Order Continuum Research Articles

Persistent Challenges in the Hepatitis C Virus Care Continuum for Patients in a Central Texas Public Health System.

BackgroundDirect-acting antiviral treatment regimens cure >95% of chronic hepatitis C virus (HCV) infections, but recent studies indicate that <25% of patients in the United States receive treatment. Patients need to overcome barriers on the steps of the care continuum in order to be prescribed treatment. We aimed to examine the steps of the HCV care continuum up to prescription of HCV therapy among patients receiving care within a large safety net health care system in Houston, Texas.MethodsWe used electronic medical records to identify patients with positive screening tests for HCV antibodies between July 1, 2017, and June 30, 2018, and abstracted data on their advancement through the care continuum for HCV. We used logistic regression to identify factors associated with patient navigation through the continuum.ResultsOf the 2450 patients screening positive for HCV antibodies, 2016 (82.3%) received quantitative RNA testing, of whom 1081 (53.6%) exhibited chronic infection. Providers referred 915 (84.6%) to specialty care for evaluation, 540 of these patients (50.0%) received their specialist evaluation, and 299 (27.7%) received a prescription for treatment. Patients with history of substance use were less likely to be prescribed treatment (adjusted odds ratio, 0.66; 95% CI, 0.49–0.88).ConclusionsWe found substantial attrition at each stage of the HCV care continuum. In particular, history of substance abuse was a predictor of nonprescription. Challenges in the care continuum motivate increased provider education as well as the adoption of recent innovations in patient care.

Does Green Tea Induce Hormesis?

Green tea, and its principal constituent (–)-epigallocatechin-3-gallate (EGCG), are commonly shown to induce biphasic concentration/dose responses in a broad range of cell types, including non-tumor cells, and tumor cell lines. The most active area of research dealt with an assessment of neural cells with application to neurodegenerative diseases such as Parkinson’s disease and Alzheimer’s disease cell models, often using preconditioning experimental protocols. The general findings demonstrate EGCG-induced hormetic effects resulting in an enhanced acquired resilience within an adaptive and temporally dependent homeodynamic framework. The biphasic dose responses displayed the typical quantitative features of the hormetic dose response with respect to the amplitude and width of the stimulatory response. These findings provide further evidence for the general occurrence of hormetic dose responses with such responses being independent of the biological model, end point, inducing agent, and mechanism. The biphasic nature of these responses has important implications since it suggests optimal dose ranges for end points of public health and therapeutic applications. These findings indicate the need to assess the entire dose-response continuum in order to better define the nature of the dose response, especially in the low-dose zone where such exposures are common in human populations.

A Hybridity Continuum

The article proposes an analytical framework in the form of a continuum in order to examine instances of hybridity in terms of mechanisms, qualities and outcomes. By foregrounding material pathways and processes through the coming together of disparate elements, the continuum provides a platform to analyse the overlapping spatio-temporalities and bleeding palettes of hybridity. The continuum is deployed to illustrate hybridity in an aspect of embodiment denoted by the term ‘bodyworld’ to mark human–non-human relationalities. Specific reference is made to athletes who operate gym machines and the psychophysical work of performers. The hybridity continuum is developed in the light of the so-called 3As of bodyworld: assemblages, affordances and actants. Reference is also made to Shaun Gallagher’s ‘body schema’ and its links with distributed cognition, as well as to Heike Jöns’s socio-material ‘dynamic hybrids’ from the field of human geography. In reading hybridity and bodyworld in the light of each other via the continuum, the article suggests a deconstructive strategy that draws attention to the material conditions of human activity, thereby shedding light on our understanding of psychosomatic practices. The focus of the continuum on material processes serves to counter the ubiquitous quality often associated with hybridity.

Continuum thermomechanics of nonlinear micromorphic, strain and stress gradient media.

A comprehensive constitutive theory for the thermo-mechanical behaviour of generalized continua is established within the framework of continuum thermodynamics of irreversible processes. It represents an extension of the class of generalized standard materials to higher order and higher grade continuum theories. It reconciles most existing frameworks and proposes some new extensions for micromorphic and strain gradient media. The special case of strain gradient plasticity is also included as a contribution to the current debate on the consideration of energetic and dissipative mechanisms. Finally, the stress gradient continuum theory emerges as a new research field for which an elastic-viscoplastic theory at finite deformations is provided for the first time. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Numerical and experimental investigation on dynamics of deployable space telescope experiencing deployment and attitude adjustment motions coupled with laminated composite shell

