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Author: Theodore Finn Gast Publisher: ISBN: Category : Languages : en Pages : 130
Book Description
Practical time steps in today's state-of-the-art simulators typically rely on Newton's method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. Recasting backward Euler as a minimization problem allows Newton's method to be stabilized by standard optimization techniques. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. Simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. Several collision formulations are presented including for self collisions and collisions against scripted bodies, which are designed for the unique demands of this solver. Finally the Material Point Method (MPM) can be formulated to use the solver, and we present formulations for its use for simulating various materials. For simulating viscoelastic fluids, foams and sponges, we design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd- B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). We show that implicit time stepping can be achieved with an optimization based approach and that this allows for high resolution simulations at practical simulation times. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit (non-optimization based) and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.
Author: Theodore Finn Gast Publisher: ISBN: Category : Languages : en Pages : 130
Book Description
Practical time steps in today's state-of-the-art simulators typically rely on Newton's method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. Recasting backward Euler as a minimization problem allows Newton's method to be stabilized by standard optimization techniques. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. Simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. Several collision formulations are presented including for self collisions and collisions against scripted bodies, which are designed for the unique demands of this solver. Finally the Material Point Method (MPM) can be formulated to use the solver, and we present formulations for its use for simulating various materials. For simulating viscoelastic fluids, foams and sponges, we design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd- B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). We show that implicit time stepping can be achieved with an optimization based approach and that this allows for high resolution simulations at practical simulation times. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit (non-optimization based) and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.
Author: Ratnanabha Sain Publisher: Stanford University ISBN: Category : Languages : en Pages : 224
Book Description
This dissertation describes numerical experiments quantifying the influence of pore-scale heterogeneities and their evolution on macroscopic elastic, electrical and transport properties of porous media. We design, implement and test a computational recipe to construct granular packs and consolidated microstructures replicating geological processes and to estimate the link between process-to-property trends. This computational recipe includes five constructors: a Granular Dynamics (GD) simulation, an Event Driven Molecular Dynamics (EDMD) simulation and three computational diagenetic schemes; and four property estimators based on GD for elastic, finite-elements (FE) for elastic and electrical conductivity, and Lattice-Boltzmann method (LBM) for flow property simulations. Our implementation of GD simulation is capable of constructing realistic, frictional, jammed sphere packs under isotropic and uniaxial stress states. The link between microstructural properties in these packs, like porosity and coordination number (average number of contacts per grain), and stress states (due to compaction) is non-unique and depends on assemblage process and inter-granular friction. Stable jammed packs having similar internal stress and coordination number (CN) can exist at a range of porosities (38-42%) based on how fast they are assembled or compressed. Similarly, lower inter-grain friction during assemblage creates packs with higher coordination number and lower porosity at the same stress. Further, the heterogeneities in coordination number, spatial arrangement of contacts, the contact forces and internal stresses evolve with compaction non-linearly. These pore-scale heterogeneities impact effective elastic moduli, calculated by using infinitesimal perturbation method. Simulated stress-strain relationships and pressure-dependent elastic moduli for random granular packs show excellent match with laboratory experiments, unlike theoretical models based on Effective Medium Theory (EMT). We elaborately discuss the reasons why Effective Medium Theory (EMT) fails to correctly predict pressure-dependent elastic moduli, stress-strain relationships and stress-ratios (in uniaxial compaction) of granular packs or unconsolidated sediments. We specifically show that the unrealistic assumption of homogeneity in disordered packs and subsequent use of continuum elasticity-based homogeneous strain theory creates non-physical packs, which is why EMT fails. In the absence of a rigorous theory which can quantitatively account for heterogeneity in random granular packs, we propose relaxation corrections to amend EMT elastic moduli predictions. These pressure-dependent and compaction-dependent (isotropic or uniaxial) correction factors are rigorously estimated using GD simulation without non-physical approximations. Further, these correction factors heuristically represent the pressure-dependent heterogeneity and are also applicable for amending predictions of theoretical cementation models, which are conventionally used for granular packs. For predicting stress-ratios in uniaxial compaction scenario, we show the inappropriateness of linear elasticity-based equations, which use elastic constants only and do not account for dissipative losses like grain sliding. We further implement and test a computational recipe to construct consolidated microstructures based on different geological scenarios, like sorting, compaction, cementation types and cement materials. Our diagenetic trends of elastic, electrical and transport properties show excellent match with laboratory experiments on core plugs. This shows the feasibility of implementing a full-scale computational-rock-physics-based laboratory to construct and estimate properties based on geological processes. However, the elastic property estimator (FE simulation) shows limitations of finite resolution while computing elastic properties of unconsolidated sediments and fluid-saturated microstructures.
Author: Oxana Sadovskaya Publisher: Springer Science & Business Media ISBN: 3642290531 Category : Technology & Engineering Languages : en Pages : 396
Book Description
This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular materials and materials with different strengths. It proposes new models helping to define zones of the strain localization. The book shows how to analyze processes of the propagation of elastic and elastic-plastic waves in loosened materials, and constructs models of mixed type, describing the flow of granular materials in the presence of quasi-static deformation zones. In a last part, the book studies a numerical realization of the models on multiprocessor computer systems. The book is intended for scientific researchers, lecturers of universities, post-graduates and senior students, who specialize in the field of the deformable materials mechanics, mathematical modeling and adjacent fields of applied and calculus mathematics.
