Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5-100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.Comment: 28 page

Bridging spatiotemporal scales in biomechanical models for living tissues : from the contracting Esophagus to cardiac growth

Appropriate functioning of our body is determined by the mechanical behavior of our organs. An improved understanding of the biomechanical functioning of the soft tissues making up these organs is therefore crucial for the choice for, and development of, efficient clinical treatment strategies focused on patient-specific pathophysiology. This doctoral dissertation describes the passive and active biomechanical behavior of gastrointestinal and cardiovascular tissue, both in the short and long term, through computer models that bridge the cell, tissue and organ scale. Using histological characterization, mechanical testing and medical imaging techniques, virtual esophagus and heart models are developed that simulate the patient-specific biomechanical organ behavior as accurately as possible. In addition to the diagnostic value of these models, the developed modeling technology also allows us to predict the acute and chronic effect of various treatment techniques, through e.g. drugs, surgery and/or medical equipment. Consequently, this dissertation offers insights that will have an unmistakable impact on the personalized medicine of the future.Het correct functioneren van ons lichaam wordt bepaald door het mechanisch gedrag van onze organen. Een verbeterd inzicht in het biomechanisch functioneren van deze zachte weefsels is daarom van cruciale waarde voor de keuze voor, en ontwikkeling van, efficiënte klinische behandelingsstrategieën gefocust op de patiënt-specifieke pathofysiologie. Deze doctoraatsthesis brengt het passieve en actieve biomechanisch gedrag van gastro-intestinaal en cardiovasculair weefsel, zowel op korte als lange termijn, in kaart via computermodellen die een brug vormen tussen cel-, weefsel- en orgaanniveau. Aan de hand van histologische karakterisering, mechanische testen en medische beeldvormingstechnieken worden virtuele slokdarm- en hartmodellen ontwikkeld die het patiënt-specifieke orgaangedrag zo accuraat mogelijk simuleren. Naast de diagnostische waarde van deze modellen, laat de ontwikkelde modelleringstechnologie ook toe om het effect van verschillende behandelingstechnieken, via medicatie, chirurgie en/of medische apparatuur bijvoorbeeld, acuut en chronisch te voorspellen. Bijgevolg biedt deze doctoraatsthesis inzichten die een onmiskenbare impact zullen hebben op de gepersonaliseerde geneeskunde van de toekomst

Experimental and Theoretical Biomechanical Analyses of the Second Stage of Labor.

Injuries during vaginal birth affect 10 to 15% of first-time mothers. The goal of this thesis was to use biomechanics to help elucidate the underlying mechanisms. Biaxial ramp-hold test results from the rodent vagina showed that term pregnancy decreased both tissue tensile stiffness and the long-term residual stress, and increased tensile strain at failure, by nearly two-fold (Chapter 2). Similar trends were observed the levator ani muscle of squirrel monkeys (Chapter 3). An anisotropic visco-hyperelastic constitutive equation was used to fit tensile tissue test data from the non-pregnant human levator ani muscle and perineal body (Chapter 4) for the purposes of finite element (FE) modeling. A 3-D axisymmetric FE model of the energetics of the second stage of labor, using a clinically recorded intrauterine pressure profile, showed that the duration of the second stage of labor is sensitive to the magnitude, number of uterine contractions, timing with respect to the peak uterine contraction, and intra-push interval. The `Peak’ pushing style was the most efficient pushing strategy, the `Triple’ style the least efficient (Chapter 5). The duration of labor was most sensitive to pelvic floor tissue stiffness, followed by long-term relaxation behavior (Chapter 6). The same simplified 3-D axisymmetric FE model was used to explore the effect of operator behavior on the pelvic floor mechanics during vacuum extraction delivery. Increasing the continuous vacuum extraction force by 25% increased muscle injury risk by 112%. Intermittent extraction forces kept the risk of maternal injury lower (Chapter 7). A motor unit-based striated muscle fatigue model was integrated into the Chapter 6 energetics model. Increasing volitional pushing magnitude did not necessarily reduce the duration of labor, due earlier fatigue onset (Chapter 8). An anatomically realistic 3-D FE model labor predicted a peak stretch of 5.04 near the origin of the pubovisceral muscle, and a value of 4.15 in the perineal body. Decreasing perineal body stiffness lowered the peak stretch and stress near pubovisceral muscle origin (Chapter 9).Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/76013/1/djing_1.pd

