A practical method for animating anisotropic elastoplastic materials

This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly‐shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious” isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re‐use popular isotropic plasticity models like the Drucker‐Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate

A Unified Particle System Framework for Multi-Phase, Multi-Material Visual Simulations

We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elasto-plastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the non-conservative Allen-Cahn equation. In contrast, materials---made of different substances---are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid interactions. Our multi-phase, multi-material system is governed by a unified Helmholtz free energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach

Towards a predictive multi-phase model for alpine mass movements and process cascades

Alpine mass movements can generate process cascades involving different materials including rock, ice, snow, and water. Numerical modelling is an essential tool for the quantification of natural hazards. Yet, state-of-the-art operational models are based on parameter back-calculation and thus reach their limits when facing unprecedented or complex events. Here, we advance our predictive capabilities for mass movements and process cascades on the basis of a three-dimensional numerical model, coupling fundamental conservation laws to finite strain elastoplasticity. In this framework, model parameters have a true physical meaning and can be evaluated from material testing, thus conferring to the model a strong predictive nature. Through its hybrid Eulerian–Lagrangian character, our approach naturally reproduces fractures and collisions, erosion/deposition phenomena, and multi-phase interactions, which finally grant accurate simulations of complex dynamics. Four benchmark simulations demonstrate the physical detail of the model and its applicability to real-world full-scale events, including various materials and ranging through five orders of magnitude in volume. In the future, our model can support risk-management strategies through predictions of the impact of potentially catastrophic cascading mass movements at vulnerable sites

A glacier–ocean interaction model for tsunami genesis due to iceberg calving

Dynamic glacier fracture and the subsequent generation and propagation of iceberg-induced tsunamis are reproduced using a unified numerical glacier-ocean model, in line with observations at the Eqip Sermia glacier in Greenland, as well as laboratory experiments.Glaciers calving icebergs into the ocean significantly contribute to sea-level rise and can trigger tsunamis, posing severe hazards for coastal regions. Computational modeling of such multiphase processes is a great challenge involving complex solid-fluid interactions. Here, a new continuum damage Material Point Method has been developed to model dynamic glacier fracture under the combined effects of gravity and buoyancy, as well as the subsequent propagation of tsunami-like waves induced by released icebergs. We reproduce the main features of tsunamis obtained in laboratory experiments as well as calving characteristics, the iceberg size, tsunami amplitude and wave speed measured at Eqip Sermia, an ocean-terminating outlet glacier of the Greenland ice sheet. Our hybrid approach constitutes important progress towards the modeling of solid-fluid interactions, and has the potential to contribute to refining empirical calving laws used in large-scale earth-system models as well as to improve hazard assessments and mitigation measures in coastal regions, which is essential in the context of climate change

Dynamic anticrack propagation in snow

Continuum numerical modeling of dynamic crack propagation has been a great challenge over the past decade. This is particularly the case for anticracks in porous materials, as reported in sedimentary rocks, deep earthquakes, landslides, and snow avalanches, as material inter-penetration further complicates the problem. Here, on the basis of a new elastoplasticity model for porous cohesive materials and a large strain hybrid Eulerian–Lagrangian numerical method, we accurately reproduced the onset and propagation dynamics of anticracks observed in snow fracture experiments. The key ingredient consists of a modified strain-softening plastic flow rule that captures the complexity of porous materials under mixed-mode loading accounting for the interplay between cohesion loss and volumetric collapse. Our unified model represents a significant step forward as it simulates solid-fluid phase transitions in geomaterials which is of paramount importance to mitigate and forecast gravitational hazards

An implicit Generalised Interpolation Material Point Method for large deformation and gradient elasto-plasticity

The ability to correctly capture large deformation behaviour in solids is important in many problems in geotechnical engineering such as slope failure or installation of foundations. The Material Point Method (MPM) is a computational method with particular suitability for modelling problems involving large deformations. In the MPM, a domain is modelled using a set of material points at which state variables are stored and tracked. These material points move through a fixed background grid upon which calculations take place with variables being mapped between the material points and the grid. This thesis sets out to develop the MPM as a method with potential for use in geotechnical problems. Problems are encountered with the original MPM when material points cross between grid cells, and one solution to this is the Generalised Interpolation Material Point (GIMP) method, where material points are able to influence nodes beyond the currently occupied grid cell. Most development of the GIMP method has used an explicit approach, however there are a number of advantages of an implicit approach including larger load steps and improved error control. This thesis focuses on the development of a large deformation elasto-plastic implicit GIMP method. A way of calculating the deformation gradient consistent with the MPM is introduced and convergence is demonstrated using this method which has previously been frequently omitted from MPM research. An alternative way of updating material point domains using the stretch tensor is also proposed. The MPM has a number of similarities to the FEM, and it is often suggested that FEM technologies are trivial to use with the MPM. The MPM can encounter localisations caused by shear banding and, to overcome this, a gradient plasticity approach previously implemented for the FEM is investigated with the GIMP method for the first time. The addition of gradient plasticity to the GIMP method introduces a length scale parameter which governs the width of these shear bands and removes the mesh dependency which is encountered with conventional approaches. It is shown that implementation is possible however, there are a number of problems that are present in the combination of the two methods which should not be overlooked in the future

