CHRONO: a parallel multi-physics library for rigid-body, flexible-body, and fluid dynamics

Abstract. The last decade witnessed a manifest shift in the microprocessor industry towards chip designs that promote parallel computing. Until recently the privilege of a select group of large research centers, Teraflop computing is becoming a commodity owing to inexpensive GPU cards and multi to many-core x86 processors. This paradigm shift towards large scale parallel computing has been leveraged in CHRONO, a freely available C++ multi-physics simulation package. CHRONO is made up of a collection of loosely coupled components that facilitate different aspects of multi-physics modeling, simulation, and visualization. This contribution provides an overview of CHRONO::Engine, CHRONO::Flex, CHRONO::Fluid, and CHRONO::Render, which are modules that can capitalize on the processing power of hundreds of parallel processors. Problems that can be tackled in CHRONO include but are not limited to granular material dynamics, tangled large flexible structures with self contact, particulate flows, and tracked vehicle mobility. The paper presents an overview of each of these modules and illustrates through several examples the potential of this multi-physics library

N-body gravitational and contact dynamics for asteroid aggregation

The development of dedicated numerical codes has recently pushed forward the study of N-body gravitational dynamics, leading to a better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an N-body numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code to predict natural aggregation phenomena

A lookup-table-based approach for spatial analysis of contact problems

The aim of this work is to present an efficient methodology to deal with general 3D-contact problems. This approach embraces three steps: geometrical definition of 3D-surfaces; detection of the candidate contact points; evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and ease to handle freeform shapes. This task is carried during preprocessing, which is performed before starting the multibody analysis. The preprocessing procedure can be condensed into four steps: a regular and representative collection of surface points is extracted from the 3D-parametric surface; for each point the tangent vectors to the u and v directions of the parametric surface and the normal vector are computed; the geometrical information on each point is saved in a lookup table, including the parametric point coordinates, the corresponding Cartesian coordinates and the components of the normal, tangent and bitangent vectors; the lookup table is rearranged such that the u-v mapping is converted into a 2D-matrix being this surface data saved as a direct access file. For the detection of the contact points, the relative distance between the candidate contact points are computed and used to check if the bodies are in contact. The actual contact points are selected as those that correspond to the maximum relative indentation. The contact forces are determined as functions of the indentation or pseudo-penetration, impact velocity and geometric and material properties of the contacting surfaces. In general, lookup tables are used to reduce the computation time in dynamic simulations. However, the application of these schemes involves an increase of memory needs. Within the proposed approach, the amount of memory used is significantly reduced, as a result of a partial upload into memory of the lookup table. A slider-crank mechanism with a cup on the top of the slider and a marble ball is used as demonstrative example. A contact pair is considered between a cup and a marble ball, being the contact forces computed using a dissipative contact model.Fundação para a Ciência e a Tecnologia (FCT

Fast Solvers and Simulation Data Compression Algorithms for Granular Media and Complex Fluid Flows

Granular and particulate flows are common forms of materials used in various physical and industrial applications. For instance, we model the soil as a collection of rigid particles with frictional contact in soil-vehicle simulations, and we simulate bacterial colonies as active rigid particles immersed in a viscous fluid. Due to the complex interactions in-between the particles and/or the particles and the fluid, numerical simulations are often the only way to study these systems apart from typically expensive physical experiments. A standard method for simulating these systems is to apply simple physical laws to each of the particles using the discrete element method (DEM) and evolve the resulting multibody system in time. However, due to the sheer number of particles in even a moderate-scale real-world system, it quickly becomes expensive to timestep these systems unless we exploit fast algorithms and high-performance computing techniques. For instance, a big challenge in granular media simulations is resolving contact between the constituent particles. We use a cone-complementarity formulation of frictional contact to resolve collisions; this approach leads to a quadratic optimization problem whose solution gives us the contact forces between particles at each timestep. In this thesis, we introduce strategies for solving these optimization problems on distributed memory machines. In particular, by imposing a locality-preserving partitioning of the rigid bodies among the computing nodes, we minimize the communication cost and construct a scalable framework for collision detecting and resolution that can be easily scaled to handle hundreds of millions of particles. For robust and efficient simulation of axisymmetric particles in viscous fluids, we introduce a fast method for solving Stokes boundary integral equations (BIEs) on surfaces of revolution. By first transforming the Stokes integral kernels into a rotationally invariant form and then decoupling the transformed kernels using the Fourier series, we reduce the dimensionality of the problem. This approach improves the time complexity of the BIE solvers by an order of magnitude; additionally we can use high-order one-dimensional singular quadrature schemes to construct highly accurate solvers. Finally, coupling our solver framework with the fast multipole method, we construct a fast solver for simulating Stokes flow past a system of axisymmetric bodies. Combining this with our complementarity collision resolution framework, we have the potential to simulate dense particulate suspensions. Physics-based simulations similar to those described above generate large amounts of output data, often in the hundreds of gigabytes range. We introduce data compression techniques based on the tensor-train decomposition for DEM simulation outputs and demonstrate the high compressibility of these large datasets. This allows us to keep a reduced representation of simulated data for post-processing or use in learning tasks. Finally, due to the high cost of physics-based models and limited computational budget, we can typically run only a limited number of simulations when exploring a high-dimensional parameter space. Formally, this can be posed as a matrix/tensor completion problem, and Bayesian inference coupled with a linear factorization model is often used in this setup. We use Markov chain Monte Carlo (MCMC) methods to sample from the unnormalized posteriors in these inference problems. In this thesis, we explore the properties of the posterior in a simple low-rank matrix factorization setup and develop strategies to break its symmetries. This leads to better quality MCMC samples and lowers the reconstruction errors with various synthetic and real-world datasets.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169614/1/saibalde_1.pd