Author: Thorsten Pöschel Publisher: Springer Science & Business Media ISBN: 354027720X Category : Science Languages : en Pages : 324
Book Description
Computer simulations not only belong to the most important methods for the theoretical investigation of granular materials, but provide the tools that have enabled much of the expanding research by physicists and engineers. The present book is intended to serve as an introduction to the application of numerical methods to systems of granular particles. Accordingly emphasis is on a general understanding of the subject rather than on the presentation of latest advances in numerical algorithms. Although a basic knowledge of C++ is needed for the understanding of the numerical methods and algorithms in the book, it avoids usage of elegant but complicated algorithms to remain accessible for those who prefer to use a different programming language. While the book focuses more on models than on the physics of granular material, many applications to real systems are presented.
Author: Publisher: ISBN: Category : Languages : en Pages : 120
Book Description
In this research, we have attempted to characterize the anisotropy in particle arrangement and particle interactions that develop when a granular material is deformed and to determine the influence of this anisotropy on the subsequent behavior of the material. The research has dealt with the behavior of an idealized granular material consisting of lass spheres and has involved the close interaction between physical experiments, numerical simulations, and the development of theory. We have focused on: (1) Understanding the relationship between the developing anisotropy of the material and the changes in volume observed in deformations in which the mean stress is held constant. In particular, we have considered the volume change of a hollow cylindrical sample in triaxial compression and extension; (2) Using elastic waves to probe the evolution of the internal structure of the granular material as it is being deformed; and (3) Developing constitutive relations for general stress paths in the triaxial/torsional device through the combined efforts of theoretical modeling and numerical simulation.
Author: Pouria Hajikarimi Publisher: Springer Nature ISBN: 9819917867 Category : Science Languages : en Pages : 170
Book Description
Viscoelasticity is a complicated theorem that is generally used in several aspects of material characterization and modeling of polymers, resins, fiber-reinforced composites, bituminous composites, etc. On the other hand, the heterogeneous nature of composites like asphalt concrete and fiber-reinforced polymers has motivated lots of researchers to investigate the mechanical and rheological properties of these materials. This book mainly consists of the theory and application of viscoelastic materials used for construction. It starts with a comprehensible presentation of the theory of linear and nonlinear viscoelasticity. Wherein, the application of viscoelastic equations and principles on constructional viscoelastic composite materials considering time, temperature, loading rate dependency, and heterogeneity of composite substances is highlighted. The principles and equations of the viscoelasticity theorem are presented in several books, but here it is tried to present them more understandable and straightforwardly. This helps in solving real problems of heterogeneous composite materials, especially those which are used in construction. Moreover, the fundamental experiments for characterizing the elastic and viscoelastic properties of fibrous and bituminous composites are introduced and summarized. Then after, some analytical and empirical formulations for deriving the material properties of composites from the properties of the basic constituents are presented. These are followed by numerical simulation techniques using the finite element method to simulate composite materials.
Author: Carlos Parés Publisher: Springer ISBN: 3319028391 Category : Mathematics Languages : en Pages : 303
Book Description
The book is mainly addressed to young graduate students in engineering and natural sciences who start to face numerical simulation, either at a research level or in the field of industrial applications. The main subjects covered are: Biomechanics, Stochastic Calculus, Geophysical flow simulation and Shock-Capturing numerical methods for Hyperbolic Systems of Partial Differential Equations. The book can also be useful to researchers or even technicians working at an industrial environment, who are interested in the state-of-the-art numerical techniques in these fields. Moreover, it gives an overview of the research developed at the French and Spanish universities and in some European scientific institutions. This book can be also useful as a textbook at master courses in Mathematics, Physics or Engineering.
Author: Mohamed El-Amin Publisher: BoD – Books on Demand ISBN: 9535126024 Category : Science Languages : en Pages : 376
Book Description
This book introduces numerous selected advanced topics in viscoelastic and viscoplastic materials. The book effectively blends theoretical, numerical, modeling and experimental aspects of viscoelastic and viscoplastic materials that are usually encountered in many research areas such as chemical, mechanical and petroleum engineering. The book consists of 14 chapters that can serve as an important reference for researchers and engineers working in the field of viscoelastic and viscoplastic materials.
Author: Dimitrios Kolymbas Publisher: Springer Science & Business Media ISBN: 3642570186 Category : Science Languages : en Pages : 558
Book Description
In view of its extreme complexity the mathematical description of the mechanical behaviour of granular materials is an extremely difficult task. Today many different models compete with each other. However, the complexity of the models hinders their comparison, and the potential users are confused and, often, disencouraged. This book is expected to serve as a milestone in the present situation, to evaluate the present methodes, to clear up the situation, to focus and encourage for further research activities.
Author: Theodore Finn Gast
Author: Theodore Finn Gast
Author: Ratnanabha Sain
Author: Oxana Sadovskaya
Author: Thorsten Pöschel
Author: 
Author: Patrick Le Tallec
Author: Pouria Hajikarimi
Author: Carlos Parés
Author: Mohamed El-Amin
Author: Dimitrios Kolymbas