Local Continuum Research Articles

One City for All? The Characteristics of Residential Displacement in Southwest Washington, DC

This paper examines two periods of renewal in Washington, DC, USA’s southwest quadrant and their relationship with displacement. The paper situates this discussion within both the local historical continuum and globally-recognized paradigms, such as “the right to the city”. This article primarily serves as an overview of urban planning consequences in Southwest Washington DC based on extant academic literature and policy briefs. Compared with the abrupt physical displacement in the 1950s and 1960s precipitated by a large-scale federally funded urban raze and rebuild project, urban planning in present-day DC includes mechanisms for public engagement and provisions for housing security. However, countervailing economic incentives and rapid demographic changes have introduced anxieties about involuntary mobility that the literature suggests may be born out of forced or responsive displacement. Two potential case studies in the area warrant future study to understand present-day mobilities in the context of the economic and socio-cultural factors shaping the actions of present and prospective residents and decision-makers.

Century-long expansion of hydrating cement counteracting concrete shrinkage due to humidity drop from selfdesiccation or external drying

A physically based model for auotgenous shrinkage and swelling of portland cement paste is necessary for computation of long-time hydgrothermal effects in concrete structures. The goal is to propose such a model. As known since 1887, the volume of cement hydration products is slightly smaller than the original volume of cement and water (chemical shrinkage). Nevertheless, this does not imply that the hydration reaction results in contraction of the concrete and cement paste. According to the authors’ recently proposed paradigm, the opposite is true for the entire lifetime of porous cement paste as a whole. The hydration process causes permanent volume expansion of the porous cement paste as a whole, due to the growth of C–S–H shells around anhydrous cement grains which pushes the neighbors apart, while the volume reduction of hydration products contributes to porosity. Additional expansion can happen due to the growth of ettringite and portlandite crystals. On the material scale, the expansion always dominates over the contraction, i.e., the hydration per se is, in the bulk, always and permanently expansive, while the source of all of the observed shrinkage, both autogenous and drying, is the compressive elastic or viscoelastic strain in the solid skeleton caused by a decrease of chemical potential of pore water, along with the associated decrease in pore relative humidity. As a result, the selfdesiccation, shrinkage and swelling can all be predicted from one and the same unified model, in which, furthermore, the low-density and high-density C–S–H are distinguished. A new thermodynamic formulation of unsaturated poromechanics with capillarity and adsorption is presented. The recently formulated local continuum model for calculating the evolution of hydration degree and a new formulation of nonlinear desorption isotherm are important for realistic and efficient finite element analysis of shrinkage and swelling. Comparisons with the existing relevant experimental evidence validate the proposed model.

Exploring chemical speciation at electrified interfaces using detailed continuum models.

We present a local free-energy functional-based generic continuum model for material interfaces with a specific emphasis on electrified solid/liquid interfaces. The model enables a description of multicomponent phases at interfaces and includes the effects of specific non-electrostatic interactions (specific adsorption), ion size disparity, and the explicit presence of neutral species. In addition to the optimization of electrostatic, non-electrostatic, and steric forces, the model can be easily modified to explore the effects of other channels for equilibration, including local chemical transformations driven by equilibrium constants and electrochemical reactions driven by the electrode potential. In this way, we show that, upon accounting for these effects, local speciation in the vicinity of the interface can be drastically different from what is expected from restricted models and minor species (from the bulk perspective) may become dominant due to the effects of local pH. We evaluate the ionic contribution to the surface tension at the interface and show how this could impact the structure of air/liquid interfaces. On the same footing, an attempt to describe electrochemical metal dissolution is made. The model allows estimates of the mutual population of newly produced ions depending on their charge and size and could be useful for interpretation of electrochemical and spectroscopic measurements if the dissolution involves different metal ions (species). With these advances, the proposed model may be used as an ingredient within a hybrid ab initio-continuum methodology to model biased interfaces.

Two Physical Constraints upon the Motions of Celestial Bodies

There exist two physical constraints upon the motions of celestial systems. Constraint 1 reveals during collapse or explosion motion of celestial bodies that there would be an unattainability upper limit for their compact intensity (total mass M/scale size R), which arises from the Lorentz invariance of the time-like metric in local four-dimensional continuum in Einstein’s theory of special relativity. Constraint 2 points that the average mass density of nucleon would be an unsurpassed upper limit for bulk normal matter in nature, which arises from Heisenberg’s uncertainty principle. A very important effect is that the combination of these two physical constraints would prevent the formation of black holes.

