Showing papers by "Michael Ortiz published in 2004"
TL;DR: In this paper, a design and method for the fabrication of microfluidic valves using multilayer soft lithography is presented, which can be used to fabricate active functions, such as pumps and mixers in integrated microfluidity chips.
Abstract: Using basic physical arguments, we present a design and method for the fabrication of microfluidic valves using multilayer soft lithography. These on-off valves have extremely low actuation pressures and can be used to fabricate active functions, such as pumps and mixers in integrated microfluidic chips. We characterized the performance of the valves by measuring both the actuation pressure and flow resistance over a wide range of design parameters, and compared them to both finite element simulations and alternative valve geometries.
294 citations
TL;DR: In this paper, the authors review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest, and present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs.
Abstract: The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs. In these tests, AVIs are found to result in substantial speed-ups, at equal accuracy, relative to explicit Newmark. A mathematical proof of convergence of the AVIs is also presented in this paper. Finally, we develop the subject of horizontal variations and configurational forces in discrete dynamics. This theory leads to exact path-independent characterizations of the configurational forces acting on discrete systems. Notable examples are the configurational forces acting on material nodes in a finite element discretisation; and the J-integral at the tip of a crack in a finite element mesh.
281 citations
TL;DR: In this paper, a model of hydrogen embrittlement based on a cohesive law dependent on impurity coverage that is calculated from first principles was presented. But the model was not applied to the case of hydrogen-assisted cracking, where the authors considered the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment and temperature.
Abstract: We present a model of hydrogen embrittlement based upon: (i) a cohesive law dependent on impurity coverage that is calculated from first principles; (ii) a stress-assisted diffusion equation with appropriate boundary conditions accounting for the environment; (iii) a static continuum analysis of crack growth including plasticity; and (iv) the Langmuir relation determining the impurity coverage from its bulk concentration. We consider the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment, and temperature. The calculations reproduce the following experimental trends: (i) time to initiation and its dependence on yield strength and stress intensity factor; (ii) finite crack jump at initiation; (iii) intermittent crack growth; (iv) stages I and II of crack growth and their dependence on yield strength; (v) the effect of the environmental impurity concentration on the threshold stress intensity factor; and (vi) the effect of temperature on stage II crack velocity in the low-temperature range. In addition, the theoretically and experimentally observed intermittent cracking may be understood as being due to a time lag in the diffusion of hydrogen towards the cohesive zone, since a buildup of hydrogen is necessary in order for the crack to advance. The predictions of the model are in good quantitative agreement with available measurements, suggesting that hydrogen-induced degradation of cohesion is a likely mechanism for hydrogen-assisted cracking.
244 citations
TL;DR: A multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp phases of Fe and a construction of kinematically compatible and equilibrated mixed phases suggests that shear stresses have a significant influence on the bCC<-->hcp transformation.
Abstract: Iron shows a pressure-induced martensitic phase transformation from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase at � 13 GPa. The exact transformation pressure (TP) and pathway are not known. Here we present a multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp phases of Fe and a construction of kinematically compatible and equilibrated mixed phases. This model suggests that shear stresses have a significant influence on the bcc $ hcp transformation. In particular, the presence of modest shear accounts for the scatter in measured TPs. The formation of mixed phases also provides an explanation for the observed hysteresis in TP.
118 citations
TL;DR: This Letter is concerned with the determination of the transition paths attendant to nanovoid growth in aluminum under hydrostatic tension, and reveals several stages of pressure buildup separated by yield points.
Abstract: This Letter is concerned with the determination of the transition paths attendant to nanovoid growth in aluminum under hydrostatic tension. The analysis is, therefore, based on energy minimization at 0 K. Aluminum is modeled by the Ercolessi-Adams embedded-atom method, and spurious boundary artifacts are mitigated by the use of the quasicontinuum method. Our analysis reveals several stages of pressure buildup separated by yield points. The first yield point corresponds to the formation of highly stable tetrahedral dislocation junctions around the surfaces of the void. The second yield point is caused by the dissolution of the tetrahedral structures and the emission of conventional 1/2 [111] and anomalous 1/2 [001] dislocation loops.