MPM study of water wave interaction with porous seawalls

Flood defences are becoming increasingly vital for protecting key coastal infrastructure from rising sea levels and storm surge waves. Waves attenuate rapidly as they propagate through porous media, corresponding to significant energy dissipation. The ability of porous armour layers to absorb wave energy is therefore of great interest to hydraulic engineers, as more and more natural and artificial porous structures are constructed to defend vulnerable coastlines or existing flood defences from wave attack. Design parameters for permeable flood defences include the grain size of the sediment particles that form the barrier and the width of the barrier. Previous studies have demonstrated that the runup height, which determines the risk of overtopping, is primarily dependent on the still water depth, wave amplitude and ground slope. This thesis investigates the effect of manipulating the mean grain size of a permeable barrier on the runup response to a dam-break flood wave and a solitary wave using the Material Point Method (MPM). Traditional methods for ascertaining the stability of protective barriers have used small-scale physical models, however, these are expensive and have been shown to suffer from scaling problems. Numerical methods are therefore gaining popularity in flood risk management applications. MPM is capable of handling large deformation problems within a Lagrangian framework, allowing for simple application of boundary conditions. MPM has been widely used to solve solid mechanics problems with history-dependent variables, but the application of this method to fluid mechanics has been rare. In MPM, the background mesh is only used to solve the governing equations. The material properties are stored at the material points so that issues arising from mesh distortions such as those exhibited in the classical finite element method (FEM) are easily avoided when coping with large deformations. Although it stores no permanent information, the background mesh allows for simple application of boundary conditions. Boundary conditions can be applied directly at the nodes, unlike in meshfree methods such as SPH where boundary conditions must be applied to a series of "boundary particles", which much first be identified. In single-point MPM, both the liquid and solid velocity fields are tracked by a single material point. The double-point MPM introduces two sets of material points representing the solid phase and liquid phase separately, so that it is capable of capturing the relative acceleration between the water and the soil skeleton. It is therefore capable of accurately modelling situations where the fluid moves significantly with respect to the soil, such as in wave run-up on structures. The goal of this research is to determine the effectiveness of sloped and vertical permeable barriers on preventing flooding resulting from storm surges and tsunami waves, and to ascertain the most effective permeability for reducing wave impact, to provide design guidance for coastal flood barriers. To this end, MPM is used to examine the influence of two key design parameters for porous, permeable flood defences, including the grain size of the composition particles and the width of the barrier. The term porosity is used to describe the dimensionless ratio of the volume of voids to solid material in the structure, and the term permeability is used to describe how resistant the porous structure is to flow, related to the mean grain size forming the material, in accordance with the Ergun equation used to determine the body force between the solid and liquid phases. This equation is presented in Chapter 3. A larger mean grain size results in larger voids in the material, so that there is less resistance to flow and the permeability increases. The multiphase version of the MPM package Anura3D (www.anura3d.com) has been adopted in this study. It is shown that increasing the grain size, and therefore the permeability, of the porous dam effectively reduces the overall runup height. The grain size, rather than the wall width, is shown to be the dominant parameter affecting the runup.EPSR

