Drucker-prager elastoplasticity for sand animation

2011

In this thesis we describe a technique for animating the behavior of viscoelastic fluids such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian methods for animating incompressible fluids. Our method computes viscoelastic fluid behavior by supplementing the basic Navier-Stokes equations with additional terms for elastic body forces. These terms can be readily computed on rectilinear grids using a staggered discretization scheme, and the use of an Eulerian formulation easily accommodates modeling flows that undergo large deformations with topological changes. These elastic terms require computing the material strain throughout the fluid. Because the fluid simulations do not make use of an explicit reference configuration, strain is computed by integrating strain rate and advecting the results. The transition from elastic resistance to viscous flow is controlled by von Mises' yield condition, and subsequent behavior is governed by a quasi-linear plasticity model.

ACM SIGGRAPH Computer Graphics, 1988

We continue our development of physically-based models for animating nonrigid objects in simulated physical environments. Our prior work treats the special case of objects that undergo perfectly elastic deformations. Real materials, however, exhibit a rich variety of inelastic phenomena. For instance, objects may restore themselves to their natural shapes slowly, or perhaps only partially upon removal of forces that cause deformation. Moreover, the deformation may depend on the history of applied forces. The present paper proposes inelastically deformable models for use in computer graphics animation. These dynamic models tractably simulate three canonical inelastic behaviors---viscoelasticity, plasticity, and fracture. Viscous and plastic processes within the models evolve a reference component, which describes the natural shape, according to yield and creep relationships that depend on applied force and/or instantaneous deformation. Simple fracture mechanics result from internal p...

2014

Recent experiences from the Darfield and Canterbury, New Zealand earthquakes have shown that the soft soil condition of saturated liquefiable sand has a profound effect on seismic response of buildings, bridges and other lifeline infrastructure. For detailed evaluation of seismic response three dimensional integrated analysis comprising structure, foundation and soil is required; such an integrated analysis is referred to as Soil Foundation Structure Interaction (SFSI) in literatures. SFSI is a three-dimensional problem because of three primary reasons: first, foundation systems are three-dimensional in form and geometry; second, ground motions are three-dimensional, producing complex multiaxial stresses in soils, foundations and structure; and third, soils in particular are sensitive to complex stress because of heterogeneity of soils leading to a highly anisotropic constitutive behaviour. In literatures the majority of seismic response analyses are limited to plane strain configuration because of lack of adequate constitutive models both for soils and structures, and computational limitation. Such two-dimensional analyses do not represent a complete view of the problem for the three reasons noted above. In this context, the present research aims to develop a three-dimensional mathematical formulation of an existing plane-strain elastoplastic constitutive model of sand developed by Cubrinovski and Ishihara (1998b). This model has been specially formulated to simulate liquefaction behaviour of sand under ground motion induced earthquake loading, and has been well-validated and widely implemented in verifcation of shake table and centrifuge tests, as well as conventional ground response analysis and evaluation of case histories. The approach adopted herein is based entirely on the mathematical theory of plasticity and utilises some unique features of the bounding surface plasticity formalised by Dafalias (1986). The principal constitutive parameters, equations, assumptions and empiricism of the existing plane-strain model are adopted in their exact form in the three-dimensional version. Therefore, the original two-dimensional model can be considered as a true subset of the three-dimensional form; the original model can be retrieved when the tensorial quantities of the three dimensional version are reduced to that of the plane-strain configuration. Anisotropic Drucker-Prager type failure surface has been adopted for the three-dimensional version to accommodate triaxial stress path. Accordingly, a new mixed hardening rule based on Mroz's approach of homogeneous surfaces (Mroz, 1967) has been introduced for the iii virgin loading surface. The three-dimensional version is validated against experimental data for cyclic torsional and triaxial stress paths. iv Table of Contents 1.0 INTRODUCTION AND SCOPE.

International Journal for Numerical and Analytical Methods in Geomechanics, 1994

The paper presents a hypoplastic constitutive model for the three-dimensional non-linear stress-strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non-linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions.

Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, 2018

This article presents a model that aims at computing deformation and simulating fractures. To allow the use of linear elasticity in small displacements for deformation of a brittle object while still enabling any rigid motion, a rigid reference is computed using the Shape Matching method and all displacements are evaluated with respect to this reference. Fractures are handled using a stress tensor computed at each vertex of the object's 3D mesh. Some accelerations are proposed, that allow a faster determination of fracture areas and a fast processing of new connected components. 2 PREVIOUS WORK Fracture simulation relies primarily on deformation computation (Nealen et al., 2006), but many approaches exist (Muguercia et al., 2014). Indeed, when a deformation is computed, different criteria can be used to make cracks appear in the structure. Geometric criteria have been proposed, such as an elongation 28

2019

The mechanical behaviour of granular materials is characterized by strong non-linearity and irreversibility. In particular, particle breakage will induce additional plastic deformations beyond those which might be expected for a rigid particle assumption. When defining a constitutive model, experimental data on the nature of the incremental response of the material is desirable. However, the experiments are very challenging and therefore test simulations using the discrete element method (DEM) are very useful. In this work, the incremental behaviour of crushable granular soils is investigated using the DEM by simulating 3D axisymmetric stress probes experiments on a Fontainebleau sand analogue. Particle breakage is permitted and the initial high stress condition is such that crushing will occur along some of the loading directions. The results show that particle crushing induces a change in the direction of the plastic flow and that this direction is independent of the loading path. Le comportement mécanique des matériaux granulaires est caractérisé par une forte non-linéarité et une irréversibilité. En particulier, la rupture des particules induira des déformations plastiques supplémentaires allant au-delà de celles auxquelles on pourrait s'attendre pour une hypothèse de particule rigide. Lors de la définition d'un modèle constitutif, des données expérimentales sur la nature de la réponse incrémentielle du matériau sont souhaitables. Cependant il est très difficile de reproduire un ensemble d'échantillons identiques à utiliser dans une étude paramétrique expérimentale. Les simulations de test utilisant la méthode des éléments discrets (DEM) sont donc très utiles. Dans ce travail, le comportement incrémental des sols granulaires déformables est étudié à l'aide du DEM en simulant des expériences de sondes de contrainte axisymétriques 3D sur un analogue de sable de Fontainebleau. La rupture de particules est autorisée et la condition initiale de fortes contraintes est telle que des écrasements se produiront dans certaines directions de chargement. Les résultats montrent que le broyage de particules induit un changement de direction du flux de plastique et que cette direction est indépendante du chemin de chargement.

This paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian methods for animating incompressible fluids with free surfaces by including additional elastic terms in the basic Navier-Stokes equations. The elastic terms are computed by integrating and advecting strain-rate throughout the fluid. Transition from elastic resistance to viscous flow is controlled by von Mises's yield condition, and subsequent behavior is then governed by a quasi-linear plasticity model.

ACM SIGGRAPH 2021 Courses, 2021

Efficient simulation of contact is of interest for numerous physics-based animation applications. For instance, virtual reality training, video games, rapid digital prototyping, and robotics simulation are all examples of applications that involve contact modeling and simulation. However, despite its extensive use in modern computer graphics, contact simulation remains one of the most challenging problems in physics-based animation. This course covers fundamental topics on the nature of contact modeling and simulation for computer graphics. Specifically, we provide mathematical details about formulating contact as a complementarity problem in rigid body and soft body animations. We briefly cover several approaches for contact generation using discrete collision detection. Then, we present a range of numerical techniques for solving the associated LCPs and NCPs. The advantages and disadvantages of each technique are further discussed in a practical manner, and best practices for implementation are discussed. Finally, we conclude the course with several advanced topics such as methods for soft body contact problems, barrier functions, and anisotropic friction modeling. Programming examples are provided in our appendix as well as on the course website to accompany the course notes.

2009

Granular materials enjoy vivid motion phenomena that make them highly visually attractive. However, simulating each and every physical grain imposes an extremely high computational cost, due to the stringent resolution requirements. In this paper, we introduce a method for simulating granular media that achieves high visual resolution and high mechanical fidelity at a lower computational cost than earlier methods. Our method is based on a novel spatial decomposition of the computation of internal and external forces. The method is also highly parallelizable and configurable, allowing the artist to simulate a large range of granular materials.

International Journal for Numerical and Analytical Methods in Geomechanics, 2014

Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three-dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by , in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void-based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non-coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data.