3D Cracks

3D cracks are currently in development and available only in OSParticulas. This page explains how to add them to 3D MPM simulations.

Introduction

3D cracks are defined by a collection of triangular facets. The corners and located using crack key points. Each facet can option input a traction law.

Planar Crack Definition

If the crack has a parallelogram shape, you can define with a few commands. In scripted files, the commands are:

NewCrack (x0),(y0),(z0),(k0)
CrackKeypoint (x1),(y1),(z1),(k1)
CrackKeypoint (x2),(y2),(z2),(k2)
CrackPlane (k0),(k1),(k2),(length),(czmID)

In XML files, a parallelogram crack is defined with one command in a <CrackList> element:

<CrackList>
  <Plane V0x='(x0)' V0y='(y0)' V0z='(z0)' V1x='(x1)' V1y='(y1)' V1z='(z1)'
         V2x='(x2)' V2y='(y2)' V2z='(z2)' length='(length)' mat='(czmnum)' matname='(czmname)'></Plane>
</CrackList>

Here V0, V1, and V2 define three points in 3D space. Vectors from V0 to V1 and V0 to V2 define two edges of the parallelogram, which is formed by reflecting the triangle connecting the three points across the edge from V1 to V2. The crack is discretized into a grid of crack points using N1 points the V0 to V1 direction and N2 points in the V0 to V2 direction (the enforced minimum for each is 2. N1 and N2 can be replace by length attribute and N1 and N2 calculate such that edges will be less than that length. Can also add mat or matname attributes to set a traction law on all points. This grid is connected into triangular elements.

• (xn),(yn),(zn) - defines three points and (kn) in scripted files are key point labels (which have to be unique). The defined crack will be parallelogram with edges along point 0 to 1 and along point 0 to 2.
• (length) - is preferred maximum length for facet edges. The parallelogram is divided into triangular facets with the maximum facet edge length given by this parameter. Typically this value should be smaller than a grid cell, such as half of a grid cell.
• (czmID) - is optional Traction Lawstraction law material ID]] to add a traction law to the entire crack plane. Scripted files can use the material ID.
• (czmnum) or tt>(czmname) - in XML files, you specify an optional traction law by number or name. If both are used, the name takes precedence.

General 3D Crack Definition

In scripting software, 3D cracks created with

```

  NewCrack x,y,z,id
  CrackKeypoint x,y,z,id
      ...
  CrackFacet id1,id2,id3,length,czm

```

Whene `NewCrack` starts to crack (or starts another crack is one already active. The argments are coordinate of one point and a label (or id) for that point. A series of `CrackPoint` commands (with same arguments) creates all the crack mesh keypoints (id's must be unique). A series of `CrackFacet` commands links keypoints (by their ids) into a triangle. Length gets preferred maximum length for facet edge and czm is options traction law ID.

Notes:

1. Meshing may deviate from preferred length to get better proportioned elements.
2. Works best if facets are similar sized or to control resolution best, start with the largest ones.
3. Works best if each new facet has two new edges. If needed, only one new edge is OK, but all edges preexisting is bad option (and never needed).
4. The crack mesh must use all defined keypoints.
5. No pair of keypoints can be connected more than twice (``i.e.``, two edges of two connected facets.

!!! 3D Crack Using a `Mesh` Element with Generated mesh options

You can also create cracks using a low-level method (a `Mesh` command) or a single command to create an initially planar crack in the shape of a parallelogram (a `Plane` command, see next section). Each `CrackList` can have one, and only one, of these commands. This `Mesh` creates a 3D crack using a single `Mesh` command within the `CrackList` command for one crack:

```

 <CrackList>
   <Mesh>
     <NodeList>
       <pt x='0' y='&yc;' z='0'/>
       <pt x='0' y='&yc;' z='&zt;'/>
       <pt x='1' y='&yc;' z='0'/>
       <pt x='1' y='&yc;' z='&zt;'/>
     </NodeList>
     <ElementList>
       <elem type='1' length='2' czm='id'>1,4,2</elem>
       <elem type='1'>1,3,4</elem>
     </ElementList>
   </Mesh>
 </CrackList>

```

The subordinate elements to the `Mesh` command define crack points on the crack surface (in the `NodeList` block) and connects those points with triangular elements (in the `ElementList` block). The three points in each `elem` command refer to three points by number in the `NodeList` (numbers are assigned automatically starting with 1).

if czm is provided it is traction law applied to each segment in the meshed area. In direct XML, czmname='name' can be used instead,

If length is provided, the edges of the element are divided up into more segments and the element is meshed into subelements as follows. First create edge objects by

1. Searching for existing edges, use if found, but edge used a third time is an error
2. Decide on number of intervals for new edges
   • Preferred number is int(length/segLength)+1. Perhaps add a preference to keep them all the same.
   • If all new- find the pair (0-1) or (1-2) that are close and match other to 0 or 1. My downgrade resolution of 0 is 1-2 pair is used.
   • If one was existing - match other two to it
   • If two existing - match new one to an existing edge. This case may not get all edges with the same number of inrtervalis
   • If three present look for two matching and use. If all differ an error. Note that can be fixed by defining triangles in order that does not surround any area.

New class for edge that will store start and end segment and sequence of interior segments. It will also count number of times the edge is used in the mesh

Meshing:

1. Create segments along any new edges
2. Set segments of each edge as no in the crack and if czmID>0 set its traction law
3. Start with edge having unique number of internal segments (or same if all the same), call it n. Let s be number of internal segments with equal intervals, then loop for i from 1 to s
   • Create n-i segments along line connect segment i of each edge
   • Create triangle strip of facets under that line, but if n-1<=0, just divide into two facets
4. When done, if n-s>0, connect each one to tip of the triangle

When crack is done, throw an error if any crack points were not connected to the crack (because their index is needed)

!!! Planar 3D Crack