Nonlinear dynamic modeling methods for a flower-like clustered deployable space telescope (DST) with laminated composite material experiencing large deployment and attitude adjustment motions is proposed in present work. The flexible mirrors are discretized into shell elements in absolute node coordinate formulation (ANCF) considering nonlinear structures instead of using conventional shell elements in hybrid coordinate formulation (HCF). Meanwhile the stress–strain relations of laminated composite mirrors with considering nonlinear material and geometric properties are respectively deduced by high order shear deformation theory and continuum mechanics. Then, the accuracy of dynamic behavior is investigated by comparison of the results obtained by using ANCF and HCF, and it is indicated that ANCF shell elements are suitable for solving large deformation and deployment dynamic analysis of DST with high accuracy and strong convergence by numerical simulations. Further, the experiments for evaluating the dynamic behavior of surrounding mirrors with simultaneous deployment in different deployment strategies are conducted. Numerical results are in good agreement with those obtained from experiments to validate the correctness of the present nonlinear modeling formulation. And, the experiment and numerical simulation of the primary mirror experiencing attitude adjustment motions are also carried out. Those results illustrate the performance of the dynamic properties of DST with different deployment strategies and laminated composite structures in the present modeling method. These conclusions will have significant theory and engineering practice values for predicting surface accuracy, pointing accuracy and vibration performance of DST mechanism.

ALMA and NACO observations towards the young exoring transit system J1407 (V1400 Cen)

Aims. Our aim was to directly detect the thermal emission of the putative exoring system responsible for the complex deep transits observed in the light curve for the young Sco-Cen star 1SWASP J140747.93-394542.6 (V1400 Cen, hereafter J1407), confirming it as the occulter seen in May 2007, and to determine its orbital parameters with respect to the star. Methods. We used the Atacama Large Millimeter/submillimeter Array (ALMA) to observe the field centred on J1407 in the 340 GHz (Band 7) continuum in order to determine the flux and astrometric location of the ring system relative to the star. We used the VLT/NACO camera to observe the J1407 system in March 2019 and to search for the central planetary mass object at thermal infrared wavelengths. Results. We detect no point source at the expected location of J1407, and derive an upper limit 3σ level of 57.6 μJy. There is a point source detected at an angular separation consistent with the expected location for a free-floating ring system that occulted J1407 in May 2007, with a flux of 89 μJy consistent with optically thin dust surrounding a massive substellar companion. At 3.8 μm with the NACO camera, we detect the star J1407 but no other additional point sources within 1.3 arcsec of the star, with a lower bound on the sensitivity of 6 MJup at the location of the ALMA source, and down to 4 MJup in the sky background limit. Conclusions. The ALMA upper limit at the location of J1407 implies that a hypothesised bound ring system is composed of dust smaller than 1 mm in size, implying a young ring structure. The detected ALMA source has multiple interpretations, including: (i) it is an unbound substellar object surrounded by warm dust in Sco-Cen with an upper mass limit of 6 MJup, or (ii) it is a background galaxy.

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

AbstractWhile current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build‐up to detonation, a new paradigm is put forth for modelling sub‐grid, reaction‐induced fluctuations (i. e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin‐type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i. e. deterministic) and diffusion (i. e. stochastic) coefficients. Additionally, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave‐like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no‐go estimation (e. g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i. e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Thus, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub‐grid stochastic behaviour of shocked heterogeneous solid explosives.

Two novel Kirchhoff plate finite elements for the modified strain gradient theory

AbstractMicroplates are vastly used in MEMS and NEMS devices. Due to size effect, classical theories of continuum mechanics can not be used to model mechanical behaviour of them. Instead, higher order continuum theories should be implemented. Modified Strain Gradient Theory (MSGT) is considered to be one of the most accurate methods for this, considering both theoretical compatibility and numerical accuracy. In this study, two sets of Kirchhoff and twist‐Kirchhoff bending rectangular plate finite elements for MSGT are developed as novel aspects. This is done by first obtaining the weak forms by using variational methods and then deriving the set of algebraic equations for the finite element formulation starting with shape functions. Although non‐conforming, the finite elements are in alignment with the existing models with the given length scale parameters. The plate finite elements are then implemented to existing models. The length scale parameters for MSGT are also identified for gold using the existing experimental results in literature. This study proposes the use of higher order theories for gold microplates for thicknesses less than 40 µm.

Small-scale energy cascade in homogeneous isotropic turbulence

The relationship between the energy flow and kinematics of the small-scale is investigated in homogeneous isotropic turbulence. The study employs a high order continuum theory to decouple the rotational motion from the translational motion and investigate the contribution of each field alone.