Advanced image analysis techniques for laboratory experiments on soils

The understanding of soil behavior is the foundation where the geotechnical engineering is built on. Experimentation is essential to improve this comprehension, and then to be able to translate it into models, theories, or laws. In a proper scientific method, experimentation is present in all phases of model development from conception to validation. This Thesis focuses on laboratory experimentation. The experiments are interesting because they are an abstraction of reality, focusing on the objective of the investigation. The main advantage of laboratory experiments is the high reproducibility, which, together with the control of the initial and contour conditions, enables to analyze the effects of different variables on the soil behavior. This Thesis focuses on the development and improvement of methodologies and techniques to provide more and better information from the laboratory experiments in a massive and non-invasive way. The developed methodologies are based on the analysis of sequential images of experiments which are able to provide the spatial distribution through the domain of the analyzed variables. The first technique presented and validated is the Particle Image Velocimetry - Numerical Particle (PIV-NP). This is a post-process to enhance the image correlation methods (PIV). The method is able to transform the instantaneous displacements measured by PIV between two consecutive images on fixed points in the space into accumulated displacements and strains on points (Numerical Particles) which represent portions of the moving soil analyzed. The method is especially suitable for the analysis of large displacements and strains experiments and combines the advantages of Eulerian and Lagrangian scheme. The validation of the method is done by means of synthetic examples and laboratory tests. For application on unsaturated soils, the Thesis presents a methodology to measure the degree of saturation (Sr) using Short-Wave InfraRed images (SWIR). The methodology is based on the relatively high absorbance of light by water in specific wavelengths of the SWIR spectrum (1400 -1550 nm and 1900 – 2000 nm) respect to the solid particles of soils. The methodology is created to be applied in a sequence of images to analyze the spatial distribution of degree of saturation and its evolution in time. The average Pixel Intensity is measured in a grid of points in each image. The Pixel Intensity is normalized and translated into its correspondent degree of saturation using the calibration curve previously calibrated. Both techniques, PIV-NP and Sr measurements from SWIR image, are combined into an integrated methodology. The result provides the position, velocity, acceleration, strains, and degree of saturation in time of the analyzed moving soil discretized into numerical particles. This allows to compare and correlate directly all the variables. The methodology offers different options to display the results: surface (2D), line (1D), and particle (0D). The information that provides each display dimension is complementary and useful for a complete understanding of the soil behavior. Finally, the integrated methodology is also applied combining the PIV-NP with a more mature technique to measure the degree of saturation in transparent soils developed in Canada. The study of the dry footprints on the seashore is the chosen case to show the capability of the combined techniques on the analysis of soil behavior. The three different options of results display are crucial to understanding the correlation between the degree of saturation and the velocity of failure. The methodology and techniques developed can be used in any geotechnical laboratory and conform a base to extend the volume of data that can be obtained from the experiments, but especially enhancing the utility of the information deduced from the data.La comprensió del comportament del sòl és el fonament sobre el qual es construeix l'enginyeria geotècnica. L'experimentació és essencial per millorar aquesta comprensió, i després poder traduir-la en models, teories o lleis. En un mètode científic adequat, l'experimentació està present en totes les fases del desenvolupament del model, des de la concepció fins a la validació. Aquesta tesi se centra en l'experimentació de laboratori. Els experiments són interessants perquè són una abstracció de la realitat, centrant-se en l'objectiu de la investigació. El principal avantatge dels experiments de laboratori és l'alta reproductibilitat, que, juntament amb el control de les condicions inicials i de contorn, permet analitzar els efectes de diferents variables en el comportament del sòl. Aquesta tesi es centra en el desenvolupament i la millora de metodologies i tècniques per a proporcionar més i millor informació dels experiments de laboratori de forma massiva i no invasiva. Les metodologies desenvolupades es basen en l'anàlisi d'imatges seqüencials d'experiments que poden proporcionar la distribució espacial de les variables analitzades en tot el domini. La primera tècnica presentada i validada és el Particle Image Velocimetry - Numerical Particle (PIV-NP). Aquest és un post-procés per millorar els mètodes de correlació d'imatges (PIV). El mètode és capaç de transformar els desplaçaments instantanis mesurats per PIV entre dues imatges consecutives en punts fixos en l'espai en desplaçaments acumulats i deformacions en punts (Partícules Numèriques) que representen parts del sòl analitzat en moviment. El mètode és especialment adequat per a l'anàlisi de grans desplaçaments i experiments de deformació, combina els avantatges dels esquemes eulerià i lagrangià. La validació del mètode es realitza mitjançant casos sintètics i experiments de laboratori. Per aplicacions en sòls no saturats, la Tesi presenta una tècnica per mesurar el grau de saturació (Sr) utilitzant imatges infraroges d'ona curta (SWIR). La metodologia es basa en l'alta absorció de la llum per l'aigua comparativament a les partícules sòlides dels sòls, en longituds d'ona específiques de l'espectre SWIR (1400-1550 