Physics-Inspired Adaptive Fracture Refinement Zhili Chen, Miaojun - - PowerPoint PPT Presentation

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Physics-Inspired Adaptive Fracture Refinement Zhili Chen, Miaojun - - PowerPoint PPT Presentation

Jan 09, 2024 129 likes •639 views

Physics-Inspired Adaptive Fracture Refinement Zhili Chen, Miaojun Yao, Renguo Feng, Huamin Wang The Ohio State University Fracture Animation Physically simulated fracture Physically accurate X Stability issue X Slow in high resolution

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Physics-Inspired Adaptive Fracture Refinement

Zhili Chen, Miaojun Yao, Renguo Feng, Huamin Wang The Ohio State University

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Fracture Animation

  • Physically simulated fracture

 Physically accurate X Stability issue X Slow in high resolution

  • Pre-defined fracture pattern

 Easier artistic control  Fast and robust X Difficult to create physically plausible detail

1 O’brien, et.al. 1999 Müller, et.al. 2013

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Physics-Inspired Fracture Refinement

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  • Physically plausible

– Material property and stress variation

  • Fast and stable

– Generate refined result in seconds

  • Easy artistic control

– Can use low-resolution animation as preview

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Input animation in low resolution

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Low-Res Animation

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Low-resolution fracture surface

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Low-Res Animation Surface Extraction

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Evolve fracture surface to higher resolution

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Extraction

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SLIDE 7

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Extraction High-Res Animation

Transfer deformation to high-resolution fracture surface

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Physics-Inspired Fracture Refinement

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Refinement Surface Extraction High-Res Animation Iterative

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SLIDE 9

Fracture Surface Extraction

Material space in final frame

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1s 1s 2s 2s 3s 3s 4s 4s 4s 4s 5s 5s 1s 1s 2s 2s 3s 3s 4s 4s

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Fracture Surface Extraction

Material space in final frame

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1s 2s 3s 4s 4s 5s 1 s 2 s 3 s 4 s

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Physics-Inspired Fracture Refinement

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Refinement Surface Extraction High-Res Animation Iterative

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Fracture Surface Evolution

  • How to advect vertices?

– Towards where the material most likely breaks – Define Separation Field in high resolution – Vertices advect in separation field

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Separation Field

Material Strength Field

Some locations within the object are more likely to break due to material property/structure

Stress Field

The object is more likely to break at where the stress is large

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Material Strength Field

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– Volumetric field as user input

  • Procedurally generated solid texture
  • Volumetric data from CT scan, etc.
  • Voxelization of 3D mesh

Darker –> Easier to break

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SLIDE 15

Stress Field

Approximation:

  • The closer to low-res fracture surface, the higher the stress

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Brighter –> Higher stress

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Separation Field

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  • =

Material Strength Field Stress Field Separation Field

W1* W2*

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Discrete Gradient Descent Flow

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dxi dt = - 1 Ai Ñxi

S j

ò

y (x)fi(x)ds - e j

i ´ n j

2Aj y (x)

S j

ò

ds æ è ç ö ø ÷

jÎNi

å

Evolve surface to minimize ( ) separation field

y (x)

Gradient descent for each vertex

S

Delaunoy, A., and Prados, E. 2011.

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SLIDE 18

Discrete Gradient Descent Flow

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dxi dt = - 1 Ai

(

jÎNi

å

1 3 AjÑy (xi)- e j

i ´ n j

2Aj y (xk)

kÎ Tj

å )

Evolve surface to minimize ( ) separation field

S

y (x)

Gradient descent for each vertex Approximation: varies linearly within triangle plane

y (x)

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Gradient Computation

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?

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Gradient Computation

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Constraints

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  • Fracture boundary

– Vertices on exterior surface only move

  • n exterior surface
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Constraints

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  • Fracture boundary

– Vertices on exterior surface only move

  • n exterior surface
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Constraints

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  • Fracture boundary

– Vertices on exterior surface only move on exterior surface

  • Intersection free

– Fracture surfaces do not intersect with each other or themselves

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Physics-Inspired Fracture Refinement

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Refinement Surface Extraction High-Res Animation Iterative

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Adaptive Remeshing

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  • Random candidate vertices
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Adaptive Remeshing

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  • Random candidate vertices
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Adaptive Remeshing

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  • Random candidate vertices
  • Select and insert candidates
  • Edge flipping optimization
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Fracture Surface Refinement

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Physics-Inspired Fracture Refinement

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Low-Res Animation Surface Evolution Adaptive Remeshing Surface Refinement Surface Extraction High-Res Animation Iterative

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High-resolution Animation Generation

  • Transfer

from low-res to high-res

(Different for Fracture surface and Exterior surface)

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Deformation Fracture time

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Fracture Surface Generation

Transfer deformation from corresponding point on fracture surface

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Exterior Surface Generation

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Exterior Surface Generation

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Exterior Surface Generation

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Exterior Surface Generation

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Transfer deformation from closet point that belongs to the same partition

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Exterior Surface Generation

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Transfer deformation from closet point that belongs to the same partition

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Exterior Surface Generation

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Transfer deformation from closet point that belongs to the same partition

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Exterior Surface Generation

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Transfer deformation from closet point that belongs to the same partition

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Examples

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Bunny Generation Time 11.7 s Refined vertex count 174 k Bunny Generation Time 11.7 s Refined vertex count 174 k

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Tree Generation Time 5.1 s Refined vertex count 123 k Tree Generation Time 5.1 s Refined vertex count 123 k

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Jello Generation Time 3.0 s Refined vertex count 32 k Jello Generation Time 3.0 s Refined vertex count 32 k

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Plastic clay Generation Time 3.0 s Refined vertex count 40 k Plastic clay Generation Time 3.0 s Refined vertex count 40 k

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Summary

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  • PRO

– Physically plausible – Fast and stable – Easy artistic control

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Summary

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Early fracture

  • PRO

– Physically plausible – Fast and stable – Easy artistic control

  • CON

– Issue with nonlinear deformation near fracture boundary

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Limitations

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  • PRO

– Physically plausible – Fast and stable – Easy artistic control

  • CON

– Issue with nonlinear deformation near fracture boundary – New collisions from refined surface not resolved

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Limitations

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1 2 3 4 5 6

  • PRO

– Physically plausible – Fast and stable – Easy artistic control

  • CON

– Issue with nonlinear deformation near fracture boundary – New collisions from refined surface not resolved – Does not create new fracture pieces

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SLIDE 48

Acknowledgement

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Thank you!