Asymptotic homogenization models for pantographic lattices with variable order rotational resistance at pivots

In this paper, different asymptotic orders of torsional resistance at the pivots for linear pantographic lattices are introduced within an asymptotic homogenization of the discrete micro-beam model associated with the summation of internal forces and moments at the pivots. The small parameter is defined by the ratio of the square root of a unit cell size for the lattice and the problem domain size. The objective is to systematically identify leading order continuum field equations and to define homogenized elasticity tensors and their properties for increasing rotational torque stiffness. To measure the effect of the torsional spring stiffness on the deformation of the lattice, the torsional resistance of a beam element between pivots which compares the torque stiffness to its bending moment stiffness is introduced as a power of the small parameter. Consistent with previous models for pantographic sheets with zero (perfect) or light torsional resistance, an asymptotic expansion with the small scaling parameter shows that the leading order continuum field equations are characterized by second gradient elasticity theory. The homogenized elasticity coefficients are determined in terms of the fiber characteristics and the torque stiffness. A shear modulus is calculated proportional to the torque stiffness. By increasing the torsional resistance to order one, the resulting field equations move to first-gradient classical elasticity with a shear modulus varying as a homographic function in the torsional resistance. By increasing torsional stiffness to higher orders, the shear modulus is obtained for the limiting case of rigid connections. Numerical results are presented for standard elongation and shear bias tests. Strain energies from the first gradient and second gradient terms present for the models with different orders of torsional resistance are computed to demonstrate the zero and infinite limiting cases, and the need to move from a second-gradient continuum model with low-order torsional resistance as scaled with the small parameter, to a first-gradient model for high-orders of torsional resistance.

Political agitation and state of mental maturity of the domestic society

In the article the author develops a typology of accents of the influence on the contemporary domestic electorate during the election of the President of Ukraine in the spring of 2019. This purpose is achieved by involving socio-philosophical methodology and the achievements of a psychoanalytic philosophical paradigm. There are four types of accents that were observed during the race. Politicians of the first accent sought to influence the critical thinking of the electorate. The second group of politicians sought to exploit a scientifically constructed myth - about themselves or “almost” about themselves. The third group focused on individual myths that were not united by a holistic political myth. The fourth group appealed to the trust that was unreasonable. Thus, political agitations form a continuum - from attempts to influence solely voter’s rationality to counting on the resonance of their subconscious mythological architectonics. In addition, it is concluded that the politicians of near future should flexibly involve all constructive from this continuum in order to strengthen their own positive influence on the electorate. In this context, the modern politicians should focus on political mythmaking necessarily, because it is scientifically correct. The author of the article shares the view of those classics of philosophy who see the basis of any cultural activity in myth. Of course, a rational component of political agitation should be present. For example, there should be very rationally compiled (and executed) political program.

Variational bounds and overall shear modulus of nano-composites with interfacial damage in anti-plane couple stress elasticity

It is well known that classical continuum theory has certain deficiencies in capturing the size effects and predicting the nanoscopic behavior of materials in the vicinity of nano-inhomogeneities and nano-defects with reasonable accuracy. Couple stress theory which is associated with an internal length scale for the medium is one of the higher order continuum theories capable of overcoming such difficulties. In this work, the problem of a nano-size fiber embedded in an unbounded isotropic elastic body for three different types of interface conditions: perfect, imperfect (partially damaged), and pure sliding (completely damaged) subjected to remote anti-plane loading is examined in this framework. The physically realistic size-dependent elastic fields for the problem will be derived analytically. The discontinuities of the displacement and rotation fields at the imperfect interfaces are assumed to be proportional to the associated reduced traction and couple traction, respectively. The effect of the interfacial damage on the stress field around the nano-fiber is also examined. Subsequently, the elastic field of a single nano-fiber with a damaged interface condition is employed in conjunction with the Mori–Tanaka theory to estimate the size-dependent overall anti-plane shear modulus of such solids enriched with unidirectional circular cylindrical fibers severely damaged at their interfaces with the matrix. The dependence of the anti-plane elastic shear modulus on several important physical parameters such as size, interface conditions, rigidity of the fiber, and the characteristic length of the constituents is analyzed. Finally, a variational approach for the estimation of the upper and lower bounds of anti-plane shear modulus will be given within couple stress elasticity and, moreover, the dependence of the bounds on the matrix–fiber interface damage and the fiber to the matrix rigidity ratio is examined.

