arXiv subjects

M. Ortiz

Publications and source records attributed to M. Ortiz.

At least 19 recordsLinked to original sources

arXiv2025

Multiscale analysis and lifetime prediction of adhesive lap joints in contact with aggressive environments

We formulate a multiscale model of adhesive layers undergoing impurity-dependent cohesive fracture. The model contemplates three scales: i) at the atomic scale, fracture is controlled by interatomic separation and the thermodynamics of separation depends on temperature and impurity concentration; ii) the mesoscale is characterized by the collective response of a large number of interatomic planes across the adhesive layer, resulting in a thickness-dependence strength; in addition, impurities are uptaken from the environment and diffuse through the adhesive layer; and iii) at the macroscale, we focus on lap joints under the action of static loads and aggressive environments. Within this scenario, we obtain closed form analytical solutions for: the dependence of the adhesive layer strength on thickness; the length of the edge cracks, if any, as a function of time; the lifetime of the joint; and the dependence of the strength of the joint on time of preexposure to the environment. Overall, the theory is found to capture well the experimentally observed trends. Finally, we discuss how the model can be characterized on the basis of atomistic calculations, which opens the way for the systematic exploration of new material specifications.

cond-mat.soft↗

arXiv2024

Homogenized Models of Mechanical Metamaterials

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the computational modeling of metastructures at macroscopic scales. In the present work, we assess the continuum limit of mechanical metamaterials via homogenized models derived rigorously from variational methods. It is shown through multiple examples that micropolar-type effective energies, derived naturally from analysis, properly capture the kinematics of discrete lattices in two and three dimensions. Moreover, the convergence of the discrete energy to the continuum limit is shown numerically. We provide open-source computational implementations for all examples, including both discrete and homogenized models.

cond-mat.mtrl-sci↗

arXiv2024

Thermalized and mixed meanfield ADP potentials for magnesium hydrides

We develop meanfield approximation and numerical quadrature schemes for the evaluation of Angular-Dependent interatomic Potentials (ADPs) for magnesium and magnesium hydrides at finite temperature (thermalization) and arbitrary atomic molar fractions (mixing) within a non-equilibrium statistical mechanical framework and derive local equilibrium relations. We numerically verify and experimentally validate the accuracy and fidelity of the resulting thermalized/mixed ADPs (TADPs) by means of selected numerical tests including free entropy, heat capacity, thermal expansion, molar volumes, equation of state and elastic constants. We show that the local equilibrium properties predicted by TADPs agree closely with those computed directly from ADP by means of Molecular Dynamics (MD).

physics.comp-ph↗

arXiv2024

Fracture and size effect in mechanical metamaterials

We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized explicitly in terms of the solution of the zeroth-order continuum problem by the method of {\Gamma}-expansion. We present explicit expressions of the second-order correction for octet frames. As an application, we evaluate the compliance of double-cantilever octet specimens to second order and use the result to elucidate the dependence of the apparent toughness of the specimen on cell size. The analysis predicts the discreteness of the metamaterial lattice to effectively shield the crack-tip, a mechanism that we term lattice shielding. The theory specifically predicts anti-shielding, i. e., coarser is weaker, in agreement with recent experimental observations.

physics.class-ph↗

arXiv2024

A discrete dislocation analysis of size-dependent plasticity in torsion

A method for solving three dimensional discrete dislocation plasticity boundary-value problems using a monopole representation of the dislocations is presented. At each time step, the displacement, strain and stress fields in a finite body are obtained by superposition of infinite body dislocation fields and an image field that enforces the boundary conditions. The three dimensional infinite body fields are obtained by representing dislocations as being comprised of points, termed monopoles, that carry dislocation line and Burgers vector information. The image fields are obtained from a three dimensional linear elastic finite element calculation. The implementation of the coupling of the monopole representation with the finite element method, including the interaction of curved dislocations with free surfaces, is presented in some detail because it differs significantly from an implementation with a line based dislocation representation. Numerical convergence and the modeling of dislocation loop nucleation for large scale computations are investigated. The monopole discrete dislocation plasticity framework is used to investigate the effect of size and initial dislocation density on the torsion of wires with diameters varying over three orders of magnitude. Depending on the initial dislocation source density and the wire diameter, three regimes of torsion-twist response are obtained: (i) for wires with a sufficiently small diameter, plastic deformation is nucleation controlled and is strongly size dependent; (ii) for wires with larger diameters dislocation plasticity is dislocation interaction controlled, with the emergence of geometrically necessary dislocations and dislocation pile-ups playing a key role, and is strongly size dependent; and (iii) for wires with sufficiently large diameters plastic deformation becomes less heterogeneous and the dependence on size is greatly diminished.

