Nonlinear material design using principal stretches

Xu, Hongyi; Sin, Funshing; Zhu, Yajie; Barbič, Jernej

doi:10.1145/2766917

Cited by 66 publications

(86 citation statements)

References 42 publications

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“…A recent work by Xu et al [XSZB15], developed concurrently to ours, succeeds to enforce conservative forces and energy convexity to materials that fulfill the Valanis-Landel hypothesis. Their focus is on user-editing of hyperelastic behaviors, mostly stiffening, not on measurement-based model estimation.…”

Section: Energymentioning

confidence: 83%

Modeling and Estimation of Energy‐Based Hyperelastic Objects

Miguel

Miraut²,

Otaduy³

2016

Computer Graphics Forum

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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.

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Section: Energymentioning

confidence: 83%

Modeling and Estimation of Energy‐Based Hyperelastic Objects

Miguel

Miraut²,

Otaduy³

2016

Computer Graphics Forum

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“…Here, we set the parameters for

\overset{boldE}{true}

by the method in the work of Xu et al For the convenience of FEM implementation, Equation can be represented in a matrix format by unrolling the strain tensors in 6 × 1 vectors (see Section 3.1), that is,

(\begin{array}{c} {\overset{ε}{true}}_{11} \\ {\overset{ε}{true}}_{22} \\ {\overset{ε}{true}}_{33} \\ 2 {\overset{ε}{true}}_{12} \\ 2 {\overset{ε}{true}}_{23} \\ 2 {\overset{ε}{true}}_{13} \end{array}) = [\begin{array}{cccccc} {((), P_{1}^{1})}^{2} & {((), P_{1}^{2})}^{2} & {((), P_{1}^{3})}^{2} & P_{1}^{1} P_{1}^{2} & P_{1}^{2} P_{1}^{3} & P_{1}^{1} P_{1}^{3} \\ {((), P_{2}^{1})}^{2} & {((), P_{2}^{2})}^{2} & {((), P_{2}^{3})}^{2} & P_{2}^{1} P_{2}^{2} & P_{2}^{2} P_{2}^{3} & P_{2}^{1} P_{2}^{...} \end{array}]

…”

Section: Our Methodsmentioning

confidence: 99%

An improved solution for deformation simulation of nonorthotropic geometric models

Cao

Yang

Ren

et al. 2019

Computer Animation & Virtual

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Physically based deformation simulation has been studied for many years in computer graphics. In order to simulate more complex geometric models and better meet the designer's requirements, many anisotropic approaches have been proposed in recent years. However, most of the approaches focus on simulating orthotropic models. In comparison with orthotropic models, nonorthotropic ones allow the objects to have anisotropic behaviors along nonorthogonal directions. In this paper, we introduce an improved approach to simulate nonorthotropic geometric models under large deformation. The improvements are mainly twofold. First, a frame field is specified on a given undeformed object, that is, each point of the object is equipped with a frame. In each local frame, we construct three independent vectors and form a nonorthogonal coordinate. Second, we design the deformation properties along each axis in the local nonorthogonal coordinate to get a local constitutive model. The final nonorthotropic model is generated by transforming the designed model from local nonorthogonal coordinates to the global standard Cartesian coordinate. To improve the stability, we introduce a time‐varying method to simultaneously track the local coordinates reorientation by pushing forward the original frame field to the deformed frame field. Experiments show that the deformation simulation using the designed nonorthotropic models exhibits anisotropic behaviors along different directions and are more stable than previous methods.

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“…This issue was alleviated by Stomakhin et al (2012) by applying the filter directly to Ψ. Xu et al (2015) proposed an alternative where users design force curves in principal stretch space. We instead present an energy that is agnostic to any reflection convention, even in the presence of inverted elements.…”

Section: Robustness Challengesmentioning

confidence: 99%

“…We examine these energies under the Valanis-Landel hypothesis (Xu et al 2015), which posits that many hyperelastic energies can be separated into length (1D), area (2D), and volume (3D) components. The above models contain length and volume terms, but no area terms.…”

Section: Existing Neo-hookean Energiesmentioning

confidence: 99%

See 1 more Smart Citation

Stable Neo-Hookean Flesh Simulation

Smith¹,

Goes²,

Kim³

2018

ACM Trans. Graph.

125

109

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Nonlinear hyperelastic energies play a key role in capturing the fleshy appearance of virtual characters. Real-world, volume-preserving biological tissues have Poisson's ratios near 1 /2, but numerical simulation within this regime is notoriously challenging. In order to robustly capture these visual characteristics, we present a novel version of Neo-Hookean elasticity. Our model maintains the fleshy appearance of the Neo-Hookean model, exhibits superior volume preservation, and is robust to extreme kinematic rotations and inversions. We obtain closed-form expressions for the eigenvalues and eigenvectors of all of the system's components, which allows us to directly project the Hessian to semipositive definiteness, and also leads to insights into the numerical behavior of the material. These findings also inform the design of more sophisticated hyperelastic models, which we explore by applying our analysis to Fung and Arruda-Boyce elasticity. We provide extensive comparisons against existing material models.

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Nonlinear material design using principal stretches

Cited by 66 publications

References 42 publications

Modeling and Estimation of Energy‐Based Hyperelastic Objects

Modeling and Estimation of Energy‐Based Hyperelastic Objects

An improved solution for deformation simulation of nonorthotropic geometric models

Stable Neo-Hookean Flesh Simulation

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