Hemitropic properties of thin non-centrosymmetric 3D woven textile composites

Due to their microstructural architecture, 3D woven textile composites, (3DWTC), exhibit complex macroscopic behavior, which cannot be effectively captured using classical continuum theories. One reason for this can be attributed to the ratio of the characteristic microscopic and macroscopic length scales, (d and L, respectively), which violates the separation of length scales requirement d/L<<1 in micromechanics. In these instances, higher order continuum theories, such as micropolar theory, are considered to effectively describe the macroscopic behavior of a material. In this study, the 3D macroscopic constitutive relation of 3D woven textile composite (3DWTC) is reported. The three different 3DWTC considered are referred to as thin asymmetric, thick asymmetric, and thick symmetric. The lack of centro-symmetry in the asymmetric microstructures produces an interesting anisotropic response, such as stress-curvature (or couple stress-strain) coupling effect. This is analogous to asymmetric plate structures and the coupling between the resultant forces and curvatures through the B-matrix. At the macroscopic (continuum) scale, the material is modeled as a micropolar continuum, where internal couple-stresses and curvature strains are introduced. To capture the stress-curvature coupling effect, a generalized Aero-Kuvshinski type constitutive model is considered. With this, the anisotropic micropolar properties and the additional hemitropic material constants of the 3DWTC are determined numerically and their results qualitatively summarized.

The Alberta oil sands eroded bitumen/sediment transitional journey: Influence on sediment transport dynamics, PAH signatures and toxicological effect

This paper investigated the sediment/contaminant continuum of bitumen containing sediment, from eroded exposed natural bitumen outcrops to river depositional zone, in order to improve our understanding of the transitional sediment, chemistry and toxicological influence on aquatic health. To achieve this aim, we linked a rainfall simulator with an annular flume to allow for connectivity between terrestrial erosion to stream flow. Bulk sediments were collected from the minable McMurray Formation (MF) on the Ells (EL) and Steepbank (STB) Rivers and from the Clearwater Formation (CF) on the STB.All plots generated similar washoff rates (~25 L hr−1) and fine eroded sediment (d50 = 5 μm) regardless of strata. The CF generated the highest total eroded sediment (TES) followed by EL-MF and STB-MF. The STB-MF generated up to three orders of magnitude lower TES than the STB-CF. The EL generated the highest PAH concentrations, however, when normalizing by TES mass delivered to the flume, STB-MF PAH was one to two orders of magnitude higher per unit mass than EL-MF. The TES concentrations were inversely proportional to the degree of bitumen within the sediment (STB-MF > EL-MF > STB-CF). Once the TES was suspended in the flume, there was a change in the dominant PAH for most classes [e.g., Dibenzothiophenes C4 (parent material) to a C3 (TES)]. Further, no flocculation and the buoyant properties of the TES suggested that the sediment and associated PAHs may travel long distances. The EL-MF proved to be the most toxic to fathead minnow embryo survival due principally to the high PAH concentrations and sediment loads. The CF exhibited no toxicological effect. This work has shown the importance of assessing sediment/contaminant characteristics over the continuum (terrestrial erosion/washoff to river deposition) in order to support basin wide management strategies for the protection of aquatic health.

Numerical Investigation of the Time Fractional Mobile-Immobile Advection-Dispersion Model Arising from Solute Transport in Porous Media

Evolution equations containing fractional derivatives can offer efficient mathematical models for determination of anomalous diffusion and transport dynamics in multi-faceted systems that cannot be precisely modeled by using normal integer order equations. In recent times, researches have found out that lots of physical processes illustrate fractional order characteristics that alters with time or space. The continuum of order in the fractional calculus permits the order of the fractional operator be accounted for as a variable. In the current research work, radial basis functions (RBFs) approximation is utilized for solving fractional mobile-immobile advection-dispersion (TF-MIM-AD) model in a bounded domain which is applied for explaining solute transport in both porous and fractured media. In this approach, firstly, the discretization process of the aforesaid equation with of convergence order $$\mathcal {O}(\delta t^{})$$ in the t-direction is described via the finite difference scheme for $$ 0< \alpha <1$$ . Afterwards, by help of the meshless methods based on RBFs, we will illustrate how to obtain the approximated solution. The stability and convergence of time-discretized scheme are also theoretically discussed in detail throughout the paper. Finally, two numerical instances are included to clarify effectiveness and accuracy of our proposed concepts which is investigated in the current research work.