Quality Assessment of Pork and Turkey Hams Using FT-IR Spectroscopy, Colorimetric, and Image Analysis.

The implementation of fast and nondestructive methods in meat products and colds cuts have become increasingly important to evaluate their quality in relation to different factors such as origin, type of processing, freshness, adulteration, and authenticity. In this study, Fourier Transform Infrared Spectroscopy (FT-IR), colorimetric, and image-analysis methods were implemented to characterize and classify ham cold cuts in terms of meat type, processing, and shelf life during refrigerated storage. Two types of commercial hams (made from pork and turkey) and three types of processing (boiled, smoked, and roasted) were selected. By using the most appropriate color parameters, a*, h, and C*, as well as the textural features’ angular second moment, long-running emphasis, and standard deviation of image intensity from the hams’ images, high-classification values for the different ham samples were achieved. The FT-IR analysis revealed the presence of absorbance bands of proteins, triglycerides, fatty acids, and carbohydrates with different intensities according to meat type and processing. Refrigeration storage caused significant alterations of color parameters and a partial degradation of triglycerides and proteins. Moreover, the image-analysis findings indicated that storage period caused significant degradation of ham images relating to local linearity, and structural and textural continuum.

Unification of local and nonlocal models within a stable integral formulation for analysis of defects

Employing the discrete Cauchy-Born rule with the principle of virtual work done, a generalized model is formulated with the hope to unify local and nonlocal continuum frameworks. Despite the conventional mapping of the microscopic bond from the undeformed configuration, the consistent derivation requires a transformation on the Average Deviation of Lattice (ADL) vector in the region of influence. The new conversion proffers flexibility to the framework for the analysis of nonuniform distribution of particles in the field. We also found a compact mapping matrix which converts surface-based forces (stresses) to the nonlocal body-based forces. The transformation matrix allows reconstructing continuum models at a lower length scale in a discrete setting. To see the credibility of the model, fracture evolution in SCB specimen made of Polymethyl methacrylate (PMMA) is simulated, and the results are compared with experiments which admit an acceptable agreement.

Balmer-dominated Shocks Exclude Hot Progenitors for Many Type Ia Supernovae

Abstract The evolutionary mechanism underlying Type Ia supernova explosions remains unknown. However, recent efforts to constrain progenitor models based on the influence that their high energy emission would have on the interstellar medium within galaxies have proven successful. For individual remnants, Balmer-dominated shocks reveal the ionization state of hydrogen in the immediately surrounding gas. Here, we report deep upper limits on the temperature and luminosity of the progenitors of four Type Ia remnants with associated Balmer filaments: SN 1006, 0509-67.5, 0519-69.0, and DEM L71. For SN 1006, existing observations of helium-line emission in the diffuse emission ahead of the shock provide an additional constraint on the helium ionization state in the vicinity of the remnant. Using the photoionization code Cloudy, we show that these constraints exclude any hot, luminous progenitor for SN 1006, including stably hydrogen or helium nuclear-burning white dwarfs (WD), as well as any Chandrasekhar-mass WD accreting matter at ≳9.5 × 10−8 M ⊙ yr−1 via a disk. For 0509-67.5, the Balmer emission alone rules out any such WD accreting ≳1.4 × 10−8 M ⊙ yr−1. For 0519-69.0 and DEM L71, the inferred ambient ionization state of hydrogen is only weakly in tension with a recently hot, luminous progenitor, and cannot be distinguished from, e.g., a relatively higher local Lyman continuum background, without additional line measurements. Future deep spectroscopic observations will resolve this ambiguity, and can either detect the influence of any luminous progenitor or rule out the same for all resolved SN Ia remnants.

Application of local elasticity continuum damping models in nonlinear dynamic analysis

In order to have a more generic representation of the damping phenomenon in seismic analysis of structures, in this paper, the already existing nonlocal elasticity continuum damping models have been adapted and extended to the inelastic domain. Adaptations of two nonlocal elasticity based damping models, Russell’s spatial hysteresis model and the extended Sorrentino model, into the nonlinear dynamic analysis is presented. Galerkin based finite element schemes are developed and the numerical implementation of the models are outlined. The performances of the nonlocal elasticity-based damping models are illustrated by studying the nonlinear dynamic responses of a four-story Reinforced Concrete frame designed to the Eurocodes. The incremental dynamic analysis study presented illustrates the fact that the proposed models are devoid of the large spurious damping actions commonly exhibited by the popular classical Rayleigh damping model. It has also been shown that in a nonlinear dynamic analysis, the proposed adaptation of the nonlocal elasticity continuum damping models might be a more realistic alternative to the popular classical Rayleigh damping model. The proposed models may be easily implemented in an existing software framework capable of solving both ordinary and integro-differential equations without adding markedly to the computational effort.