nm i 1900-2000 nm). La tècnica es crea per ser aplicada a una seqüència d'imatges, per analitzar la distribució espacial del grau de saturació i la seva evolució en el temps. La intensitat de píxel mitjana es mesura en una quadrícula de punts en cada imatge. La intensitat del píxel es normalitza i es tradueix en la seva corresponent grau de saturació utilitzant la corba de calibratge prèviament calibrada. Les dues tècniques, els mesuraments PIV-NP i Sr a partir d'imatges SWIR, es combinen en una metodologia integrada. El resultat proporciona l'evolució en el temps de la posició, la velocitat, l'acceleració, les deformacions i el grau de saturació del sòl analitzat en moviment, discretitzat en partícules numèriques. Això permet comparar i correlacionar directament totes les variables. La metodologia ofereix diferents opcions per mostrar els resultats: superfície (2D), línia (1D) i partícula (0D). La informació que proporciona cada dimensió de visualització és complementària i útil per a una comprensió completa del comportament del sòl. Finalment, la metodologia integrada també s'aplica combinant el PIV-NP amb una tècnica més madura desenvolupada al Canadà per mesurar el grau de saturació en sòls transparents. L'estudi de les petjades seques a la vora de la platja és el cas triat per mostrar la capacitat de les tècniques combinades en l'anàlisi del comportament del sòl. Les tres diferents opcions de visualització de resultats són crucials per comprendre la correlació entre el grau de saturació i la velocitat de trencament. La metodologia i les tècniques desenvolupades es poden utilitzar en qualsevol laboratori geotècnic i conformen una base per ampliar el volum de dades que es poden obtenir dels experiments, però especialment millorant la utilitat de la informació deduïda de les dadesLa comprensión del comportamiento del suelo es el cimiento sobre el cual se construye la ingeniería geotécnica. La experimentación es esencial para mejorar esta comprensión, y luego poder traducirla en modelos, teorías o leyes. En un método científico adecuado, la experimentación está presente en todas las fases del desarrollo del modelo, desde la concepción hasta la validación. La experimentación comprende dos tipos diferentes de datos: datos de campo y de laboratorio. Ambos enfoques son esenciales y complementarios, considerando sus debilidades y fortalezas. Esta tesis se centra en la experimentación de laboratorio. Los experimentos son interesantes porque son una abstracción de la realidad, centrándose en el objetivo de la investigación. La principal ventaja de los experimentos de laboratorio es la alta reproducibilidad, que, junto con el control de las condiciones iniciales y de contorno, permite analizar los efectos de diferentes variables en el comportamiento del suelo. Esta tesis se centra en el desarrollo y la mejora de metodologías y técnicas para proporcionar más y mejor información de los experimentos de laboratorio de forma masiva y no invasiva. Las metodologías desarrolladas se basan en el análisis de imágenes secuenciales de experimentos que pueden proporcionar la distribución espacial a través del dominio de las variables analizadas. La primera técnica presentada y validada es la Particle Image Velocimetry – Numerical Particle (PIV-NP). Este es un postproceso para mejorar los métodos de correlación de imágenes (PIV). El método es capaz de transformar los desplazamientos instantáneos medidos por PIV entre dos imágenes consecutivas en puntos fijos en el espacio en desplazamientos acumulados y deformaciones en puntos (Partículas Numéricas) que representan partes del suelo analizado en movimiento. El método es especialmente adecuado para el análisis de grandes desplazamientos y experimentos de deformación, combina las ventajas del esquema euleriano y lagrangiano. La validación del método se realiza mediante ejemplos sintéticos y pruebas de laboratorio. viii Para aplicaciones en suelos no saturados, la Tesis presenta una metodología para medir el grado de saturación (Sr) utilizando imágenes infrarrojas de onda corta (SWIR). La metodología se basa en la alta absorción de la luz por el agua con respecto a las partículas sólidas de los suelos, en longitudes de onda específicas del espectro SWIR (1400-1550 nm y 1900-2000 nm). La metodología se crea para ser aplicada en una secuencia de imágenes, para analizar la distribución espacial del grado de saturación y su evolución en el tiempo. La intensidad de píxel promedio se mide en una cuadrícula de puntos en cada imagen. La intensidad del píxel se normaliza y se traduce en su correspondiente grado de saturación utilizando la curva de calibración previamente calibrada. Ambas técnicas, las mediciones PIV-NP y Sr a partir de imágenes SWIR, se combinan en una metodología integrada. El resultado proporciona la evolución en el tiempo de la posición, la velocidad, la aceleración, las deformaciones y el grado de saturación del suelo analizado en movimiento, discretizado en partículas numéricas. Esto permite comparar y correlacionar directamente todas las variables. La metodología ofrece diferentes opciones para mostrar los resultados: superficie (2D), línea (1D) y partícula (0D). La información que proporciona cada dimensión de visualización es complementaria y útil para una comprensión completa del comportamiento del suelo. Finalmente, la metodología integrada también se aplica combinando el PIV-NP con una técnica más madura desarrollada en Canadá para medir el grado de saturación en suelos transparentes. El estudio de las pisadas secas en la orilla de la playa es el caso elegido para mostrar la capacidad de las técnicas combinadas en el análisis del comportamiento del suelo. Las tres opciones diferentes de visualización de resultados son cruciales para comprender la correlación entre el grado de saturación y la velocidad de rotura. La metodología y las técnicas desarrolladas se pueden utilizar en cualquier laboratorio geotécnico y conforman una base para ampliar el volumen de datos que se pueden obtener de los experimentos, pero especialmente mejorando la utilidad de la información deducida de los dato