Download or read book Coupled Simulation of Deformable Solids Rigid Bodies and Fluids with Surface Tension written by Craig Allen Schroeder and published by Stanford University. This book was released on 2011 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the numerical simulation of a variety of phenomena, particularly rigid bodies, deformable bodies, and incompressible fluids. We consider each of these simulations types in isolation, addressing challenges specific to each. We also address the problem of monolithic two-way coupling of each of these phenomena. First we address the stability of rigid body simulation with large time steps. We develop an energy correction for orientation evolution and another correction for collisions. In practice, we have found these two corrections to be sufficient to produce stable simulations. We also explore a simple scheme for rigid body fracture that is as inexpensive as prescoring rigid bodies but more flexible. Next we develop a method for simulating deformable but incompressible solids. Many constitutive models for deforming solids, such as the neo-Hookean model, break down in the incompressible limit. Simply enforcing incompressibility per tetrahedron leads to locking, where the mesh non-physically resists deformation. We present a method that uses a pressure projection similar to what is commonly used to simulate incompressible solids and apply it to deforming solids. We also address the complications that result from the interaction of this new force with contacts and collisions. Then, we turn to two coupling problems. The first problem is to couple deformable bodies to rigid bodies. We develop a fully-unified time integration scheme, where individual steps like collisions and contact are each fully two-way coupled. The resulting coupling scheme is monolithic with fully coupled linear systems. This leads to a robust and strongly coupled simulation framework. We use state-of-the-art integrators for rigid bodies and deformable bodies as the basis for the coupling scheme and maintain the ability to handle other phenomena, such as articulation and controllers on the rigid bodies and incompressibility on the deformable bodies. We follow this up by developing a scheme for coupling solids to incompressible fluids. The method handles both deformable bodies and rigid bodies. Unlike many existing methods for fluid structure interaction, which often typically lead to indefinite linear systems, the developed scheme results in a symmetric and positive definite (SPD) linear system. In addition to strongly coupling solids and fluids, the method also strongly couples viscosity with fluid pressure. This allows it to accurately treat simulations with high viscosity or where the primary coupling between solid and fluid is through fluid viscosity rather than fluid pressure. The method can be interpreted as a means of converting symmetric indefinite KKT systems with a particular form into SPD systems. Finally, we propose a method for applying implicit Lagrangian forces to an Eulerian Navier-Stokes simulation. We utilize the SPD framework to produce an SPD system with these implicit forces. We use this method to apply implicit surface tension forces. This implicit surface tension treatment reduces the tight time step restriction that normally accompanies explicit treatments of surface tension.

Download or read book Coupled Simulation of Deformable Solids Rigid Bodies and Fluids with Surface Tension written by Craig Allen Schroeder and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the numerical simulation of a variety of phenomena, particularly rigid bodies, deformable bodies, and incompressible fluids. We consider each of these simulations types in isolation, addressing challenges specific to each. We also address the problem of monolithic two-way coupling of each of these phenomena. First we address the stability of rigid body simulation with large time steps. We develop an energy correction for orientation evolution and another correction for collisions. In practice, we have found these two corrections to be sufficient to produce stable simulations. We also explore a simple scheme for rigid body fracture that is as inexpensive as prescoring rigid bodies but more flexible. Next we develop a method for simulating deformable but incompressible solids. Many constitutive models for deforming solids, such as the neo-Hookean model, break down in the incompressible limit. Simply enforcing incompressibility per tetrahedron leads to locking, where the mesh non-physically resists deformation. We present a method that uses a pressure projection similar to what is commonly used to simulate incompressible solids and apply it to deforming solids. We also address the complications that result from the interaction of this new force with contacts and collisions. Then, we turn to two coupling problems. The first problem is to couple deformable bodies to rigid bodies. We develop a fully-unified time integration scheme, where individual steps like collisions and contact are each fully two-way coupled. The resulting coupling scheme is monolithic with fully coupled linear systems. This leads to a robust and strongly coupled simulation framework. We use state-of-the-art integrators for rigid bodies and deformable bodies as the basis for the coupling scheme and maintain the ability to handle other phenomena, such as articulation and controllers on the rigid bodies and incompressibility on the deformable bodies. We follow this up by developing a scheme for coupling solids to incompressible fluids. The method handles both deformable bodies and rigid bodies. Unlike many existing methods for fluid structure interaction, which often typically lead to indefinite linear systems, the developed scheme results in a symmetric and positive definite (SPD) linear system. In addition to strongly coupling solids and fluids, the method also strongly couples viscosity with fluid pressure. This allows it to accurately treat simulations with high viscosity or where the primary coupling between solid and fluid is through fluid viscosity rather than fluid pressure. The method can be interpreted as a means of converting symmetric indefinite KKT systems with a particular form into SPD systems. Finally, we propose a method for applying implicit Lagrangian forces to an Eulerian Navier-Stokes simulation. We utilize the SPD framework to produce an SPD system with these implicit forces. We use this method to apply implicit surface tension forces. This implicit surface tension treatment reduces the tight time step restriction that normally accompanies explicit treatments of surface tension.

