A new and general formulation of the parametric HFGMC micromechanical method for two and three-dimensional multi-phase composites

AbstractThe recent two-dimensional (2D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2D parametric and orthogonal HFGMC are special cases of the present 3D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, and discontinuous aligned short fiber. A 3D repeating unit-cell for foam material composite is simulated

Nonlinear micromechanical formulation of the high fidelity generalized method of cells

AbstractThe recent High Fidelity Generalized Method of Cells (HFGMC) micromechnical modeling framework of multiphase composites is formulated in a new form which facilitates its computational efficiency that allows an effective multiscale material–structural analysis. Towards this goal, incremental and total formulations of the governing equations are derived. A new stress update computational method is established to solve for the nonlinear material constituents along with the micromechanical equations. The method is well-suited for multiaxial finite increments of applied average stress or strain fields. Explicit matrix form of the HFGMC model is presented which allows an immediate and convenient computer implementation of the offered method. In particular, the offered derivations provide for the residual field vector (error) in its incremental and total forms along with an explicit expression for the Jacobian matrix. This enables the efficient iterative computational implementation of the HFGMC as a stand alone. Furthermore, the new formulation of the HFGMC is used to generate a nested local-global nonlinear finite element analysis of composite materials and structures. Applications are presented to demonstrate the efficiency of the proposed approach. These include the behavior of multiphase composites with nonlinearly elastic, elastoplastic and viscoplastic constituents

Thermoelastic stress analysis for detecting wrinkles and associated resin pockets in polymer composites

A thermos elastic stress analysis method is proposed consisting of an array of infrared measurement sensors used for evaluation the wrinkling defects and associated resin pockets in a fiber reinforced polymer (FRP) composite structure. Wrinkling or fiber waviness defects results when out of plane distortions occur in some or all of the composite layers of the laminate. The wrinkles result in significant reductions of mechanical properties in the composite structure. The method involves instrumentation and device for application of internal energy in the material such as transient or cyclic mechanical excitations. These external excitations are induced in a prescribed or measurable cyclic or transient function of time. Infrared measurements from the surface of the composite are synchronized with the applied excitation energy. The results are used to provide for a map detailing the inner wrinkle defects and associated resin pockets in the laminated composite structure

A New and General Formulation of the Parametric HFGMC Micromechanical Method for Three-Dimensional Multi-Phase Composites

The recent two-dimensional (2-D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3-D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2-D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3-D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2-D parametric and orthogonal HFGMC are special cases of the present 3-D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3-D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3-D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, discontinuous aligned short fiber. A 3-D repeating unit-cell for foam material composite is simulated

A method for estimating constitutive properties of a C/C-SiC composite materials based on a Brazilian disc specimen

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Nonlinear constitutive models for FRP composites using artificial neural networks

Abstract This paper presents a new approach to generate nonlinear and multi-axial constitutive models for fiber reinforced polymeric (FRP) composites using artificial neural networks (ANNs). The new nonlinear ANN constitutive models are complete and have been integrated with displacement-based FE software for the nonlinear analysis of composite structures. The proposed ANN constitutive models are trained with experimental data obtained from off-axis tension/compression and pure shear (Arcan) tests. The proposed ANN constitutive model is generated for plane-stress states with assumed functional response in some parts of the multi-axial stress space with no experimental data. The ability of the trained ANN models to predict material response is examined directly and through FE analysis of a notched composite plate. The experimental part of this study involved coupon testing of thick-section pultruded FRP E-glass/polyester material. Nonlinear response was pronounced including in the fiber direction due to the relatively low overall fiber volume fraction (FVF). Notched composite plates were also tested to verify the FE, with ANN material models, to predict general nonhomogeneous responses at the structural level

The Parametric High-Fidelity-Generalized-Method-of-Cells (PHFGMC) Micromechanical Model for Compression Failure of FRP Composites

A multiscale model based on finite element (FE) and the Parametric High-Fidelity-GeneralizedMethod-of-Cells (PHFGMC) micromechanical model was formulated and implemented to solve the compression problem in unidirectional IM7/977-3 carbon epoxy composite. The nonlinear PHFGMC governing equations were obtained from a two-layered (local-global) virtual work principle and solved using a incremental-iterative formulation. In addition, the semi-analytical modified Lo and Chim failure criterion (based on the buckling of Timoshenko's beam) for unidirectional fiber-reinforced composite materials under compression [1] was adopted and combined with the FE-PHFGMC multiscale model. In this study, the criterion was employed for the general case of a multi-axial loading state accompanied with a nonlinear polymeric matrix behavior, where the local and thus effective properties of the composite change continuously throughout the loading path. Therefore the predicted lamina strength was incrementally reevaluated. In the present model, the use of the nonlinear constitutive model RambergOsgood was used for the matrix media and a linear-elastic transversely-isotropic law for the fiber, as common for carbon fibrous composites. This extends the existing criterion to account for the material microstructure with a refined parametric discretization, as well as the effect of a nonlinear constitutive law. The advantage of the proposed model is to predict the compressive damage (kink band formation and its width) and the compressive strength (within 11% of experimental data)

Damage and Failure Initiation in Lap Shear Tests

Issued as final reportLockheed Martin Aeronautic

Global estimates on the number of people blind or visually impaired by cataract: a meta-analysis from 2000 to 2020

Background: To estimate global and regional trends from 2000 to 2020 of the number of persons visually impaired by cataract and their proportion of the total number of vision-impaired individuals. Methods: A systematic review and meta-analysis of published population studies and gray literature from 2000 to 2020 was carried out to estimate global and regional trends. We developed prevalence estimates based on modeled distance visual impairment and blindness due to cataract, producing location-, year-, age-, and sex-specific estimates of moderate to severe vision impairment (MSVI presenting visual acuity &lt;6/18, ≥3/60) and blindness (presenting visual acuity &lt;3/60). Estimates are age-standardized using the GBD standard population. Results: In 2020, among overall (all ages) 43.3 million blind and 295 million with MSVI, 17.0 million (39.6%) people were blind and 83.5 million (28.3%) had MSVI due to cataract blind 60% female, MSVI 59% female. From 1990 to 2020, the count of persons blind (MSVI) due to cataract increased by 29.7%(93.1%) whereas the age-standardized global prevalence of cataract-related blindness improved by −27.5% and MSVI increased by 7.2%. The contribution of cataract to the age-standardized prevalence of blindness exceeded the global figure only in South Asia (62.9%) and Southeast Asia and Oceania (47.9%). Conclusions: The number of people blind and with MSVI due to cataract has risen over the past 30 years, despite a decrease in the age-standardized prevalence of cataract. This indicates that cataract treatment programs have been beneficial, but population growth and aging have outpaced their impact. Growing numbers of cataract blind indicate that more, better-directed, resources are needed to increase global capacity for cataract surgery.</p

Global, regional, and national burden of colorectal cancer and its risk factors, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Funding: F Carvalho and E Fernandes acknowledge support from Fundação para a Ciência e a Tecnologia, I.P. (FCT), in the scope of the project UIDP/04378/2020 and UIDB/04378/2020 of the Research Unit on Applied Molecular Biosciences UCIBIO and the project LA/P/0140/2020 of the Associate Laboratory Institute for Health and Bioeconomy i4HB; FCT/MCTES through the project UIDB/50006/2020. J Conde acknowledges the European Research Council Starting Grant (ERC-StG-2019-848325). V M Costa acknowledges the grant SFRH/BHD/110001/2015, received by Portuguese national funds through Fundação para a Ciência e Tecnologia (FCT), IP, under the Norma Transitória DL57/2016/CP1334/CT0006.proofepub_ahead_of_prin