Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

A virtual environment for the modelling, simulation and manufacturing of orthopaedic devices

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The objective of this work is to investigate whether the game physics based modelling is accurate enough to be used in modelling the motion of the human body, in particular musculoskeletal motion. Hitherto, the implementation of game physics in the medical field focused only on anatomical representation for education and training purposes. Introducing gaming platforms and physics engines into orthopaedics applications will help to overcome several difficulties encountered in the modelling of articular joints. Implementing a physics engine (PhysX), which is mainly designed for video games, handles intensive computations in optimized ways at an interactive speed. In this study, the capabilities of the physics engine (PhysX) and gaming platform for modelling and simulating articular joints are evaluated. First, a preliminary validation is carried out for mechanical systems with analytical solutions, before constructing the musculoskeletal model to evaluate the consistency of gaming platforms. The developed musculoskeletal model deals with the human joint as an unconstrained system with 6 DOF which is not available with other joint modeller. The model articulation is driven by contact surfaces and the stiffness of surrounding tissues. A number of contributions, such as contact modelling and muscle wrapping, have been made in this research to overcome some existing challenges in joint modelling. Using muscle segmentation, the proposed technique effectively handles the problem of muscle wrapping, a major concern for many; thus the shortest path and line of action are no longer problematic. Collision behaviour has also shown a stable response for colliding as well as resting objects, provided that it is based on the principles of surface properties and the conservation of linear and angular momentums. The precision of collision detection and response are within an acceptable tolerance controllable by varying the mesh density. An image based analysis system is developed in this thesis, mainly in order to validate the proposed physics based modelling solution. This minimally invasive method is based on the analysis of marker positions located at bony positions with minimal skin movement. The image based system overcomes several challenges associated with the currently existing methods, such as inaccuracy, complication, impracticability and cost. The analysis part of this research has considered the elbow joint as a case study to investigate and validate the proposed physics based model. Beside the interactive 3D simulation, the obtained results are validated by comparing them with the image based system developed within the current research to investigate joint kinematics and laxity and also with published material, MJM and results from experiments performed at the Brunel Orthopaedic Research and Learning Centre. The proposed modelling shows the advantageous speed, reliability and flexibility of the proposed model. It is shown that the gaming platform and physics engine provide a viable solution to human musculoskeletal modelling. Finally, this thesis considers an extended implementation of the proposed platform for testing and assessing the design of custom-made implants, to enhance joint performance. The developed simulation software is expected to give indicative results as well as testing different types of prosthetic implant. Design parameterization and sensitivity analysis for geometrical features are discussed. Thus, an integrated environment is proposed to link the real-time simulation software with a manufacturing environment so as to assist the production of patient specific implants by rapid manufacturing

Virtual reality for assembly methods prototyping: a review

Assembly planning and evaluation is an important component of the product design process in which details about how parts of a new product will be put together are formalized. A well designed assembly process should take into account various factors such as optimum assembly time and sequence, tooling and fixture requirements, ergonomics, operator safety, and accessibility, among others. Existing computer-based tools to support virtual assembly either concentrate solely on representation of the geometry of parts and fixtures and evaluation of clearances and tolerances or use simulated human mannequins to approximate human interaction in the assembly process. Virtual reality technology has the potential to support integration of natural human motions into the computer aided assembly planning environment (Ritchie et al. in Proc I MECH E Part B J Eng 213(5):461–474, 1999). This would allow evaluations of an assembler’s ability to manipulate and assemble parts and result in reduced time and cost for product design. This paper provides a review of the research in virtual assembly and categorizes the different approaches. Finally, critical requirements and directions for future research are presented

A numerical method for fluid-structure interactions of slender rods in turbulent flow

