Sun Research Group at Columbia University
  • Home
  • News
  • PI
  • Team Members
  • Publications
  • Research
  • Teaching
  • Software & Data
  • Presentations
  • Recruitment & Advice
  • ML for Mechanics
  • Home
  • News
  • PI
  • Team Members
  • Publications
  • Research
  • Teaching
  • Software & Data
  • Presentations
  • Recruitment & Advice
  • ML for Mechanics

Our research on geometric prior of yielding manifold and the local closest point projection for nearly non-smooth plasticity has been accepted by CMAME

7/25/2022

0 Comments

 
When predicting plastic responses of complex microstructures, we often propose mechanisms to explain the physics of the yielding, then propose mathematical expressions to recapture what we describe in words, then propose algorithms to generate the constitutive updates. However, what if the materials are so complex that we cannot easily find a single equation to express them precisely? What if our symbolic regression skill is not sufficient to recover the surface to which those data points belong? The yield function or damage criterion of a material is a common example where our abilities to compose equations precisely and accurately are often put to test. A yield function may take many different types of variables (stress invariants, strain, sometimes also other descriptors such as volume fraction).  A simple solution we proposed is to not propose the yield surface as a function in the parametric space but directly regard it as a manifold.

In this work (first author = Mian Xiao), Mian and I explore the use of geometric prior to generating the yielding manifold based on point cloud data obtained from direct numerical simulations or experiments. By modifying the geometric approach by Williams, et al. CVPR 2019 to incorporate plastic flow information to regularize the yield surface, we have successfully recovered a highly complex yield surface through the construction of a collection of coordinate charts and the atlas, a task that is difficult to complete via training a single neural network. Meanwhile, we also show that the availability of local patches also enables us to overcome the longstanding slow convergence issue commonly exhibited in classical non-smooth plasticity models and leads to a very robust reconstruction of yield surface even with noisy data. Preprint available via ResearchGate. [PDF]



0 Comments



Leave a Reply.

    Group News

    News about Computational Poromechanics lab at Columbia University.

    Categories

    All
    Invited Talk
    Job Placements
    Journal Article
    Presentation
    Special Events

    Archives

    March 2023
    December 2022
    November 2022
    August 2022
    July 2022
    May 2022
    April 2022
    March 2022
    December 2021
    November 2021
    October 2021
    September 2021
    August 2021
    July 2021
    June 2021
    May 2021
    April 2021
    March 2021
    February 2021
    January 2021
    October 2020
    August 2020
    July 2020
    June 2020
    May 2020
    February 2020
    January 2020
    December 2019
    September 2019
    July 2019
    June 2019
    May 2019
    April 2019
    March 2019
    February 2019
    December 2018
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    May 2018
    April 2018
    March 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    July 2017
    June 2017
    May 2017
    April 2017
    March 2017
    February 2017
    January 2017
    December 2016
    November 2016
    October 2016
    May 2016
    April 2016
    March 2016
    February 2016
    January 2016
    November 2015
    October 2015
    September 2015
    August 2015
    July 2015
    June 2015
    May 2015
    March 2015
    February 2015
    January 2015
    December 2014
    November 2014
    October 2014
    September 2014
    August 2014
    July 2014
    June 2014
    May 2014
    April 2014
    March 2014
    February 2014
    January 2014
    November 2013
    September 2013

    RSS Feed

Contact Information
Prof. Steve Sun
Phone: 212-851-4371 
Fax: +1 212-854-6267
Email: wsun@columbia.edu
Copyright @ 2014-2022.  All rights reserved.