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Hypo-elastoplasticity is a framework suitable for modeling the mechanics of many hard materials that have small elastic deformation and large plastic deformation. In laboratory tests for these materials the Cauchy stress is often in quasi-static equilibrium. Rycroft et al. discovered a mathematical correspondence between this physical system and the incompressible Navier–Stokes equations, and developed a projection method similar to Chorin's projection method (1968) for incompressible Newtonian fluids. Here, we improve the original projection method to simulate quasi-static hypo-elastoplasticity, by making three improvements. First, drawing inspiration from the second-order projection method for incompressible Newtonian fluids, we formulate a second-order in time numerical scheme for quasi-static hypo-elastoplasticity. Second, we implement a finite element method for solving the elliptic equations in the projection step, which provides both numerical benefits and flexibility. Third, we develop an adaptive global time-stepping scheme, which can compute accurate solutions in fewer timesteps. Our numerical tests use an example physical model of a bulk metallic glass based on the shear transformation zone theory, but the numerical methods can be applied to any elastoplastic material.
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A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics
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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- PAR ID:
- 10493918
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Proceedings of the ACM on Computer Graphics and Interactive Techniques
- Volume:
- 6
- Issue:
- 3
- ISSN:
- 2577-6193
- Page Range / eLocation ID:
- 1 to 20
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3606925