This thesis presents a numerical method for the simulation of fluid-structure interaction (FSI) problems on high-performance computers. The proposed method is specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic structures, the latter being modeled as Cosserat rods. From a numerical point of view, such kind of FSI requires special techniques to reach numerical stability. When using a partitioned fluid-structure coupling approach this is usually achieved by an iterative procedure, which drastically increases the computational effort. In the present work, an alternative coupling approach is developed based on an immersed boundary method (IBM). It is unconditionally stable and exempt from any global iteration between the fluid part and the structure part. The proposed FSI solver is employed to simulate the flow over a dense layer of vegetation elements, usually designated as canopy flow. The abstracted canopy model used in the simulation consists of 800 strip-shaped blades, which is the largest canopy-resolving simulation of this type done so far. To gain a deeper understanding of the physics of aquatic canopy flows the simulation data obtained are analyzed, e.g., concerning the existence and shape of coherent structures

Impulse-based discrete element modelling of rock impact and fragmentation, with applications to block cave mining

Impulse-based methods efficiently and accurately model high-frequency collisions of complex shapes based on the enforcement of non-penetrating constraints. It does not rely on penalty parameters nor requires the computation of penetration between bodies. This work presents a novel necessary condition for energy conservation in impulse-based methods. In previous versions of the impulse methods, such as sequential and simultaneous impulse methods, the relative velocity at the contact points after collision is directly derived from the relative velocity before collision, in a purely simultaneous or sequential manner. This work presents a novel energy tracking method (ETM), in which the relative velocities are iteratively but gradually adjusted, simultaneously modelling their interaction at each iteration. ETM ensures the energy conservation while capturing the propagation of forces during collision. The ETM is applied to model the dynamics of fragment collision in the context of fragmentation. Two approaches of fragmentation are proposed: a finite-discrete element approach, and a low cost, fragmentation pattern-based approach. The first approach models the growth of fractures using the finite element method (FEM) and advanced re-meshing technology. This finite-discrete element approach suffers from the drawback of massive computational cost. The low-cost, fragmentation pattern-based approach separate colliding bodies directly. The fragmentation pattern is generated using Weibull distribution equations, the patterns and size distributions computed using full finite/discrete element simulations and experimental results. This work investigates the influence of fragmentation on the frequency of hang-up events and on the gravity flow of rock fragments within a block caving system. Numerical results indicate that models that do not consider fragmentation tend to overestimate the frequency of hang-up accidents.Open Acces

Structure Preserving and Scalable Simulation of Colliding Systems

Predictive computational tools to study granular materials are important in fields ranging from the geosciences and civil engineering to computer graphics. The simulation of granular materials, however, presents many challenges. The behavior of a granular medium is fundamentally multi-scale, with pair-wise interactions between discrete granules able to influence the continuum-scale evolution of a bulk material. Computational techniques for studying granular materials must therefore contend with this multi-scale nature. This research first addresses both the question of how to accurately model interactions between grains and the question of how to achieve multi-scale simulations of granular materials. We propose a novel rigid body contact model and a time integration technique that, for the first time, are able to simultaneously capture five key features of rigid body impact. We further validate this new model and time integration method by reproducing computationally challenging phenomena from granular physics. We next propose a technique to couple discrete and continuum models of granular materials to one another. This hybrid model reveals a family of possible discretizations suitable for simulation. We derive an explicit integration technique from this framework that is able to capture phenomena previously reserved for discrete treatments, including frictional jamming, while treating bulk regions of the material with a continuum model. To effectively handle the large plastic deformations inherent in the evolution of a granular medium, we further propose a method to dynamically update which regions are treated with a discrete model and which regions are treated with a continuum model. We demonstrate that hybrid simulations of a dynamically evolving granular material are possible and practical, and lay the foundation for further algorithmic development in this space. Finally, as the the tools used in computational science and engineering become progressively more complex, the ability to effectively train students in the field becomes increasingly important. We address the question of how to train students from a computer science background in numerical computation techniques by proposing a new system to automatically vet and identify problems in numerical simulations. This system has been deployed at the undergraduate and graduate level in a course on physical simulation at Columbia University, and has increased both student retention and student satisfaction with the course