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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.

 

In this paper, we propose Energetically Consistent Inelasticity (ECI), a new formulation for modeling and discretizing finite strain elastoplasticity/viscoelasticity in a way that is compatible with optimization-based time integrators. We provide an in-depth analysis for allowing plasticity to be implicitly integrated through an augmented strain energy density function. We develop ECI on the associative von-Mises J2 plasticity, the non-associative Drucker-Prager plasticity, and the finite strain viscoelasticity. We demonstrate the resulting scheme on both the Finite Element Method (FEM) and the Material Point Method (MPM). Combined with a custom Newton-type optimization integration scheme, our method enables simulating stiff and large-deformation inelastic dynamics of metal, sand, snow, and foam with larger time steps, improved stability, higher efficiency, and better accuracy than existing approaches. 

In this paper, we propose a neural network-based approach for learning to represent the behavior of plastic solid materials ranging from rubber and metal to sand and snow. Unlike elastic forces such as spring forces, these plastic forces do not result from the positional gradient of any potential energy, imposing great challenges on the stability and flexibility of their simulation. Our method effectively resolves this issue by learning a generalizable plastic energy whose derivative closely matches the analytical behavior of plastic forces. Our method, for the first time, enables the simulation of a wide range of arbitrary elasticity-plasticity combinations using time step-independent, unconditionally stable optimization-based time integrators. We demonstrate the efficacy of our method by learning and producing challenging 2D and 3D effects of metal, sand, and snow with complex dynamics. 

Abstract Motivation Mapping genetic interactions (GIs) can reveal important insights into cellular function and has potential translational applications. There has been great progress in developing high-throughput experimental systems for measuring GIs (e.g. with double knockouts) as well as in defining computational methods for inferring (imputing) unknown interactions. However, existing computational methods for imputation have largely been developed for and applied in baker’s yeast, even as experimental systems have begun to allow measurements in other contexts. Importantly, existing methods face a number of limitations in requiring specific side information and with respect to computational cost. Further, few have addressed how GIs can be imputed when data are scarce. Results In this article, we address these limitations by presenting a new imputation framework, called Extensible Matrix Factorization (EMF). EMF is a framework of composable models that flexibly exploit cross-species information in the form of GI data across multiple species, and arbitrary side information in the form of kernels (e.g. from protein–protein interaction networks). We perform a rigorous set of experiments on these models in matched GI datasets from baker’s and fission yeast. These include the first such experiments on genome-scale GI datasets in multiple species in the same study. We find that EMF models that exploit side and cross-species information improve imputation, especially in data-scarce settings. Further, we show that EMF outperforms the state-of-the-art deep learning method, even when using strictly less data, and incurs orders of magnitude less computational cost. Availability Implementations of models and experiments are available at: https://github.com/lrgr/EMF. Supplementary information Supplementary data are available at Bioinformatics online.