Download or read book Simulation of Coupled Rigid and Deformable Solids and Multiphase Fluids written by Tamar Shinar and published by . This book was released on 2008 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents methods for the physically-based simulation of various solid and fluid phenomena, including coupled rigid and deformable bodies, multiphase incompressible flow, and rigid and deformable volumes or shells coupled to incompressible flows.

Download or read book Efficient and Scalable Simulation of Solids and Fluids written by Jonathan Bernard Su and published by Stanford University. This book was released on 2011 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the numerical simulation of rigid and deformable bodies, as well as compressible fluids. We consider each of these types of simulations independently, and in particular we focus on what it takes to make these simulations both efficient and scalable. First, we develop a robust parallelized method for simulating cloth and we demonstrate simulations consisting of up to 2 million triangles. This added level of detail allows us to achieve high detailed folds and wrinkles. We propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. Next, we propose a method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species, etc. The relaxed CFL condition allows us to simulate shocks, contacts and rarefactions accurately while taking much larger time steps than before. Then, we turn to the simulation of rigid bodies, where we present an algorithm for conserving energy and momentum when advancing rigid body orientations. Furthermore, we develop a technique for clamping energy gain during contact and collisions. Together, these methods allow us to prevent energy increase during rigid body simulations, regardless of the time step size. This allows us to reduce the computation needed while still producing stable and physically plausible simulations. We also introduce a technique for fast and realistic fracture of rigid bodies using a novel collision-centered prescoring algorithm. Finally, we extend the use of energy preservation techniques to the simulation of deformable bodies, again with the goal of reducing the cost of these simulations. We propose a new spring that, in one spatial dimension, gives the exact solution regardless of the size of the time step chosen. In multiple spatial dimensions, the problem becomes nonlinear because the direction of the spring changes over time, and thus we propose an iterative approach. Then, we consider the simulation of more complicated elements such as triangles, tetrahedra, and finally full meshes and propose a novel technique that allows us to cut the iterative approach short and instead apply a final correction globally to the mesh.

Download or read book Efficient and Scalable Simulation of Solids and Fluids written by Jonathan Bernard Su and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the numerical simulation of rigid and deformable bodies, as well as compressible fluids. We consider each of these types of simulations independently, and in particular we focus on what it takes to make these simulations both efficient and scalable. First, we develop a robust parallelized method for simulating cloth and we demonstrate simulations consisting of up to 2 million triangles. This added level of detail allows us to achieve high detailed folds and wrinkles. We propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. Next, we propose a method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species, etc. The relaxed CFL condition allows us to simulate shocks, contacts and rarefactions accurately while taking much larger time steps than before. Then, we turn to the simulation of rigid bodies, where we present an algorithm for conserving energy and momentum when advancing rigid body orientations. Furthermore, we develop a technique for clamping energy gain during contact and collisions. Together, these methods allow us to prevent energy increase during rigid body simulations, regardless of the time step size. This allows us to reduce the computation needed while still producing stable and physically plausible simulations. We also introduce a technique for fast and realistic fracture of rigid bodies using a novel collision-centered prescoring algorithm. Finally, we extend the use of energy preservation techniques to the simulation of deformable bodies, again with the goal of reducing the cost of these simulations. We propose a new spring that, in one spatial dimension, gives the exact solution regardless of the size of the time step chosen. In multiple spatial dimensions, the problem becomes nonlinear because the direction of the spring changes over time, and thus we propose an iterative approach. Then, we consider the simulation of more complicated elements such as triangles, tetrahedra, and finally full meshes and propose a novel technique that allows us to cut the iterative approach short and instead apply a final correction globally to the mesh.