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics

Mathematical foundations of elasticity

[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute

Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling

There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed. Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus

Finite volume modelling of low speed structural impact problems

Two investigations are described in this thesis on the common theme of applying finite volume methods to simulate structural impact problems. The first investigation is the application of the Eulerian Finite Volume Method (EFVM) to simulate the low-speed impact of ductile materials. Simulation results are validated against experiment showing that it is possible to accurately predict crater deformation profiles over the low speed speed impact regime for different projectile and substrate materials. We demonstrate how the rate dependent Johnson-Cook plasticity model is crucial to ensure correspondence to experiment. The second investigation is concerned with the application of EFVM to simulate impact damage to thin polymeric coatings applied to the surface of metals. The aim of this work is to demonstrate how new simulation methods can help understand coating damage due stone impact. We simulate the debonding phenomenon of single layer coatings under impact by setting boundary conditions at the plate and paint interface. We show how EFVM can capture two limits of interface behaviour, sliding and separation 'slip' at one extreme and zero sliding 'welded' at the other. Results compare well to previously published experimental and simulation work, and our own finite element simulations in Abaqus. We also demonstrate how EFVM brings greater robustness and stability compared to FEM when modelling adhesive failure and higher energy impact penetration

Numerical Constitutive Modelling for Continuum Mechanics Simulation

Three investigations are described in this dissertation, on the common theme of obtaining constitutive laws describing bulk properties of crystalline materials. We use ‘first-principles’ techniques where possible, an approach offering results which are predictive, with applicability to a wide class of materials, and with a systematic way to apply the techniques to any particular material of interest. We apply these techniques to silicon. The first investigation aims at developing an equation of state model for temperature dependent, anisotropic non-linear hyperelasticity. A method is presented for finding deformed states of a material on the same isentrope as a given starting configuration. The energies and stresses of a number of elastic deformations are sampled from dft molecular dynamics using this method, over a given range of the seven-dimensional space of deformation and potential temperature. The complete energy surface within this range can then be reliably reconstructed using the technique of Gaussian process regression. This is a machine learning technique that has particular merit here due to its ability to reconstruct a smooth surface without over-fitting. An equation of state model is then constructed for dft silicon, and demonstrated within a finite-volume continuum elasticity simulation for several problems of interest involving shock waves. The second investigation is concerned with the computation of properties of shock waves. We describe a simple annealing procedure to obtain the Hugoniot locus (states accessible by a shock wave) for a given material in a computationally efficient manner, particularly suited to first-principles calculations. We apply this method to determine the Hugoniot locus in bulk silicon from ab initio molecular dynamics with forces from density-functional theory, up to 70 GPa. In addition, we perform direct non-equilibrium molecular dynamics simulations of shock waves using empirical interatomic potentials and compare with our indirect method. We also present a direct ab initio molecular dynamics simulation of an elastic shock-wave in silicon, the first performed, to our knowledge. The third and final investigation is into the computation of thermal conductivity from atomistic simulations. We produce a number of model interatomic potentials for silicon, using the non-parametric, Bayesian approach of Gaussian Approximation Potentials, which are improved systematically through a database of training configurations. We compute the thermal conductivity from these at the level of the phonon-Boltzmann transport equation. The best of these potentials reproduces the dft value of phonon-Boltzmann conductivity to within a few percent, which is itself in good agreement with experiment. We consider several issues relating to computing thermal conductivity from molecular dynamics simulations.Orica Lt