Fetus safety in motor vehicle accidents

Motor vehicle accidents are statistically the major cause of accidental severe injuries for pregnant women and fetuses fatality. Volunteers, post mortem human surrogates, anthropomorphic crash test devices and computational occupant models are used to improve human safety in motor vehicle accidents. However, due to the ethical issues, pregnant women and their fetuses cannot be used as volunteers or post mortem human surrogates to investigate the effects of crashes on them. The only anthropomorphic test device representing pregnant women is very limited in design and lacks a fetus. There is no computational pregnant occupant model with a fetus other than 'Expecting'. This thesis focuses on understanding the risk of placental abruption for pregnant drivers involved in road accidents, hence assessing the risk to fetus fatality. An extensive review of existing models in general and pregnant women models in particular is reported. The time line of successive development of crash test dummies and their positive effect on automotive passive safety design are examined. 'Expecting', the computational pregnant occupant model with a finite element uterus and a multibody fetus, is used in this research to determine the strain levels in the uteroplacental interface. External factors, such as the effect of restraint systems and crash speeds are considered. Internal factors, such as the effect of placental location in the uterus, and the inclusion and exclusion of a fetus are investigated. The head of the multibody fetus is replaced with a deformable head model to investigate the effects of a deformable fetus head on strain levels. The computational pregnant driver model with a fetus offers a more realistic representation of the response to crash impact hence provides a useful tool to investigate fetus safety in motor vehicle accidents. Seat belt, airbag and steering wheel interact directly with the pregnant abdomen and play an important role on fetus safety in motor vehicle accidents. The results prove that the use of a three-point seat belt with the airbag offer the greatest protection to the fetus for frontal crash impacts. The model without a fetus underestimates the strain levels. The outcome of this research should assist automobile manufacturers to address the potential safety issues at the design level

Contact detection between a small ellipsoid and another quadric

[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition, named smallness condition, is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of the expressions in a discriminant system of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial. As an application of these results, a method to detect contact between a small ellipsoid and a combination of quadrics is given

DEVELOPMENT OF NEW METHODOLOGIES FOR ROAD ACCIDENT RECONSTRUCTION WITH CDR TOOL

Road accidents are a constant reality these days, therefore to reduce and understand these accidents and, as a result, improve road safety, an analysis will be carried out on modern and old accident reconstruction methods and how they can be improved. With the new 2022 European Union regulation coming in, which enforces the use of Event Data Recorders (EDR) on newly made vehicles, suddenly there’s a system that can record vehicle dynamic data and driver inputs, in case of an accident. This project’s objective is to analyze this data in an accident context and simplify the reconstruction process. This project aims for a seamless interpretation of the accident scene and vehicle dynamics to better understand the data in the scene’s context. Some methodologies and tools used for the reconstruction of the accident scene will be studied, culminating in a system that digitizes the scene for later use in computer software. The dynamic data from the accident can be divided into three phases: pre-crash, impact, and post-crash. Each phase requires a different approach which depends on the type of data to obtain the trajectory of the vehicle throughout the phases

DEVELOPMENT OF NEW METHODOLOGIES FOR ROAD ACCIDENT RECONSTRUCTION WITH CDR TOOL

Road accidents are a constant reality these days, therefore to reduce and understand these accidents and, as a result, improve road safety, an analysis will be carried out on modern and old accident reconstruction methods and how they can be improved. With the new 2022 European Union regulation coming in, which enforces the use of Event Data Recorders (EDR) on newly made vehicles, suddenly there’s a system that can record vehicle dynamic data and driver inputs, in case of an accident. This project’s objective is to analyze this data in an accident context and simplify the reconstruction process. This project aims for a seamless interpretation of the accident scene and vehicle dynamics to better understand the data in the scene’s context. Some methodologies and tools used for the reconstruction of the accident scene will be studied, culminating in a system that digitizes the scene for later use in computer software. The dynamic data from the accident can be divided into three phases: pre-crash, impact, and post-crash. Each phase requires a different approach which depends on the type of data to obtain the trajectory of the vehicle throughout the phases

Discrete element model for general polyhedra

We present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast. © 2021, The Author(s)