Download or read book Physically based Simulation of Solids and Solid fluid Coupling written by Eran Guendelman and published by . This book was released on 2006 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hybrid Techniques for High fidelity Physical Simulation of Solids and Fluids written by Andrew Paul Selle and published by . This book was released on 2008 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rigid Melting and Flowing Fluid written by Mark Thomas Carlson and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed Lagrange multipliers are used to ensure two-way coupling that generates realistic motion for both the solid objects and the fluid as they interact with one another. The rigid fluid method is so named because the simulator treats the rigid objects as if they were made of fluid. The rigidity of such an object is maintained by identifying the region of the velocity field that is inside the object and constraining those velocities to be rigid body motion. The rigid fluid method is straightforward to implement, incurs very little computational overhead, and can be added as a bridge between current fluid simulators and rigid body solvers. Many solid objects of different densities (e.g., wood or lead) can be combined in the same animation. The rigid body solver used in this work is the impulse based solver, with shock propagation introduced by Guendelman et al. in [36]. The rigid body solver allows for collisions ranging from completely elastic, where an object can bounce around forever without loss of energy, to completely inelastic where all energy is spent in the collision. Static and dynamic frictional forces are also incorporated. The details of this rigid body solver will not be discussed, but the small changes needed to couple this solver to interact with fluid will be. When simulating fluids, the fluid-air interface (free surface) is an important part of the simulation. In [8], the free surface is modelled by a set of marker particles, and after running a simulation we create detailed polygonal models of the fluid by splatting particles into a volumetric grid and then render these models using ray tracing with sub-surface scattering. In [7], I model the free surface with a particle level set technique [14]. The surface is then rendered by first extracting a triangulated surface from the level set and then ray tracing that surface with the Persistence of Vision Raytracer (http://povray.org).

Download or read book Physics based Animation written by Kenny Erleben and published by . This book was released on 2005 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: The booming computer games and animated movie industries continue to drive the graphics community's seemingly insatiable search for increased realism, believability, ad speed. To achieve the quality expected by audiences of today's games and movies, programmers need to understand and implement physics-based animation. To provide this understanding, this book is written to teach students and practitioners and theory behind the mathematical models and techniques required for physics-based animation. It does not teach the basic principles of animation, but rather how to transform theoretical techniques into practical skills. It details how the mathematical models are derived from physical and mathematical principles, and explains how these mathematical models are solved in an efficient, robust, and stable manner with a computer. This impressive and comprehensive volume covers all the issues involved in physics-based animation, including collision detection, geometry, mechanics, differential equations, matrices, quaternions, and more. There is excellent coverage of collision detection algorithms and a detailed overview of a physics system. In addition, numerous examples are provided along with detailed pseudo code for most of the algorithms. This book is ideal for students of animation, researchers in the field, and professionals working in the games and movie industries. Topics Covered: * The Kinematics: Articulated Figures, Forward and Inverse Kinematics, Motion Interpolation * Multibody Animation: Particle Systems, Continuum Models with Finite Differences, the Finite Element Method, Computational Fluid Dynamics * Collision Detection: Broad and Narrow Phase Collision Detection, Contact Determination, Bounding Volume Hierarchies, Feature-and Volume-Based Algorithms

