Extended material point method for the three‐dimensional crack problems

Self Cite

A novel explicit phase field material point method (ex‐PFMPM) is proposed for modeling dynamic fracture problems. The rate‐dependent phase field governing equation is discretized by a set of particles, and the phase field is updated by the explicit forward‐difference time integration. Furthermore, the stability of the ex‐PFMPM is studied. A novel explicit critical time step formula is obtained based on the system eigenvalues in one dimension and then extended to two and three dimensions. The critical time step formula takes the effect of particle position and neighboring cell interaction into consideration, and can also be used in an explicit phase field finite element method. Several numerical examples, including a dynamic crack branching, a plate with pre‐existing crack under velocity boundary conditions and a three point bending problem are studied to verify the proposed ex‐PFMPM. The use of the history field in the explicit method is studied, which shows that it will lead to fake phase field update and overestimation of the fracture energy in the unloading case. All of the numerical results show that the proposed ex‐PFMPM has the capacity of modeling the crack initiation and propagation problems with both accuracy and efficiency.

Section: Numerical Examplesmentioning

confidence: 99%

“…Since the orthogonal equidistant background grids are widely used in MPM, the aforementioned analysis does not consider the nonequidistant grids. However, our time step criterion can be easily generalized to nonequidistant grids by replacing Equation (48) with…”

Section: Stability Analysismentioning

confidence: 99%

An explicit phase field material point method for modeling dynamic fracture problems

Zeng

Zhang

et al. 2023

Self Cite

“…As shown in the previous works, the material point method (MPM), a particle-based method proposed by Sulsky et al, 26 has been developed to deal with several fracture and failure problems involving large deformation, contact and impact. [27][28][29][30] Recently, Kakouris and his co-workers coupled the PFM and MPM successfully and simulated the quasi-static and dynamic fracture behaviors. 31,32 Hu et al developed a coupled PFM-MPM for the fracture in geomaterials involving finite deformation.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

et al. 2023

The rubber‐like solids, as commonly observed materials in nature and engineering areas, often show high extensibility and weak compressibility, which lead to difficulties for modeling the fracture behavior of these materials. In this paper, we propose a mixed three‐field total Lagrangian material point method (TLMPM) to deal with the fracture of nearly incompressible rubber‐like solids. In this method, the phase‐field method combining with perturbed Lagrangian approach is developed to describe the fracture of nearly incompressible materials. Based on the Lagrangian equation, the governing equations of the displacement, pressure and phase fields are derived for the system considering dynamic effect. Then, a mixed three‐field TLMPM discrete formulation with a remapping strategy is then built to solve the problem involving large deformation. Besides, a staggered solving scheme with explicit time integration is developed for the three‐field problem. The accuracy and capabilities of the proposed method for dealing with the fracture of incompressible materials are demonstrated by modeling several quasi‐static and dynamic numerical problems and comparing the results with other numerical methods and experiments. Moreover, the applicability of the method is further proved by an out‐of‐plane tearing case.

“…55,56,[67][68][69] Other diverse MPM discontinuity methods range from velocity basis treatments 70 to sharp cutting augmentations. 71 Most recently, the eXtended MPM (XMPM) utilizes local enrichment functions, 72 the extended B-spline MPM (EBS-MPM) detects boundary cells and fixes their degenerate bases, 73 and the total Lagrangian MPM (TLMPM) computes stress and strain with respect to the reference configuration, avoiding cell-crossing instabilities and numerical fracture, 74 but requires a special treatment for contact. 75 These techniques have the potential to be used for high-resolution fracture simulation with near predictive-accuracy, but a crucial challenge still remains: how might one determine the comparative accuracy of these methods?…”

Section: Introductionmentioning

confidence: 99%

“…Other diverse MPM discontinuity methods range from velocity basis treatments 70 to sharp cutting augmentations 71 . Most recently, the eXtended MPM (XMPM) utilizes local enrichment functions, 72 the extended B‐spline MPM (EBS‐MPM) detects boundary cells and fixes their degenerate bases, 73 and the total Lagrangian MPM (TLMPM) computes stress and strain with respect to the reference configuration, avoiding cell‐crossing instabilities and numerical fracture, 74 but requires a special treatment for contact 75 …”

Section: Introductionmentioning

confidence: 99%

Evaluating material point methods on problems involving free surfaces and strong gradients

Wolper,

Garyfallogiannis,

Purohit

et al. 2023

The material point method (MPM) enables large‐deformation simulations of complex material behaviors with natural multi‐material coupling. However, MPM struggles to accurately capture fields related to material discontinuities, for example, traction‐free surfaces, making MPM fracture simulation challenging. Many MPMs seek to alleviate this challenge, but comparing these approaches has been elusive. This work presents a benchmarking process for evaluating and comparing discontinuous MPM approaches. The benchmarks focus field quantities near a circular hole in a plate and a planar crack with comparisons to accurate finite element solutions.