Towards Real-Time Simulation of Hyperelastic Materials / Tiantian Liu.

Format:

Book

Thesis/Dissertation

Author/Creator:

Liu, Tiantian, author.

Contributor:

Badler, Norman I., degree supervisor.

Kavan, Ladislav, degree supervisor.

Taylor, Camillo J., degree committee member.

Sifakis, Eftychios, degree committee member.

Jiang, Chenfanfu, degree committee member.

University of Pennsylvania. Computer and Information Science, degree granting institution.

Language:

English

Subjects (All):

Computer science.

Computer and Information Science--Penn dissertations.

Penn dissertations--Computer and Information Science.

Local Subjects:

Computer science.

Computer and Information Science--Penn dissertations.

Penn dissertations--Computer and Information Science.

Genre:

Academic theses.

Physical Description:

1 online resource (99 pages)

Contained In:

Dissertation Abstracts International 79-10B(E).

Place of Publication:

[Philadelphia, Pennsylvania]: University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2018.

Language Note:

English

System Details:

Mode of access: World Wide Web.

text file

Summary:

We propose a new method for physics-based simulation supporting many different types of hyperelastic materials from mass-spring systems to three-dimensional finite element models, pushing the performance of the simulation towards real-time. Fast simulation methods such as Position Based Dynamics exist, but support only limited selection of materials; even classical materials such as corotated linear elasticity and Neo-Hookean elasticity are not supported. Simulation of these types of materials currently relies on Newton's method, which is slow, even with only one iteration per timestep. In this work, we start from simple material models such as mass-spring systems or as-rigid-as-possible materials. We express the widely used implicit Euler time integration as an energy minimization problem and introduce auxiliary projection variables as extra unknowns. After our reformulation, the minimization problem becomes linear in the node positions, while all the non-linear terms are isolated in individual elements. We then extend this idea to efficiently simulate a more general spatial discretization using finite element method. We show that our reformulation can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than ten times faster than one iteration of Newton's method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton's method. Our method is also easier to implement, implying reduced software development costs.

Notes:

Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.

Advisors: Ladislav Kavan; Norman I. Badler; Committee members: Chenfanfu Jiang; Eftychios Sifakis; Camillo J. Taylor.

Department: Computer and Information Science.

Ph.D. University of Pennsylvania 2018.

Local Notes:

School code: 0175

ISBN:

9780438037175

Access Restriction:

Restricted for use by site license.