Quantifying the non-equilibrium characteristics of heterogeneous gas–solid flow of smooth, inelastic spheres using a computational fluid dynamics–discrete element method

Continuum modelling of dense gas–solid flows strongly depends on the constitutive relations used, including the interphase drag force, particle phase stress and the boundary condition for particle–wall interactions. The lack of scale separation is usually claimed to cause the breakdown of the Navier–Stokes (NS) order continuum theory. In this study, computational fluid dynamics–discrete element method (CFD-DEM) simulations of bubbling, turbulent and fast fluidization of smooth, inelastic spheres were conducted to systematically analyse the valid range of NS theory. An entropy-based criterion $I_{s}$ and Knudsen numbers defined using different characteristic length scales ($Kn_{frac}$, $Kn_{gran}$ and $Kn_{vel}$) were quantified. It was found that (i) except at the centre of bubbles where the solid concentration is quite low, NS theory for discrete particles was valid for bubbling fluidization irrespective of the breakdown criterion. Even at the boundary of the bubbles, values of $I_{s}$ and $Kn$ were small; and (ii) the conclusion depended on the criterion used in turbulent and fast fluidization. If $Kn_{frac}$ was used, NS theory would be generally valid. If $I_{s}$ was chosen, NS theory would be still valid but with lower confidence. However, if $Kn_{vel}$ or $Kn_{gran}$ was selected, NS theory broke down. Because $I_{s}$ includes the non-equilibrium effects caused by the gradient of hydrodynamic fields and particle inelasticity, we may conclude that NS theory was valid for all tested cases. This means that the continuum description of discrete particles is not the main source of the breakdown of NS theory.

Hα plumes or arms associated with the nucleus of NGC 7020

AbstractWe imaged the galaxy NGC 7020 with Gemini and GMOS-S interference filters centered on the Hα emission line and nearby continuum in order to detect and quantify the HII regions. Among about 200 HII regions, we detected two Hα emitting plumes or arms emerging from the galactic nucleus which, together with the nuclear emission, might indicate a process of feedback from the central region.

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

A new vegetation heavy metal pollution index for detecting the pollution degree of different varieties of maize under copper stress

ABSTRACTThis study proposed a new vegetation heavy metal pollution index VHMPI to detect the pollution degree of different varieties of maize under copper stress, which provides a new idea for the detection of heavy metal pollution in vegetation. In order to ensure the outdoor growth environment of maize, we put all maize into outdoor greenhouse. The spectral reflectance interval of 450 nm–850 nm of maize leaves was processed by the first order differential (D) and continuum removal (CR), and the DCR spectral curve was obtained. The Pearson correlation coefficient (R) was used to analyze the DCR data and the biochemical data and select characteristic bands that sensitive to heavy metal Cu. The calculated Pearson correlation coefficients suggested that the DCR value at 490 nm–520 nm and 680 nm–700 nm presented a linear positive correlation close to 1 with the Cu2+ contents in soil and leaves, and a linear negative correlation close to −1 was present in the range of 630 nm–650 nm and 710 nm–750 nm. We selected the DCR value of wavelengths 505 nm, 640 nm, 690 nm and 730 nm to establish VHMPI, and compared it with conventional vegetation indices (VIs) by calculating Pearson correlation coefficient between them and Cu contents in soil and leaves, Vegetation indices include WBI (Water Band Index), PSNDa (Pigment Specific Normalized Difference a), PRI (Photochemical Reflectance Index), NDVI (Normalized Difference Vegetation Index). Maize leaf spectral data obtained from experiments in 2017 were used for verification, VHMPI was also compared with WBI, PSNDa, PRI and NDVI.The results suggested that VHMPI showed a significant correlation with Cu2+ stress concentration,and the correlation of VHMPI was much stronger than that of other vegetation indices. The proposed VHMPI detects the pollution degree of maize with different varieties and in different periods under copper stress has advantages of straightforward calculation, robustness, and high effectiveness. This study focused on the laboratory leaf scale, so it is expected that future work extends it to a wide range of field scale and image scale.

Parametrically homogenized continuum damage mechanics (PHCDM) models for composites from micromechanical analysis

This paper develops a parametrically homogenized continuum damage mechanics (PHCDM) model for unidirectional fiber reinforced epoxy composites undergoing progressive damage. The PHCDM models are designed to overcome limitations of prohibitive computational overhead associated with many homogenization methods. They are thermodynamically consistent, reduced order continuum models with explicit representation of microstructural morphology through strategically determined parameters. The PHCDM model is derived from detailed micromechanics simulations of the representative volume element (RVE) using energy equivalence principles. Micromechanical failure is due to fiber–matrix interface debonding and matrix cracking. The macroscopic PHCDM models represent damage anisotropy through a second order damage tensor that contributes to the evolution of a damage surface in the space of damage work conjugate. The damage surface characterizes the initiation and evolution of damage in the composite. The constitutive relation between damage and its work conjugate is represented by an anisotropic fourth order damage surface tensor Pijkl, whose components are expressed as functions of current damage state. These are calibrated and validated from homogenized micromechanics (HMM) simulations. The PHCDM model is incorporated in a commercial finite element code and structural analysis of macroscopic composite components are executed for understanding concurrent damage and failure at multiple scales.