Modeling and Estimation of Energy‐Based Hyperelastic Objects

Abstract

Figure 1: Deformations of real-world objects are nonlinear, anisotropic, and heterogeneous. Our general energy-based model of hyperelasticity allows the estimation of accurate and robust models for diverse real-world examples, including cloth, skin, or internal anatomy. AbstractIn this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real-world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross-modal effects. Our method avoids these problems by relying on a general energy-based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy-limiting constraints. We combine our energy-based model with an optimization method to estimate model parameters from force-deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.

ADMM Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints

“…Soft materials of interest in graphics, like cloth, rubber, muscle, and skin, exhibit a strongly nonlinear elastic response when undergoing large deformations. Much previous work in graphics has focused on acquiring nonlinear constitutive models of volumetric soft tissue [1,4] and cloth [2,3] from observed data; their results show that nonlinearity leads to more realistic visual behavior than linear elastic models. Furthermore, Xu et al [10] recently showed that allowing artists to directly specify the nonlinear elastic response of a simulated material enables desirable animation effects to be achieved.…”

“…An important application of nonlinear constitutive models is the use of data-driven materials acquired from real objects. Unfortunately, with the exception of the recent work of [4], most existing techniques [1,2,3] represent the acquired material as a stress-strain response function, which may not necessarily correspond to a hyperelastic (conservative) material. Finding a hyperelastic model whose stress-strain response best fits a given response function would allow existing databases of acquired nonlinear materials to be used in optimization-based integration techniques such as ours.…”

“…To achieve truly realistic behavior, simulation techniques must be able to support the complex, nonlinear deformation behavior of real materials. Soft materials such as cloth, rubber, and biological soft tissue exhibit significantly nonlinear elastic behavior, and much work has gone into acquiring their constitutive properties for use in computer graphics [1,2,3,4]. However, general nonlinear materials are difficult to robustly simulate in real time.…”

Example-based damping design

“…FEM simulations are greatly in uenced by the speci c strain-stress material relationship, and the damping model. Since the pioneering work of deformable object simulation [Terzopoulos et al 1987], there has been a lot of research on extending the expressive range of materials [Bargteil et al 2007;Irving et al 2004;Müller and Gross 2004], forward design of materials [Li and Barbič 2014;Martin et al 2011;Miguel et al 2016;Schumacher et al 2012;Xu et al 2015b] or material parameter optimizations [Becker and Teschner 2007;Bickel et al 2009;Xu et al 2015a]. However, few publications focused on the design of damping for physically-based simulation.…”

Strain Rate Dissipation for Elastic Deformations

“…We build our damping model on top of the concept of dissipation potential from classical mechanics [GPS14]. This approach parallels the design of elastic deformation models based on energy formulations [XSZB15, MMO16], and same as energy‐based elastic models simplify the enforcement of good elasticity conditions, dissipation potentials simplify the enforcement of good damping conditions. As described in Section 3, we propose a framework for damping models with dissipation potentials based on strain rate.…”