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A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics

Published: 24 August 2023 Publication History

Abstract

We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

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    cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
    Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 6, Issue 3
    August 2023
    403 pages
    EISSN:2577-6193
    DOI:10.1145/3617582
    Issue’s Table of Contents
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    Published: 24 August 2023
    Published in PACMCGIT Volume 6, Issue 3

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    Author Tags

    1. differentiable physics
    2. elasticity
    3. generalized constitutive model
    4. material point method
    5. plasticity
    6. viscosity

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