Defining Cracks
This section explains how to add explicit cracks to an MPM simulation.
Introduction
The extension of MPM to model explicit cracks is called CRAMP for CRAcks in the Material Point Method. The commands is this section are used to define the explicit cracks (and there can be any number of them). In addition, whenever a simulation has cracks you can use various crack settings commands to customize the features of the crack physics and set various material fracture properties.
The development of CRAMP is described first in a paper by Nairn (2003)[1] (and its development was done using NairnMPM). Some other papers discuss calculation of J integral and stress intensity factor,[2], propose energy balance propagation,[3] handle cracks in 3D[4] (although not currently available in NairnMPM), use cracks to model imperfect interfaces,[5], and use traction laws with cracks.[6] Some applications of using cracks in MPM include wood fracture,[7] use of cracks to model glue bods in oriented strand board,[8] simulation of dynamic fracture,[9] and simulation of crack growth with fiber bridging.[10]
Crack Definition Commmands
In CRAMP,[1] a crack is defined as series of massless particles connected by crack segments.
The first particle is the "start" tip and the last particle is the "end" tip. When CRAMP is active, nodes around the crack will be divided into two velocity fields to separately model motion of particle "above" the crack and "below" the crack. In addition, CRAMP fully accounts for crack contact, can model cracks with frictional contact, can use cracks to model imperfect interfaces, and can insert traction laws to model cohesive zones. The commands in this section are used to define the crack geometry and optionally set crack contact mechanics, set crack tip materials, and insert traction laws.
In scripted files, a single crack is started with a NewCrack command, which is followed by one or more of the other commands to complete the crack definition:
NewCrack GrowCrack GrowCrackLine GrowCrackArc CrackInterface Friction CrackThickness
In XML files, each crack is defined in a CrackList element:
<CrackList friction='0.1' Dn='200' Dnc='-1' Dnt='200' Dt='5'>
<pt units='mm' x='50.5' y='0' tip='1'/>
<pt x='53' y='0'/>
.
.
.
<pt x='100.5' y='0'/>
<Line xmin="102" ymin="0" xmax="130" ymax="10" resolution="5"
start_tip="1" end_tip="1"/>
<Circle xmin="102" ymin="0" xmax="130" ymax="10" resolution="10"
start_tip="1" end_tip="1" start_angle="0" end_angle="90"/>
<Thickness>1.0</Thickness>
</CrackList>
Interacting Cracks
References
- ↑ 1.0 1.1 J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," Computer Modeling in Engineering & Sciences, 4, 649-664 (2003). (See PDF)
- ↑ Y. Guo and J. A. Nairn, "Calculation of J-Integral and Stress Intensity Factors using the Material Point Method," Computer Modeling in Engineering & Sciences, 6, 295-308 (2004). (See PDF)
- ↑ J. A. Nairn, "Simulation of Crack Growth in Ductile Materials,"; Engr. Fract. Mech., 72, 961-979 (2005). (See PDF)
- ↑ Y. Guo and J. A. Nairn, "Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method," Computer Modeling in Eng. & Sci., 16, 141-156 (2006). (See PDF)
- ↑ J. A. Nairn, "Numerical Implementation of Imperfect Interfaces, Computational Materials Science, 40, 525-536 (2007). (See PDF)
- ↑ J. A. Nairn, "Analytical and Numerical Modeling of R Curves for Cracks with Bridging Zones," Int. J. Fracture, 155, 167-181 (2009). (See PDF)
- ↑ J. A. Nairn, "Material Point Method Simulations of Transverse Fracture in Wood with Realistic Morphologies," Holzforschung, 61, 375-381 (2007). (See PDF)
- ↑ J. A. Nairn and E. Le, "Numerical Modeling and Experiments on the Role of Strand-to-Strand Interface Quality on the Properties of Oriented Strand Board," Proc of 9th Int. Conf. on Wood Adhesives, Lake Tahoe, Neveda, USA, Sept. 28-30, 2009. (See PDF)
- ↑ S. G. Bardenhagen, J.A. Nairn, and H. Lu, "Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach," Int. J. Fracture, 170, 49-66 (2011).
- ↑ N. Matsumoto and J.A. Nairn, "Fracture Toughness of Wood and Wood Composites During Crack Propagation," Wood and Fiber Science, 44, 121-133 (2012). (See PDF)