A multi-mesh MPM for simulating the meshing process of spur gears

Hu, Wenqing; Chen, Zhen

doi:10.1016/s0045-7949(03)00260-8

Cited by 57 publications

(30 citation statements)

References 14 publications

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“…To reduce computational time, we avoid additional calculations pertaining to the classification of nodes and particles across the interface by letting the material points in the upper and lower parts of the plate (with respect to the interface) to convect in their own velocity fields. Thus, by adopting multiple velocity fields (Hu and Chen 2003;Nairn and Guo 2005), there is no interaction between the material points on either side of the interface and surfaces on both sides of the interface are connected to each other only through the cohesive zone model. The interface is discretized into cohesive segments and, each segment is defined by two cohesive nodes, forming a line for 2D description of the crack surface.…”

Section: Cohesive Zone In Gimpmentioning

confidence: 99%

“…Consequently it offers an advantage in the simulation of some dynamic problems over finite element and meshless methods (Nairn and Guo 2005). Multiple velocity-field technique (Hu and Chen, 2003;Nairn and Guo, 2005) can be used to model discontinuities in the displacements and velocities across the propagating crack surfaces. In this paper, a methodology incorporating cohesive zone model in GIMP is presented to simulate the damage zone at the cracktip.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Daphalapurkar

Çöker

et al. 2007

Int J Fract

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Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999[( ) Science 284:1337[( -1340. The simulations are capable of handling crack growth with cracktip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between √ 2c S (c S is the shear wave speed)

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Section: Cohesive Zone In Gimpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Daphalapurkar

Çöker

et al. 2007

Int J Fract

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“…The impenetrability condition equation (2) is not satisfied, and the nodal velocities v k bi should be adjusted to new valuesṽ k bi so that the conditioñ (24) holds. In Equations (23) and (24)…”

Section: The Second Contact Methodsmentioning

confidence: 99%

“…Equation (24) indicates that the normal component of the adjusted nodal velocities is set equal to the normal component of the center-of-mass velocity. That is…”

Section: The Second Contact Methodsmentioning

confidence: 99%

Contact algorithms for the material point method in impact and penetration simulation

Huang¹,

Zhang²,

Ma³

et al. 2010

Numerical Meth Engineering

145

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SUMMARYThe inherent no-slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration.

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“…To release the inherent noslip contact constraint in MPM while avoiding interpenetration, contact/sliding/separation schemes were proposed [49][50][51]. The idea is that if the bodies are moving toward one another, the material points are moved in the usual center-of-mass velocity field which automatically enforces the no-penetration condition.…”

Section: Contact Algorithmmentioning

confidence: 99%