6,218 research outputs found
Recommended from our members
A Material Point Method for Simulating Frictional Contact with Diverse Materials
We present an extension to the Material Point Method (MPM) for simulating elastic objects with various co-dimensions like hair (1D), thin shells (2D), and volumetric objects (3D). We simulate 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. Furthermore our technique naturally couples with other traditional MPM methods for simulating granular materials. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. For the simulation of hair and volumetric elastic objects, we utilize a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While the updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy is effective in simulating thin shells, its frictional contact response strategy does not generalize to volumetric objects. Therefore, we develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling
Recommended from our members
The Material Point Method for Solid and Fluid Simulation
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
Asynchronous Variational Contact Mechanics
An asynchronous, variational method for simulating elastica in complex
contact and impact scenarios is developed. Asynchronous Variational Integrators
(AVIs) are extended to handle contact forces by associating different time
steps to forces instead of to spatial elements. By discretizing a barrier
potential by an infinite sum of nested quadratic potentials, these extended
AVIs are used to resolve contact while obeying momentum- and
energy-conservation laws. A series of two- and three-dimensional examples
illustrate the robustness and good energy behavior of the method
Advances in contact algorithms and their application to tires
Currently used techniques for tire contact analysis are reviewed. Discussion focuses on the different techniques used in modeling frictional forces and the treatment of contact conditions. A status report is presented on a new computational strategy for the modeling and analysis of tires, including the solution of the contact problem. The key elements of the proposed strategy are: (1) use of semianalytic mixed finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) use of perturbed Lagrangian formulation for the determination of the contact area and pressure; and (3) application of multilevel iterative procedures and reduction techniques to generate the response of the tire. Numerical results are presented to demonstrate the effectiveness of a proposed procedure for generating the tire response associated with different Fourier harmonics
Orthotropic rotation-free thin shell elements
A method to simulate orthotropic behaviour in thin shell finite elements is
proposed. The approach is based on the transformation of shape function
derivatives, resulting in a new orthogonal basis aligned to a specified
preferred direction for all elements. This transformation is carried out solely
in the undeformed state leaving minimal additional impact on the computational
effort expended to simulate orthotropic materials compared to isotropic,
resulting in a straightforward and highly efficient implementation. This method
is implemented for rotation-free triangular shells using the finite element
framework built on the Kirchhoff--Love theory employing subdivision surfaces.
The accuracy of this approach is demonstrated using the deformation of a
pinched hemispherical shell (with a 18{\deg} hole) standard benchmark. To
showcase the efficiency of this implementation, the wrinkling of orthotropic
sheets under shear displacement is analyzed. It is found that orthotropic
subdivision shells are able to capture the wrinkling behavior of sheets
accurately for coarse meshes without the use of an additional wrinkling model.Comment: 10 pages, 8 figure
Improved Models of Cable-to-Post Attachments for High-Tension Cable Barriers
Computer simulation models were developed to analyze and evaluate a new cable-to-post attachment for high-tension cable barriers. The models replicated the performance of a keyway bolt currently used in the design of a high-tension cable median barrier being developed at the Midwest Roadside Safety Facility. Component tests of the keyway bolts were simulated and compared to the component test results. Accurate friction, fracture strain, and stress-strain material properties were determined for a solid element model of the keyway bolt by applying actual load curve measured from the test to a simulated pull cable. By simulating the material properties of the solid element keyway bolt in bending, torsion, and tension of a rod, load curves were developed for a simplified beam element model of the keyway bolt as well. When material properties were finalized, the solid and beam element models of the keyway bolt were inserted in bogie test models and simulated again. By analyzing the bogie testing results, it was determined that due to the very small size of the keyway bolt and potential contact difficulties, solid element models of the keyway bolt may be impractical for full-scale simulation purposes. However, the beam element models were determined to be advantageous and had a very small computational cost in comparison
Geometry and Mechanics
IASS-IACM 2008 Session: Geometry and Mechanics --
Session Organizers: Kai-Uwe BLETZINGER (TU Munich), Fehmi CIRAK (University of Cambridge) --
Keynote Lecture:
"Modeling and computation of patient-specific vascular fluid-structure interaction using Isogeometric Analysis" by
Yuri BAZILEVS , Victor M. CALO, Thomas J. R. HUGHES (University of Texas at Austin), Yongie ZHANG (Carnegie Mellon University) --
Keynote Lecture:
"Optimal shapes of mechanically motivated surfaces" by
Kai-Uwe BLETZINGER , Matthias FIRL, Johannes LINHARD, Roland WUCHNER
(TU Munich) --
"Subdivision shells for nonsmooth and branching geometries" by
Quan LONG, Fehmi CIRAK (University of Cambridge) --
"Water landing analyses with explicit finite element method" by
John T. WANG (NASA Langley Research Center) --
"On a geometrically exact contact description for shells: From linear approximations for shells to high-order FEM" by
Alexander KONYUKHOV, Karl SCHWEIZERHOF (University of Karlsruhe
Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method
The doctoral thesis "Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method" aims to contribute to the development of finite element methods for the analysis of stamping processes, a problematic area with a clear industrial application.
