5 The most attractive property of hyperelastic materials is their abilities to undergo large deformations under small loads and retain their initial configurations without considerable permanent deformation after the load is removed. 6 In the field of computational mechanics, many numerical methods, such as the finite element method, 7 the material point method, 8 and the discontinuous Galerkin method, 9 have been proposed to describe the mechanical behaviors of hyperelastic materials. In these methods, the constitutive equations of hyperelastic materials are indispensable.…”