Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation timesteps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically refactoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167,000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, for which linear elastic models and small deformations are sufficient, is included

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Asynchronous haptic simulation of contacting deformable objects with variable stiffness

International audienceAbstract--This paper presents a new asynchronous approach for haptic rendering of deformable objects. When stiff nonlinear deformations take place, they introduce important and rapid variations of the force sent to the user. This problem is similar to the stiff virtual wall for which a high refresh rate is required to obtain a stable haptic feedback. However, when dealing with several interacting deformable objects, it is usually impossible to simulate all objects at high rates. To address this problem we propose a quasi-static framework that allows for stable interactions of asynchronously computed deformable objects. In the proposed approach, a deformable object can be computed at high refresh rates, while the remaining deformable virtual objects remain computed at low refresh rates. Moreover, contacts and other constraints between the different objects of the virtual environment are accurately solved using a shared Linear Complementarity Problem (LCP). Finally, we demonstrate our method on two test cases: a snap-in example involving non-linear deformations and a virtual thread interacting with a deformable object

Investigating the evolution of microtextured region in Ti-6242 using FE-FFT multiscale modeling method

Titanium alloy Ti-6242 (Ti-6Al-2Sn-4Zr-2Mo) is frequently used in the high-pressure compressor of aero engines due to its excellent resistance to fatigue and creep failure at high temperature. While exhibiting high strength at elevated temperatures, it is susceptible to dwell fatigue at temperatures below 473 K due in part to the presence of microtextured regions (MTRs), also known as macrozones. MTRs are clusters of similarly orientated alpha particles, which form during alpha/beta processing and remain stable even after large deformation. The major objective of this dissertation is to quantify the evolution of MTRs under different thermomechanical processing parameters, and predict the optimal processing parameters to eliminate the MTRs.Idealized MTRs with pure initial orientation are first employed as the benchmark case to investigate the loading direction effect on its breakdown efficiency. Three high-temperature compression processes are simulated with different loading directions using crystal plasticity finite element method, and the results are validated against high-temperature compression experiments and EBSD measurement. The evolution of equivalent plastic strain, accumulated shear strain, and misorientation distribution is analyzed in detail to reveal the relationship between loading direction and MTR breakdown efficiency. Lastly, the reorientation velocity divergence of arbitrary loading direction is expressed in the Rodrigues\u27 space in order to predict the optimal processing parameters for MTR elimination. The MTR breakdown efficiency also depends on the morphology and its position within the specimen. Two different length scales have to be analyzed in order to consider both factors, which present great challenge to the numerical simulation. In this dissertation, a high-efficient FE-FFT multiscale modeling framework is derived and developed to overcome this challenge. The Fourier-Galerkin method is utilized to solve the microscale unit cell problem, while total Lagrangian nite element is used to solve the macroscopic boundary value problems. Several numerical improvements are derived and implemented to further improve its numerical efficiency, including consistent linearization, consistent homogenized tangent stiffness, and inexact Newton method. A series of numerical studies is conducted to investigate the accuracy, efficiency, and robustness of this algorithm

Virtual reality training and assessment in laparoscopic rectum surgery

Background: Virtual-reality (VR) based simulation techniques offer an efficient and low cost alternative to conventional surgery training. This article describes a VR training and assessment system in laparoscopic rectum surgery. Methods: To give a realistic visual performance of interaction between membrane tissue and surgery tools, a generalized cylinder based collision detection and a multi-layer mass-spring model are presented. A dynamic assessment model is also designed for hierarchy training evaluation. Results: With this simulator, trainees can operate on the virtual rectum with both visual and haptic sensation feedback simultaneously. The system also offers surgeons instructions in real time when improper manipulation happens. The simulator has been tested and evaluated by ten subjects. Conclusions: This prototype system has been verified by colorectal surgeons through a pilot study. They believe the visual performance and the tactile feedback are realistic. It exhibits the potential to effectively improve the surgical skills of trainee surgeons and significantly shorten their learning curve. © 2014 John Wiley & Sons, Ltd