An analytical study of wave propagation in a peridynamic bar with nonuniform discretization

In this paper, we use an analytical approach to study the propagation of a plane wave and its spurious reflection in a peridynamic bar using two different methods. In the first method, a coupled peridynamic–finite element approach is used in which peridynamic formulation is used in one part of the domain and finite element is used in the other part. In the second method, peridynamic formulation is used in the entire domain but the bar is discretized by two grids of different sizes. In both cases, the size of the grid of each zone does not change and the two grids share one node with each other. The incident wave travels from the finer grid toward the coarser grid. For the case when peridynamics is used on the entire domain, the size of the peridynamics horizon changes based on the size of the gird. For both cases, we investigate the impact of the relative size of the girds on the amplitude and energy of the transmitted and reflected waves. Our analytical and numerical results show that more spurious reflections occur when the size mismatch between the two grids is larger. In both cases, the issue of spurious wave reflection becomes more severe when the peridynamic horizon size increases. For the case of coupled peridynamic–finite element, even when the size of the two grids are the same, spurious wave reflection occurs which is due to the change in the formulation from a nonlocal to a local continuum. The spurious reflection reduces when the wavelength of the incident wave is large compared with the coarse grid.

Analysis of Gold Microbeams with Higher Order Continuum Theories

AbstractMicrobeams are building blocks for many microstructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects based on their micro‐scale. These size effects can be taken into account by the so‐called higher order continuum theories. Modified Strain Gradient Theory (MSGT) and Modified Couple Stress Theory (MCST) are two commonly used theories, which extend the classical local continuum theories of grade one with the introduction of additional length scale parameters. In this contribution, the variational problem governing the elasticity of higher order beam formulation and the finite element implementation based upon, are briefly introduced. To this end, well known Euler‐Bernoulli beam formulation assumptions are used. The size effect for gold‐micro beams is demonstrated and the length scale parameters of gold microbeams for MSGT and MCST are identified form the existing experimental data from literature for the first time. As a novel aspect, significant size effect is demonstrated for the length‐scales associated with the state of the art gold microbeam structures developed for MEMS applications, which reveals the necessity of the use of higher order theories at these length scales. Advantages and drawbacks of these theories are also identified. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Using Participatory System Dynamics Modeling to Examine the Local HIV Test and Treatment Care Continuum in Order to Reduce Community Viral Load.

Achieving community-level goals to eliminate the HIV epidemic requires coordinated efforts through community consortia with a common purpose to examine and critique their own HIV testing and treatment (T&T) care system and build effective tools to guide their efforts to improve it. Participatory system dynamics (SD) modeling offers conceptual, methodological, and analytical tools to engage diverse stakeholders in systems conceptualization and visual mapping of dynamics that undermine community-level health outcomes and identify those that can be leveraged for systems improvement. We recruited and engaged a 25-member multi-stakeholder Task Force, whose members provide or utilize HIV-related services, to participate in SD modeling to examine and address problems of their local HIV T&T service system. Findings from the iterative model building sessions indicated Task Force members' increasingly complex understanding of the local HIV care system and demonstrated their improved capacity to visualize and critique multiple models of the HIV T&T service system and identify areas of potential leverage. Findings also showed members' enhanced communication and consensus in seeking deeper systems understanding and options for solutions. We discuss implications of using these visual SD models for subsequent simulation modeling of the T&T system and for other community applications to improve system effectiveness.

A survey on buckling analysis of nanostructures via nonlocal elasticity theory

Present paper reviews the research work dealing with buckling analysis of nanostructure designed through the theory of nonlocal elasticity. A variety of mathematical techniques reviewed to determine buckling load and applicability of nonlocal continuum models over local continuum models are discussed. The impact of various parameters like size of nanostructures, nonlocal parameter and length-to-width ratio for various boundary conditions are observed and summarized.