Download or read book The Material Point Method for Solid and Fluid Simulation written by Qi Guo and published by . This book was released on 2020 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Material Point Method (MPM) has shown its high potential for physics-based simulation in the area of computer graphics. In this dissertation, we introduce a couple of improvements to the traditional MPM for different applications and demonstrate the advantages of our methods over the previous methods. First, we present a generalized transfer scheme for the hybrid Eulerian/Lagrangian method: the Polynomial Particle-In-Cell Method (PolyPIC). PolyPIC improves kinetic energy conservation during transfers, which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted L2 norm. Indeed our notion of transfers reproduces the original Particle-In-Cell Method (PIC) and recent Affine Particle-In-Cell Method (APIC). Furthermore, we derive a polynomial basis that is mass orthogonal to facilitate the rapid solution of the optimality condition. Our method applies to both of the collocated and staggered grid. As the second contribution, we present a novel method for the simulation of thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high-resolution examples. Furthermore, we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials. In the third part, we present a new hybrid Lagrangian Material Point Method for simulating volumetric objects with frictional contact. The resolution of frictional contact in the thin shell simulation cannot be generalized to the case of volumetric materials directly. Also, even though MPM allows for the natural simulation of hyperelastic materials represented with Lagrangian meshes, it usually coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts, e.g., numerical cohesion. We demonstrate that our hybrid method can efficiently resolve these issues. We show the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

Download or read book MSC Nastran 2012 Quick Reference Guide written by MSC Software and published by MSC Software. This book was released on 2011-11-15 with total page 3917 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theoretical Fluid Mechanics written by Richard Fitzpatrick and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model."--Prové de l'editor.

Download or read book ACM SIGGRAPH Symposium on Computer Animation written by and published by . This book was released on 2005 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulating Fluid solid Interaction Using Smoothed Particle Hydrodynamics Method written by Kai Pan (Ph. D.) and published by . This book was released on 2017 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fluid-solid interaction (FSI) is a challenging process for numerical models since it requires accounting for the interactions of deformable materials that are governed by different equations of state. It calls for the modeling of large deformation, geometrical discontinuity, material failure, including crack propagation, and the computation of flow induced loads on evolving fluid-solid interfaces. Using particle methods with no prescribed geometric linkages allows high deformations to be dealt with easily in cases where grid-based methods would introduce difficulties. Smoothed Particle Hydrodynamics (SPH) method is one of the oldest mesh-free methods, and it has gained popularity over the last decades to simulate initially fluids and more recently solids. This dissertation is focused on developing a general numerical modeling framework based on SPH to model the coupled problem, with application to wave impact on floating offshore structures, and the hydraulic fracturing of rocks induced by fluid pressure. An accurate estimate of forces exerted by waves on offshore structures is vital to assess potential risks to structural integrity. The dissertation first explores a weakly compressible SPH method to simulate the wave impact on rigid-body floating structures. Model predictions are validated against two sets of experimental data, namely the dam-break fluid impact on a fixed structure, and the wave induced motion of a floating cube. Following validation, this framework is applied to simulation of the mipact of large waves on an offshore structure. A new numerical technique is proposed for generating multi-modal and multi-directional sea waves with SPH. The waves are generated by moving the side boundaries of the fluid domain according to the sum of Fourier modes, each with its own direction, amplitude and wave frequency. By carefully selecting the amplitudes and the frequencies, the ensemble of wave modes can be chosen to satisfy a real sea wave spectrum. The method is used to simulate an extreme wave event, with generally good agreement between the simulated waves and the recorded real-life data. The second application is the modeling of hydro-fracture initiation and propagation in rocks. A new general SPH numerical coupling method is developed to model the interaction between fluids and solids, which includes non-linear deformation and dynamic fracture initiation and propagation. A Grady-Kipp damage model is employed to model the tensile failure of the solid and a Drucker-Prager plasticity model is used to predict material shear failures. These models are coupled together so that both shear and tensile failures can be simulated within the same scheme. Fluid and solid are treated as a single system for the entire domain, and are computed using the same stress representation within a uniform SPH framework. Two new stress coupling approaches are proposed to maintain the stress continuity at the fluid-solid interface, namely, a continuum approach and stress-boundary-condition approach. A corrected form of the density continuity equation is implemented to handle the density discontinuity of the two phases at the interface. The method is validated against analytic solutions for a hydrostatic problem and for a pressurized borehole in the presence of in-situ stresses. The simulation of hydro-fracture initiation and propagation in the presence of in-situ stresses is also presented. Good results demonstrate that SPH has the potential to accurately simulate the hydraulic-fracturing phenomenon in rocks.