cs.CE↗

arXiv2024

Homogenization and continuum limit of mechanical metamaterials

When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional homogenization theory on account of the flexural, or bending, response of their members, including torsion. We show that homogenization theory, based on calculus of variations and notions of Gamma-convergence, can be extended to account for bending. The resulting homogenized metamaterials exhibit intrinsic generalized elasticity in the continuum limit. We illustrate these properties in specific examples including two-dimensional honeycomb and three-dimensional octet-truss metamaterials.

math.AP↗

arXiv2023

Modeling hard-soft block copolymers as a liquid crystalline polymer

We report a new computational approach to model hard-soft block copolymers like polyurea as a liquid crystalline polymer to understand their microstructural evolution due to mechanical loading. The resulting microstructure closely resembles the microstructure observed in polyurea. The stress-strain relations in uniaxial compression and tension loading obtained from the model are also in close quantitative agreement with the experimental data for polyurea. We use the model to elucidate the evolution of the hard and the soft domains during loading, which is consistent with the experimental measurements characterizing microstructural evolution in polyurea.

cond-mat.soft↗

arXiv2022

Interatomic-Potential-Free, Data-Driven Molecular Dynamics

We present a Data-Driven (DD) paradigm that enables molecular dynamics calculations to be performed directly from sampled force-field data such as obtained, e.g., from ab initio calculations, thereby eschewing the conventional step of modeling the data by empirical interatomic potentials entirely. The data required by the DD solvers consists of local atomic configurations and corresponding atomic forces and is, therefore, fundamental, i.e., it is not beholden to any particular model. The resulting DD solvers, including a fully explicit DD-Verlet algorithm, are provably convergent and exhibit robust convergence with respect to the data in selected test cases. We present an example of application to C60 buckminsterfullerenes that showcases the feasibility, range and scope of the DD molecular dynamics paradigm.

physics.chem-ph↗

arXiv2019

A Dynamical Model of Oncotripsy by Mechanical Cell Fatigue: Selective Cancer Cell Ablation by Low-Intensity Pulsed Ultrasound (LIPUS)

The method of oncotripsy, first proposed in [S. Heyden and M. Ortiz (2016). Oncotripsy: Targeting cancer cells selectively via resonant harmonic excitation. Journal of the Mechanics and Physics of Solids, 92:164-175], exploits aberrations in the material properties and morphology of cancerous cells in order to ablate them selectively by means of tuned low-intensity pulsed ultrasound (LIPUS). We propose a dynamical model of oncotripsy that follows as an application of cell dynamics, statistical mechanical theory of network elasticity and 'birth-death' kinetics to describe processes of damage and repair of the cytoskeleton. We also develop a reduced dynamical model that approximates the three-dimensional dynamics of the cell and facilitates parametric studies, including sensitivity analysis and process optimization. We show that the dynamical model predicts---and provides a conceptual basis for understanding---the oncotripsy effect and other trends in the data of [D. R. Mittelstein, J. Ye, E. F. Schibber, A. Roychoudhury, L. T. Martinez, M. H. Fekrazad, M. Ortiz, P. P. Lee, M. G. Shapiro, M. Gharib (2019). Selective Ablation of Cancer Cells with Low Intensity Pulsed Ultrasound. BioRxiv] for cells in suspension, including the dependence of cell-death curves on cell and process parameters.

physics.bio-ph↗

arXiv2018

A Line-free Method of Monopoles for 3D Dislocation Dynamics

We develop an approximation scheme for three-dimensional dislocation dynamics in which the dislocation line density is concentrated at points, or monopoles. Every monopole carries a Burgers vector and an element of line. The monopoles move according to mobility kinetics driven by elastic and applied forces. The divergence constraint, expressing the requirement that the monopoles approximate a boundary, is enforced weakly. The fundamental difference with traditional approximation schemes based on segments is that in the present approach an explicit linear connectivity, or 'sequence', between the monopoles need not be defined. Instead, the monopoles move as an unstructured point set subject to the weak divergence constraint. In this sense, the new paradigm is 'line-free', i. e., it sidesteps the need to track dislocation lines. This attribute offers significant computational advantages in terms of simplicity, robustness and efficiency, as demonstrated by means of selected numerical examples.