104 citations
TL;DR: In this paper, a discontinuous Galerkin method for linear elasticity is proposed, which derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation.
Abstract: We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.
97 citations
Book Chapter•
01 Jan 2004TL;DR: In this paper, the authors present a survey of recent advances in variational integration for both finite dimensional mechanical systems as well as continuum and discrete mechanical systems, including applications to dissipative systems, collisions, spacetime integration algorithms, and asynchronous variational integrators.
Abstract: The purpose of this paper is to survey some recent advances in variational
integrators for both finite dimensional mechanical systems as well as continuum
mechanics. These advances include the general development of discrete
mechanics, applications to dissipative systems, collisions, spacetime integration algorithms,
AVI’s (Asynchronous Variational Integrators), as well as reduction for
discrete mechanical systems. To keep the article within the set limits, we will only
treat each topic briefly and will not attempt to develop any particular topic in
any depth. We hope, nonetheless, that this paper serves as a useful guide to the
literature as well as to future directions and open problems in the subject.
93 citations
TL;DR: In this article, a variational r-adaption method for finite-deformation elastostatic problems is proposed, where the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system.
Abstract: This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions.
85 citations
TL;DR: In this paper, the density functional theory (DFT) local quasicontinuum method is used to predict the onset of dislocation nucleation in both single crystals and those with inclusions.
Abstract: We introduce the density functional theory (DFT) local quasicontinuum method: a first principles multiscale material model that embeds DFT unit cells at the subgrid level of a finite element computation. The method can predict the onset of dislocation nucleation in both single crystals and those with inclusions, although extension to lattice defects awaits new methods. We show that the use of DFT versus embedded-atom method empirical potentials results in different predictions of dislocation nucleation in nanoindented face-centered-cubic aluminum.
79 citations
TL;DR: In this article, a universal relation for crack surface cohesion including surface relaxation is presented, where the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energydisplacement curves collapse onto a single universal curve.
Abstract: We present a universal relation for crack surface cohesion including surface relaxation. Specifically, we analyze how N atomic planes respond to an opening displacement at its boundary, producing structurally relaxed surfaces. Via density-functional theory, we verify universality for metals ~Al!, ceramics (a-Al2O3), and semiconductors ~Si!. When the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energydisplacement curves collapse onto a single universal curve.
66 citations
TL;DR: A simple class of Lagrangians and variational integrators derived by time discretization of the action functional is established and the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm is established.
Abstract: For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we establish (i) the Γ-convergence of the discrete action sum to the action functional; (ii) the relation between Γ-convergence and weak* convergence of the discrete trajectories in {itW{su1,℞}}({ofR};{ofr{sun}; and (iii) the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm.
TL;DR: In this article, a finite deformation constitutive theory for non-cohesive granular media is presented, which falls in the family of the so-called Cam-clay theories.
TL;DR: In this article, a phase-field model of slip over a slip plane is described by means of multiple integer-valued phase fields, and all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field.
Abstract: In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289–98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957–635) to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers.
TL;DR: In this article, a theory of single-crystal plasticity with microstructure was applied to the simulation of the ECAE process and the specific microstructures considered in the simulations are of the sequential lamination type.
21 Jul 2004
TL;DR: In this paper, a cohesive fatigue-crack nucleation and growth model for ferroelectric materials under electro-mechanical loading is presented, which couples the mechanical and electrical fields.
Abstract: A cohesive fatigue-crack nucleation and growth model for ferroelectric materials under electro-mechanical loading is presented. The central feature of the model is a hysteretic cohesive law which couples the mechanical and electrical fields. This law can be used in conjunction with general constitutive relations of bulk behavior, possibly including domain switching, in order to predict fatigue crack growth under arbitrary loading conditions. Another appealing feature of the model is its ability to predict fatigue-crack nucleation. Despite the scarcity and uncertainty of the experimental data, comparisons with PZT fatigue-life data are encouraging.
TL;DR: In this article, a model for the mechanical response of the soft tissue to high speed loading regime is presented, which combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles.
Abstract: In a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime.
The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small-strain to the finite deformation range. In that way the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner.
By numerical experiments we study the shock-wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)