Download or read book Fluid Simulation for Computer Graphics written by Robert Bridson and published by CRC Press. This book was released on 2015-09-18 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical introduction, the second edition of Fluid Simulation for Computer Graphics shows you how to animate fully three-dimensional incompressible flow. It covers all the aspects of fluid simulation, from the mathematics and algorithms to implementation, while making revisions and updates to reflect changes in the field since the first edition. Highlights of the Second Edition New chapters on level sets and vortex methods Emphasizes hybrid particle–voxel methods, now the industry standard approach Covers the latest algorithms and techniques, including: fluid surface reconstruction from particles; accurate, viscous free surfaces for buckling, coiling, and rotating liquids; and enhanced turbulence for smoke animation Adds new discussions on meshing, particles, and vortex methods The book changes the order of topics as they appeared in the first edition to make more sense when reading the first time through. It also contains several updates by distilling author Robert Bridson’s experience in the visual effects industry to highlight the most important points in fluid simulation. It gives you an understanding of how the components of fluid simulation work as well as the tools for creating your own animations.

Download or read book Effect Of Surface Tension On Deformation Of Soft Solids written by Xuejuan Xu and published by . This book was released on 2016 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical continuum mechanics often neglects the contribution of interfaces to the deformation of solids. This is usually reasonable for stiff (e.g. crystalline) materials, whose elastic energy of the bulk almost always overwhelms contributions from the surface except for very small objects that are hardly measurable. However, for compliant materials such as elastomers and hydrogels, solid surface tension can play an important role in either driving or resisting their deformation at relatively large length scale that is well within the continuum description. With applications ranging from MEMS (Micro-Electro-Mechanical System) to drug delivery, from soft robotics to biomimetic systems, it is of great technological significance to understand the underlying mechanisms of the deformation in these compliant elastomers and gels in a quantitative manner. It is for this reason, we attempt to develop theoretical and numerical models to capture the coupled effect of surface tension and elasticity in deformation of compliant solids. In this dissertation, I present our theoretical and experimental understanding of the effect of surface tension as it applies to a variety of phenomena involving deformation of compliant solids. Chapter 1 constructs a deformation map in which shape change of an elastic solid is captured by two dimensionless material parameters with a simple scaling argument. To enable accurate predictions, a finite element modelling technique, which incorporates surface tension effect, is used to quantify the shape change of a free standing elastic solid circular cylinder driven by both gravity and surface tension. Chapter 2 and 3 outline two independent approaches of measuring surface tension of a solid by monitoring its deformation. Chapter 2 describes a method that is applicable to materials with a low moduli (less than 100 kPa). We mould gelatine against patterned master surfaces. The sharp features on gel surface are rounded compared to the master and can be significantly flattened upon demoulding. We model this phenomenon using finite element technique as an elastic deformation driven by surface stress, and thus estimate the values of the solid-air surface tension of these gels. It is however limited when apply this method to stiffer materials, for the bulk elasticity in these materials often dominates the deformation. An alternative technique of surface tension measurement described in Chapter 3 is specifically designed for not-so-compliant materials with moduli larger than 100 kPa. A thin solid film is deflected with a rigid indenter and its deflection can be modelled using a version of nonlinear von Karman plate theory incorporating surface tension. We apply this method to polydimethylsiloxane (PDMS) and obtained a value of its surface tension consistent with that reported in the literature. Chapter 4, 5 and 6 study the mechanics of contact and adhesion between solids, in which classical theories are extended to include surface tension of the solid surfaces outside the contact region. Chapter 4 models the adhesive contact between an elastic half-space and a rigid sphere in the absence of external load. We present a finite element solution of such a problem, which shows the transition between classical Johnson-Kendall-Roberts (JKR) deformation and surface-tensiondominant deformation. Chapter 5 extends the problem to include non-zero external load as well as non-adhesive contact. Besides the contact configuration of a rigid sphere and elastic half space, we also simulate contact between an elastic sphere and rigid plates. Both frictionless and no slip contacts are modelled and the results are compared to provide some insights on the effect of interface conditions. We also assess the validity of Hui et al.'s (2015) small-strain theory on contact of soft solids, which includes surface tension effect, in large deformation regime. Chapter 6 focuses on modelling the surface displacement of the elastic substrate when being indented by a rigid sphere. Using the same FEM model from the previous two chapters, we compare the modelled surface profile of the substrate to an experiment performed by Jensen et al. (2015). Chapter 7 lists some suggestions for future work.