physics.comp-ph↗

arXiv2017

The Anomalous Yield Behavior of Fused Silica Glass

We develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. The MD data also reveals an evolution towards a critical state of constant volume under pressure-shear deformation. The trend towards constant volume is from above, when the glass is overconsolidated, or from below, when it is underconsolidated. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant volume states denotes the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems.

cond-mat.soft↗

arXiv2016

Efficient fluorescence quenching in electrochemically exfoliated graphene decorated with gold nanoparticles

High surface area graphene sheets were obtained by electrochemical exfoliation of graphite in an acid media under constant potential conditions. Filtration and centrifugation processes played an important role in order to obtain stable dispersions in water. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) imaging revealed highly exfoliated crystalline samples of ~5(\mum). Raman, FT-IR and XPS spectroscopy further confirmed the high quality of the exfoliated material. The electrochemically exfoliated graphene (EEG) was decorated with gold nanoparticles (AuNP) using sodium cholate (SC) as a buffer layer. This approach allowed for a non-covalent functionalization without altering the desirable electronic properties of the EEG. The AuNP-EEG samples were characterized with various techniques including absorbance and fluorescence spectroscopy. These samples displayed a fluorescence signal using an excitation wavelength of 290nm. The calculated quantum yield (?) for these samples was 40.04%, a high efficiency compared to previous studies using solution processable graphene.

cond-mat.mtrl-sci↗

arXiv2012

Thermalization of rate-independent processes by entropic regularization

We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to "thermalize" the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of the unperturbed process. It is shown that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are those of a non-linear gradient descent in the original energetic potential with respect to a different and non-trivial effective dissipation potential.

math.PR↗

arXiv2012

Optimal uncertainty quantification for legacy data observations of Lipschitz functions

We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.

math.PR↗

arXiv2012

The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact.

cs.DM↗

arXiv2008

The Air-Fluorescence Yield

Detection of the air-fluorescence radiation induced by the charged particles of extensive air showers is a well-established technique for the study of ultra-high energy cosmic rays. Fluorescence telescopes provide a nearly calorimetric measure of the primary energy. Presently the main source of systematic uncertainties comes from our limited accuracy in the fluorescence yield, that is, the number of fluorescence photons emitted per unit of energy deposited in the atmosphere by the shower particles. In this paper the current status of our knowledge on the fluorescence yield both experimental an theoretical will be discussed.

astro-ph↗

arXiv2006

The yield of air fluorescence induced by electrons

The fluorescence yield for dry air and pure nitrogen excited by electrons is calculated using a combination of well-established molecular properties and experimental data of the involved cross sections. Particular attention has been paid to the role of secondary electrons from ionization processes. At high pressure and high energy, observed fluorescence turns out to be proportional to the ionization cross section which follows the Born-Bethe law. Predictions on fluorescence yields in a very wide interval of electron energies (eV - GeV) and pressures (1 and 1013 hPa) as expected from laboratory measurements are presented. Experimental results at energies over 1 MeV are in very good agreement with our calculations for pure nitrogen while discrepancies of about 20% are found for dry air, very likely associated to uncertainties in the available data on quenching cross sections. The relationship between fluorescence emission, stopping power and deposited energy is discussed.

astro-ph↗

arXiv2002

A Constrained Sequential-Lamination Algorithm for the Simulation of Sub-Grid Microstructure in Martensitic Materials

We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the microstructure during a deformation process is required to satisfy a continuity constraint, in the sense that the new microstructure should be reachable from the preceding one by a combination of branching and pruning operations. All microstructures generated by the algorithm are in static and configurational equilibrium. Owing to the continuity constrained imposed upon the microstructural evolution, the predicted material behavior may be path-dependent and exhibit hysteresis. In cases in which there is a strict separation of micro and macrostructural lengthscales, the proposed relaxation algorithm may effectively be integrated into macroscopic finite-element calculations at the subgrid level. We demonstrate this aspect of the algorithm by means of a numerical example concerned with the indentation of an Cu-Al-Ni shape memory alloy by a spherical indenter.

cond-mat.mtrl-sci↗