Nonlocal nonlinear finite element analysis of composite plates using TSDT

In this work, nonlocal nonlinear finite element analysis of laminated composite plates using Reddy’s third-order shear deformation theory (TSDT) (Reddy, 1984) and Eringen’s nonlocality Eringen and (Edelen, 1972) is presented. The governing equations of third order shear deformation theory with the von Kármán strains are derived employing the Eringen’s (Eringen and Edelen, 1972) stress-gradient constitutive model. The principle of virtual displacement is used to derive the weak forms, and the displacement finite element models are developed using the weak forms. Four-noded rectangular conforming element with 8 degrees of freedom per node has been used. The coefficients of stiffness matrix and tangent stiffness matrix are presented along with nonlocal force vector. The developed finite element model can be employed to capture the small scale deviations from local continuum models caused by material inhomogeneity and the inter atomic and inter molecular forces. Numerical examples are presented to illustrate the effects of nonlocality, anisotropy, and the von Kármán type nonlinearity on the bending behaviour of laminated composite plates.

Coupling atomistic and continuum modelling of magnetism

In this article, a new energy-based atomistic–continuum partitioned-domain multiscale method for magnetisation dynamics is proposed. The main feature of the method is the minimised mismatch between the local continuum description and the non-local atomistic description (in which non-nearest neighbour interatomic interactions are present). The error at the atomistic–continuum interface is minimised by constructing an intermediate region consisting of transition atoms, which interact differently with the neighbouring atomistic and continuum regions. When the mesh of the continuum region is refined to the atomistic scale at the atomistic–continuum interface and an energy-conserving time-stepping scheme is used for the entire computational domain, the method conserves the total energy of the system. The second feature of the method is the introduction of a damping band at the atomistic–continuum interface, which absorbs high-frequency waves that are otherwise reflected from the interface and thereby contribute to the error inside the atomistic region. Several examples of domain wall motion and spin wave propagation in one- and two-dimensional structures are used to illustrate the applicability of the method and to investigate its limitations.

On the Nonexistence of a Feasible Solution in the Context of the Differential Form of Eringen’s Constitutive Model: A Proposed Iterative Model Based on a Residual Nonlocality Formulation

The motivation of this paper is to highlight and discuss critically the details of two main aspects related to Eringen’s nonlocal constitutive model. The first aspect is to point out the inconsistency of the integral and differential forms of Eringen’s nonlocal constitutive model. In addition, to point out the ill-posed form and physical infeasibility of the results which may be obtained by using the differential form of the model. The critical analysis focuses on the lack of consistency between the set of the boundary constraints required by the differential form of Eringen’s model and the set of the prescribed boundary conditions of the nonlocal static equilibrium problem. Because of this lack of consistency between the two constitutive forms, it can be concluded that the formulation in context of the differential form is ill-posed and the existence of a feasible solution is questionable and might not be admitted. The second aspect deals with the intractability of the analytical solution of the nonlocal continuum problems based on the integral form of Eringen’s nonlocal constitutive model (IENCM). In the meantime, it mentions the cumbersome of numerical work required by the direct computational methods such as the nonlocal finite element method. The complexity of using the integral form of Eringen’s constitutive model and the lack of existence of a feasible solution by using the differential form of Eringen’s constitutive model lead to the mandatory need for developing an efficient iterative computational approach based on the integral form of Eringen’s constitutive model. In this paper, an iterative computational method, based on the nonlocality residual formulation for nonlocal continuums, capable to investigate different elasticity problems, is proposed. The traditional local continuum solution is taken as an initial solution. To point out the inconsistences between the integral and differential forms of Eringen’s nonlocal constitutive model, and to illustrate the efficiency and capability of the proposed iterative model, four static bending of beam problems with different nature are solved.

ANALYSIS OF GOLD MICRO-BEAMS WITH MODIFIED STRAIN GRADIENT THEORY

Micro-beams are building blocks for many micro- and nano-structures as well as micro-electro-mechanical systems (MEMS) and cannot accurately be modeled by classical continuum theories due to significant size effects at the length scales associated with these structures. Size effects can be taken into account by the so-called higher order continuum theories. In this study, Euler-Bernoulli micro-beams are analyzed with the Modified Strain Gradient Theory (MSGT), which extends the classical local continuum theories of grade one with the introduction of three additional length scale parameters. In this contribution, finite element implementation is briefly demonstrated by using Galerkin discretization techniques for Euler-Bernoulli beams. The size effect for gold-micro beams is demonstrated and the length scale parameters of gold micro-beams for MSGT are identified form the existing experimental data from literature for the first time . As a novel aspect, significant size effect is demonstrated for the length-scales associated with the state of the art gold micro-beam structures developed for NEMS and MEMS applications, which reveals the necessity of the use of higher order theories at these length scales.

