Physically based multiscale-viscoplastic model for metals and steel alloys: theory and computation

The main requirement of large deformation problems such as high-speed machining, impact, and various primarily metal forming, is to develop constitutive relations which are widely applicable and capable of accounting for complex paths of deformation. Achieving such desirable goals for material like metals and steel alloys involves a comprehensive study of their microstructures and experimental observations under different loading conditions. In general, metal structures display a strong rate- and temperature-dependence when deformed non-uniformly into the inelastic range. This effect has important implications for an increasing number of applications in structural and engineering mechanics. The mechanical behavior of these applications cannot be characterized by classical (rate-independent) continuum theories because they incorporate no ‘material length scales’. It is therefore necessary to develop a rate-dependent (viscoplasticity) continuum theory bridging the gap between the classical continuum theories and the microstructure simulations. Physically based vicoplasticity models for different types of metals (body centered cubic, face centered cubic and hexagonal close-packed) and steel alloys are derived in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the rate-dependent behavior. The concept of thermal activation energy, dislocations interactions mechanisms and the role of dislocations dynamics in crystals are used in the derivation process taking into consideration the contribution of the plastic strain evolution of dislocation density to the flow stress of polycrystalline metals. Material length scales are implicitly introduced into the governing equations through material rate-dependency (viscosity). The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh due to the successful incorporation of the material length scale in the model formulations. It is shown that the model predicted results compare very well with different experimental data over a wide range of temperatures (77K°-1000K°) and strain rates (10-3-104s-1). It is also concluded from this dissertation that the width of localization zone (shear band) exhibits tremendous changes with different initial temperatures (i.e., different initial viscosities and accordingly different length scales)

Finite Element Based Tracking of Deforming Surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.Comment: additional experiment

A novel rate-dependent cohesive-zone model combining damage and visco-elasticity

This is the author’s post-print version of a work that was accepted for publication in Computers & Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.The published paper is available from the link below.This paper presents a novel rate-dependent cohesive-zone model combining damage and visco-elasticity and based on two fundamental assumptions. Firstly we postulate the existence of an intrinsic (i.e. rate-independent) fracture energy. Secondly, within a thermodynamically consistent damage-mechanics framework we assume that the evolution of the damage variable is related to the current free energy and to the intrinsic fracture energy. The underlying idea is that the energy of the bonds at the micro-level is rate-independent and that the rate-dependence of the overall dissipated energy during crack propagation is a natural by-product of the visco-elastic dissipation lumped on the zero-thickness interface. Quite good agreement within an expected range of loading rates was obtained between numerical and experimental results for a DCB specimen with steel arms bonded through a rubber interface. This is despite the fact that for this application the model has been kept as simple as possible using a quadratic elastic energy and linear visco-elasticity with one relaxation time only. Therefore, the presented results support the fundamental principles behind the proposed approach and indicate that the model has the potential to be refined into a highly accurate tool of analysis based on sound physical arguments.EPSR

Conjugates, Filters and Quantum Mechanics

The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of states). The key assumption is that each system A can be paired with an isomorphic $\textit{conjugate}$ system, $\overline{A}$, by means of a non-signaling bipartite state $\eta_A$ perfectly and uniformly correlating each basic measurement on A with its counterpart on $\overline{A}$. In the case of a quantum-mechanical system associated with a complex Hilbert space $\mathcal H$, the conjugate system is that associated with the conjugate Hilbert space $\overline{\mathcal H}$, and $\eta_A$ corresponds to the standard maximally entangled EPR state on ${\mathcal H} \otimes \overline{\mathcal H}$. A second ingredient is the notion of a $\textit{reversible filter}$, that is, a probabilistically reversible process that independently attenuates the sensitivity of detectors associated with a measurement. In addition to offering more flexibility than most existing reconstructions of finite-dimensional quantum theory, the approach taken here has the advantage of not relying on any form of the "no restriction" hypothesis. That is, it is not assumed that arbitrary effects are physically measurable, nor that arbitrary families of physically measurable effects summing to the unit effect, represent physically accessible observables. An appendix shows how a version of Hardy's "subspace axiom" can replace several assumptions native to this paper, although at the cost of disallowing superselection rules.Comment: 33 pp. Minor corrections throughout; some revision of Appendix

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory

Calipso: Physics-based Image and Video Editing through CAD Model Proxies

We present Calipso, an interactive method for editing images and videos in a physically-coherent manner. Our main idea is to realize physics-based manipulations by running a full physics simulation on proxy geometries given by non-rigidly aligned CAD models. Running these simulations allows us to apply new, unseen forces to move or deform selected objects, change physical parameters such as mass or elasticity, or even add entire new objects that interact with the rest of the underlying scene. In Calipso, the user makes edits directly in 3D; these edits are processed by the simulation and then transfered to the target 2D content using shape-to-image correspondences in a photo-realistic rendering process. To align the CAD models, we introduce an efficient CAD-to-image alignment procedure that jointly minimizes for rigid and non-rigid alignment while preserving the high-level structure of the input shape. Moreover, the user can choose to exploit image flow to estimate scene motion, producing coherent physical behavior with ambient dynamics. We demonstrate Calipso's physics-based editing on a wide range of examples producing myriad physical behavior while preserving geometric and visual consistency.Comment: 11 page

Unsteady wake modelling for tidal current turbines

The authors present a numerical model for three-dimensional unsteady wake calculations for tidal turbines. Since wakes are characterised by the shedding of a vortex sheet from the rotor blades, the model is based on the vorticity transport equations. A vortex sheet may be considered a jump contact discontinuity in tangential velocity with, in inviscid hydrodynamic terms, certain kinematic and dynamic conditions across the sheet. The kinematic condition is that the sheet is a stream surface with zero normal fluid velocity; the dynamic condition is that the pressure is equal on either side of the sheet. The dynamic condition is explicitly satisfied at the trailing edge only, via an approximation of the Kutta condition. The shed vorticity is the span-wise derivative of bound circulation, and the trailed vorticity is the time derivative of bound circulation, and is convected downstream from the rotors using a finite-volume solution of vorticity transport equations thus satisfying the kinematic conditions. Owing to an absence in the literature of pressure data for marine turbines, results from the code are presented for the NREL-UAE Phase IV turbine. Axial flow cases show a close match in pressure coefficients at various spanwise stations; however, yawed flow cases demonstrate the shortcomings of a modelling strategy lacking viscosity

Three dimensional loop quantum gravity: coupling to point particles

We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin foam amplitudes. In addition we provide an explicit expression of the (physical) distance operator between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde

Sequential non-rigid structure from motion using physical priors

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft