Showing papers by "Michael Ortiz published in 2001"
TL;DR: In this article, the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction is investigated.
Abstract: We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.
417 citations
TL;DR: A streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al is presented and the effect of the summation rules on accuracy, rate of convergence and refinement tolerance are analyzed.
Abstract: The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. (Philos. Mag. A 73 (1996) 1529; Langmuir 12 (1996) 4529) and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of the refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.
404 citations
TL;DR: In this article, the subdivision shell elements of Cirak et al. were extended to the finite-deformation range, allowing for finite membrane and thickness stretching, as well as for large deflections and bending strains.
Abstract: We have extended the subdivision shell elements of Cirak et al. [18] to the finite-deformation range. The assumed finite-deformation kinematics allows for finite membrane and thickness stretching, as well as for large deflections and bending strains. The interpolation of the undeformed and deformed surfaces of the shell is accomplished through the use of subdivision surfaces. The resulting ‘subdivision elements’ are strictly C1-conforming, contain three nodes and one single quadrature point per element, and carry displacements at the nodes only. The versatility and good performance of the subdivision elements is demonstrated with the aid of a number of test cases, including the stretching of a tension strip; the inflation of a spherical shell under internal pressure; the bending and inflation of a circular plate under the action of uniform pressure; and the inflation of square and circular airbags. In particular, the airbag solutions, while exhibiting intricate folding patterns, appear to converge in certain salient features of the solution, which attests to the robustness of the method.
268 citations
TL;DR: In this article, a cohesive formulation of fracture is taken as a basis for the simulation of processes of combined tension-shear damage and mixed-mode fracture in specimens subjected to dynamic loading, and the model accurately captures the experimentally observed fracture patterns and displacement fields, as well as crack paths and cracktip velocities, as a function of pre-crack geometry and loading conditions.
Abstract: A cohesive formulation of fracture is taken as a basis for the simulation of processes of combined tension-shear damage and mixed-mode fracture in specimens subjected to dynamic loading. Our three-dimensional finite-element calculations account explicitly for crack nucleation, microcracking, the development of macroscopic cracks and inertia. In particular, a tension-shear damage coupling arises as a direct consequence of slanted microcrack formation in the process zone. We validate the model against the three-point-bend concrete beam experiments of Guo et al. (International Journal of Solids and Structures 1995; 32(17/18):2951–2607), John (PhD Thesis, Northwestern University, 1988), and John and Shah (Journal of Structural Engineering 1990; 116(3):585–602) in which a pre-crack is shifted from the central cross-section, leading to asymmetric loading conditions and the development of a mixed-mode process zone. The model accurately captures the experimentally observed fracture patterns and displacement fields, as well as crack paths and crack-tip velocities, as a function of pre-crack geometry and loading conditions. In particular, it correctly accounts for the competition between crack-growth and nucleation mechanisms.
223 citations
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TL;DR: The data structures and methods presented here are straightforward to implement, and enable the efficient tracking of complex fracture and fragmentation processes, and are demonstrated with the aid of two examples of application to dynamic fracture.
Abstract: We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior faces in the triangulation are perfectly coherent, i.e., conforming in the usual finite element sense. Cohesive elements are inserted adaptively at interior faces when the effective traction acting on those face reaches the cohesive strength of the material. The insertion of cohesive elements changes the geometry of the boundary and, frequently, the topology of the model as well. The data structures and methods presented here are straightforward to implement and enable the efficient tracking of complex fracture and fragmentation processes. The efficiency and versatility of the approach is demonstrated with the aid of two examples of application to dynamic fracture.
181 citations
TL;DR: The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of linear ODEs.
Abstract: We describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the Taylor expansion and the spectral representation. We also provide guidelines for switching between those representations on the basis of the size of the argument. The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations. This representation does not require the use of perturbation formulae for eigenvalues and eigenvectors. Our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument.
107 citations
TL;DR: In this paper, a finite-element model of dry sliding wear in metals is presented, which is formulated within a Lagrangian framework capable of accounting for large plastic deformations and history-dependent material behavior.
Abstract: This paper is concerned with the calibration and validation of a finite‐element model of dry sliding wear in metals. The model is formulated within a Lagrangian framework capable of accounting for large plastic deformations and history‐dependent material behavior. We resort to continuous adaptive meshing as a means of eliminating deformation‐induced element distortion, and of resolving fine features of the wear process such as contact boundary layers. Particular attention is devoted to a generalization of Archard’s law in which the hardness of the soft material is allowed to be a function of temperature. This dependence of hardness on temperature provides a means of capturing the observed experimental transition between severe wear rates at low speeds to mild wear rates at high speeds. Other features of the numerical model include: surface evolution due to wear; finite‐deformation J2 thermoplasticity; heat generation and diffusion in the bulk; non‐equilibrium heat‐transfer across the contact interface; and frictional contact. The model is validated against a conventional test configuration consisting of a brass pin rubbing against a rotating steel plate.