To achieve the proposed objectives, the first part of this thesis covers the solid-shell elements. This type of element is attractive for the simulation of forming processes, since any type of three-dimensional constitutive law can be formulated without the need to consider any additional conjecture. Additionally, the contact of both sides can be easily treated.
This work first presents the development of a triangular prismatic solid-sheet element, for the analysis of thick and thin sheets with capacity for large deformations. This element is in total Lagrangian formulation, and uses neighboring elements to compute a field of quadratic displacements. In the original formulation, a modified right Cauchy tensor was obtained; however, in this work, the formulation is extended obtaining a modified strain gradient, which allows the concepts of push-forward and pull-back to be used. These concepts provide a mathematically consistent method for the definition of temporary derivatives of tensors and, therefore, can be used, for example, to work with elasto-plasticity.
This work continues with the development of the contact formulation used, a methodology found in the bibliography on computational contact mechanics for implicit simulations. This formulation consists of an exact integration of the contact interface using mortar methods, which allows obtaining the most consistent integration possible between the integration domains, as well as the most exact possible solution. The most notable contribution of this work is the consideration of dual augmented Lagrange multipliers as an optimization method. To solve the system of equations, a semi-smooth Newton method is considered, which consists of an active set strategy, also extensible in the case of friction problems. The formulation is functional for both frictionless and friction problems, which is essential for simulating stamping processes. This frictional formulation is framed in traditional friction models, such as Coulomb friction, but the development presented can be extended to any type of friction model.
The remaining necessary component for the simulation of industrial processes are the constitutive models. In this work, this is materialized in the formulation of plasticity considered. These constitutive models will be considered plasticity models for large deformations, with an arbitrary combination of creep surfaces and plastic potentials: the so-called non-associative models. To calculate the tangent tensor corresponding to these general laws, numerical implementations based on perturbation methods have been considered.
Another fundamental contribution of this work is the development of techniques for adaptive remeshing, of which different approaches will be presented. On the one hand, metric-based techniques, including the level-set and Hessian approaches. These techniques are general-purpose and can be considered in both structural problems and fluid mechanics problems. On the other hand, the SPR error estimation method, more conventional than the previous ones, is presented. In this area, the contribution of this work consists in the estimation of error using the Hessian and SPR techniques for the application to numerical contact problems.La tesis doctoral "Modelos matemáticos y numéricos innovadores para el estudio de la deformación de láminas durante los procesos de conformado industrial por el Método de los Elementos Finitos" pretende contribuir al desarrollo de métodos de elementos finitos para el análisis de procesos de estampado, un área problemática con una clara aplicación industrial. De hecho, este tipo de problemas multidisciplinares requieren el conocimiento de múltiples disciplinas, como la mecánica de medios continuos, la plasticidad, la termodinámica y los problemas de contacto, entre otros.
Para alcanzar los objetivos propuestos, la primera parte de esta tesis abarca los elementos de sólido lámina. Este tipo de elemento resulta atractivo para la simulación de procesos de conformado, dado que cualquier tipo de ley constitutiva tridimensional puede ser formulada sin necesidad de considerar ninguna conjetura adicional. Además, este tipo de elementos permite realizar una descripción tridimensional del cuerpo deformable, por tanto, el contacto de ambas caras puede ser tratado fácilmente.
Este trabajo presenta en primer lugar el desarrollo de un elemento de sólido-lámina prismático triangular, para el análisis de láminas gruesas y delgadas con capacidad para grandes deformaciones.
Este elemento figura en formulación Lagrangiana total, y emplea los elementos vecinos para poder computar un campo de desplazamientos cuadráticos. En la formulación original, se obtenía un tensor de Cauchy derecho modificado (¯C); sin embargo, en este trabajo, la formulación se extiende obteniendo un gradiente de deformación modificado (¯F), que permite emplear los conceptos de push-forward y pull-back.
Dichos conceptos proveen de un método matemáticamente consistente para la definición de derivadas temporales de tensores y, por tanto, puede ser usado, por ejemplo, para trabajar con elasto-plasticidad.
El elemento se basa en tres modificaciones: (a) una aproximación clásica de deformaciones transversales de corte mixtas impuestas; (b) una aproximación de deformaciones impuestas para las Componentes en el plano tangente de la lámina; y (c) una aproximación de deformaciones impuestas mejoradas en la dirección normal a través del espesor, mediante la consideración de un grado de libertad adicional. Los objetivos son poder utilizar el elemento para la simulación de láminas sin bloquear por cortante, mejorar el comportamiento membranal del elemento en el plano tangente, eliminar el bloqueo por efecto Poisson y poder tratar materiales elasto-plásticos con un flujo plástico incompresible, así como materiales elásticos cuasi-incompresibles o materiales con flujo plástico isocórico. El elemento considera un único punto de Gauss en el plano, mientras que permite considerar un número cualquiera de puntos de integración en su eje, con el objetivo de poder considerar problemas con una significativa no linealidad en cuanto a plasticidad.
Este trabajo continúa con el desarrollo de la formulación de contacto empleada, una metodología que se encuentra en la bibliografía sobre la mecánica de contacto computacional para simulaciones implícitas.
Dicha formulación consiste en una integración exacta de la interfaz de contacto mediante métodos de mortero, lo que permite obtener la integración más consistente posible entre los dominios de integración, así como la solución más exacta posible. La implementación también considera varios algoritmos de optimización, como la optimización mediante penalización. La contribución más notable de este trabajo es la consideración de multiplicadores de Lagrange aumentados duales como método de optimización. Estos permiten condensar estáticamente el sistema de ecuaciones, lo que permite eliminar los multiplicadores de Lagrange de la resolución y, por lo tanto, permite la consideración de solvers iterativos. Además, la formulación ha sido adecuadamente linealizada, asegurando la convergencia cuadrática del problema.
Para resolver el sistema de ecuaciones, se considera un método de Newton semi-smooth, que consiste en una estrategia de set activo, extensible también en el caso de problemas friccionales. La formulación es funcional tanto para problemas sin fricción como para problemas friccionales, lo que es esencial para la simulación de procesos de estampado. Esta formulación friccional se enmarca en los modelos de fricción tradicionales, como la fricción de Coulomb, pero el desarrollo presentado puede extenderse a cualquier tipo de modelo de fricción. Esta formulación de contacto es totalmente compatible con el elemento sólido-lámina introducido en este trabajo.
El componente necesario restante para la simulación de procesos industriales son los modelos constitutivos. En este trabajo, esto se ve materializado en la formulación de plasticidad considerada.
Estos modelos constitutivos se considerarán modelos de plasticidad para grandes deformaciones, con una combinación arbitraria de superficies de fluencia y potenciales plásticos: los llamados modelos no asociados. Para calcular el tensor tangente correspondiente a estas leyes generales, se han considerado implementaciones numéricas basadas en métodos de perturbación. Otra contribución fundamental de este trabajo es el desarrollo de técnicas para el remallado adaptativo, de las que se presentarán distintos enfoques. Por un lado, las técnicas basadas en métricas, incluyendo los enfoques level-set y Hessiano. Estas técnicas son de propósito general y pueden considerarse tanto en la aplicación de problemas estructurales como en problemas de mecánica de fluidos. Por otro lado, se presenta el método de estimación de errores SPR, más convencional que los anteriores. En este ámbito, la contribución de este trabajo consiste en la estimación de error mediante las técnicas de Hessiano y SPR para la aplicación a problemas de contacto numérico. Con los desarrollos previamente introducidos, estaremos en disposición de introducir los casos de aplicación centrados en el contexto de procesos de estampado. Es relevante destacar que estos ejemplos son comparados con las soluciones de referencia disponibles en la bibliografía como forma de validar los desarrollos presentados hasta este punto.
El presente documento está organizado de la siguiente manera. El primer capítulo establece los objetivos y revisa la bibliografía acerca de los temas clave de este trabajo. El segundo capítulo hace una introducción de la mecánica de medios continuos y los conceptos relativos al Método de los Elementos Finitos (MEF), necesarios en los desarrollos que se presentarán en los capítulos siguientes. El tercer capítulo aborda la formulación del elemento sólido-lámina, así como del elemento de lámina sin grados de libertad de rotación que inspira el sólido-lámina desarrollado. Esta parte muestra varios ejemplos académicos que son comúnmente empleados en la bibliografía como problemas de referencia de láminas.
El cuarto capítulo presenta la formulación desarrollada para la resolución de problemas de contacto numérico, consistente en una formulación implícita de integración exacta mediante métodos mortero y multiplicadores de Lagrange aumentados duales. Este capítulo incluye, asimismo, varios ejemplos comúnmente encontrados en la bibliografía, que generalmente son considerados para su validación. El quinto capítulo presenta la formulación de plasticidad empleada, incluyendo algunos detalles técnicos desde el punto de vista de la implementación, así como varios ejemplos de validación. El sexto capítulo muestra los algoritmos de remallado adaptativo desarrollados en el contexto de este trabajo, y presenta varios ejemplos, que incluyen no solo casos estructurales, sino también de mecánica de fluidos. El séptimo capítulo encapsula algunos casos de validación y aplicación para procesos de estampado. El capítulo final comprende las conclusiones, así como los trabajos que podrían continuar el presente estudio.Postprint (published version
- …