Bond-level deformation gradients and energy averaging in peridynamics

Peridynamic models that aim to incorporate a given classical local continuum stress-deformation response function typically start with a nonlocal averaged analog to the deformation gradient as input to the given local stress-deformation response function. This approach has been observed to allow unphysical deformations such as interpenetration and cause loss of linear stability. This paper describes an approach to deal with this shortcoming. The strategy is based on (1) defining a bond-level analog to the deformation gradient tensor – in contrast to the usual vector deformation measure in peridynamics – that captures both the average deformation in the neighborhood of the bond as well as the deviation of the bond stretch from this average deformation, and (2) using this bond-level deformation gradient in the classical local strain energy response to obtain the energy of each bond. Compared to the standard approach that applies the energy to the averaged deformation gradient, this approach instead averages the energy applied to the bond-level deformation gradient.

Study of Nonequilibrium Size and Concentration Effects on the Heat and Mass Diffusion of Indistinguishable Particles Using Steepest-Entropy-Ascent Quantum Thermodynamics

Conventional first-principle approaches for studying nonequilibrium processes depend on the mechanics of individual particles or quantum states and as a result require many details of the mechanical features of the system to arrive at a macroscopic property. In contrast, thermodynamics, which has been successful in the stable equilibrium realm, provides an approach for determining macroscopic properties without the mechanical details. Nonetheless, this phenomenological approach is not generally applicable to a nonequilibrium process except in the near-equilibrium realm and under the local equilibrium and continuum assumptions, both of which limit its ability to describe nonequilibrium phenomena. Furthermore, predicting the thermodynamic features of a nonequilibrium process (of entropy generation) across all scales is difficult. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides a first-principle thermodynamic-ensemble based approach applicable to the entire nonequilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics, which crosses all temporal and spatial scales. Based on prior developments by the authors, SEAQT is used here to study the heat and mass diffusion of indistinguishable particles. The study focuses on the thermodynamic features of far-from-equilibrium state evolution, which is separated from the specific mechanics of individual particle interactions. Results for nonequilibrium size (volume) and concentration effects on the evolutionary state trajectory are presented for the case of high temperature and low particle concentration, which, however, do not impact the generality of the theory and will in future studies be relaxed.

On Thermodynamic Consistency of Homogenization-Based Multiscale Theories

In this paper, the necessary and sufficient conditions for fulfilling the thermodynamic consistency of computational homogenization schemes in the framework of hierarchical multiscale theories are defined. The proposal is valid for arbitrary homogenization based multiscale procedures, including continuum and discontinuum methods in either scale. It is demonstrated that the well-known Hill–Mandel variational criterion for homogenization scheme is a necessary, but not a sufficient condition for the micro–macro thermodynamic consistency when dissipative material responses are involved at any scale. In this sense, the additional condition to be fulfilled considering that the multiscale thermodynamic consistency is established. The general case of temperature-dependent, higher order elastoplasticity is considered as theoretical framework to account for the material dissipation at micro and macro scales of observation. It is shown that the thermodynamic consistency enforces the homogenization of the nonlocal terms of the finer scale's free energy density; however, this does not lead to nonlocal gradient effects on the coarse scale. Then, the particular cases of local isothermal elastoplasticity and continuum damage are considered for the purpose of the proposed thermodynamically consistent approach for multiscale homogenizations.

Two-scale computational approach using strain gradient theory at microlevel

Realistic description of heterogeneous material behavior demands more accurate modeling at macroscopic and microscopic scales. In this frame, the multiscale techniques employing homogenization scheme offer several solutions. Most recently developed two-scale scheme employing second-order homogenization requires the nonlocal theory at the macrolevel, while the classical local continuum theory is kept at the microlevel. In this paper, a new second-order computational homogenization scheme is proposed employing the higher-order theory at both macro- and microlevel. Discretization is performed by means of the C1 finite element developed using the strain gradient theory. The new gradient boundary conditions employed on representative volume element (RVE) are derived. The relation between the internal length scale parameter and the RVE size has been found. The new procedure is tested on a benchmark example, where the results have been compared to the solutions obtained by the usual second-order homogenization using the local concept on the RVE.