86 citations
TL;DR: The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender.
Abstract: The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e.g., the December 1999 issue of MRS Bulletin).
67 citations
TL;DR: In this paper, the authors present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials, including the effect of temperature and strain-rate on the hardening rate.
Abstract: In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.
41 citations
TL;DR: In this article, a two-dimensional axisymmetric computational study of the penetration of a tungsten heavy alloy (WHA) rod into a 6061-T6 aluminum target has been performed using a Lagrangian formulation.
40 citations
TL;DR: In this article, an artificial viscosity scheme tailored to finite deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order is presented.
Abstract: We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected tests, including: a two-dimensional shock tube problem on an ideal gas; a two-dimensional piston problem on tantalum without strength; and a three-dimensional plate impact problem on tantalum with strength. In all cases, the artificial viscosity scheme returns stable and ostensibly oscillation-free solutions on meshes which greatly underresolve the actual shock thickness. The scheme typically spreads the shock over 4 to 6 elements and captures accurately the shock velocities and jump conditions.
TL;DR: An algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets, and uses the results of Rajan which re‐formulate Delaunay triangulation as a linear programming problem.
Abstract: We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set apriori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a constraining facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem.
TL;DR: This paper considers the task of converting a tesselation (triangulation) of the surface of a solid into a BRep, and proposes a robust and efficient set of algorithms for this purpose.
Abstract: Many computational science tools employ finite element meshes as discretizations of the geometrical domains, and automatic mesh generation has become an indispensable part of the discretization process. Boundary representations (BRep) of solids are the means of describing the geometrical model to the mesher, thus enabling the generator to proceed without user intervention. Significant effort has been devoted in the past to BRep construction in the frame-work of solid modelling systems. In this paper we consider the task of converting a tesselation (triangulation) of the surface of a solid into a BRep, and propose a robust and efficient set of algorithms for this purpose. Applications include, among others, remeshing of finite element discretizations during simulations involving not only geometric distortion but also changes in topology (coalescence and fragmentation of solids, flow, and so on).
TL;DR: In this article, the authors present a streamlined and fully three-dimensional version of the quasicontinuum theory of Tadmor et al. and analyze its accuracy and convergence characteristics.
Abstract: The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of the refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.
TL;DR: In this paper, the macroscopic cohesive laws based on energy relaxation and the renormalization group were analyzed for coarse-graining interplanar potentials and two approaches for coarsegraining potentials were presented.
Abstract: We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large---but finite---number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.
01 Jan 2001
TL;DR: In this article, the authors apply cohesive theories of fracture (interface laws), now widely accepted and validated in isotropic materials, to anisotropic material, and consider transversely isotropically fiber-reinforced polymeric matrix composites (graphite-epoxy).
Abstract: Some theoretical and practical aspects of finite element modelling of dynamic fracture in composites are discussed. Our concerns are devoted to composites characterized by material symmetries, showing a typical orthotropic or transversely isotropic structure. Our aim is to apply cohesive theories of fracture (interface laws), now widely accepted and validated in isotropic materials, to anisotropic material. Specifically, we consider transversely isotropic fibre-reinforced polymeric matrix composites (graphite-epoxy). Recent research programs demonstrated the existence of a strong relationship between the fracture toughness and the fibre orientation. A cohesive law can easily be modified in order to account for such dependence. In the same way, self-adaptive algorithms that permit the explicit simulation of dynamic fracture processes (by performing topological changes of the finite element mesh) can be easily modified to include this relationship.
01 Jan 2001
TL;DR: In this article, a model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced, which accounts for the number and arrangement of dislocation lines over a slip plane.
Abstract: A model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced. The theory accounts for: and arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and applied resolved shear stress field; and the dissipative in teractions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics are modeled with Metropolis Monte Carlo simulations and a mean field approximation. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication under monotonic loading and hysteresis loops under under cyclic loading. The flow stress was found to be dependent on the temperature and on the strain rate only at finite temperature.
TL;DR: In this article, the authors present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials, including the effect of temperature and strain-rate on the hardening rate.
Abstract: In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.
TL;DR: In this article, a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals was developed to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases.
Abstract: The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.