Rami Haj-Ali

AUTOPROGRESSIVE TRAINING OF NEURAL NETWORK CONSTITUTIVE MODELS

A new method, termed autoprogressive training, for training neural networks to learn complex stress–strain behaviour of materials using global load–deflection response measured in a structural test is described. The richness of the constitutive information that is generally implicitly contained in the results of structural tests may in many cases make it possible to train a neural network material model from only a small number of such tests, thus overcoming one of the perceived limitations of a neural network approach to modelling of material behaviour; namely, that a voluminous amount of material test data is required. The method uses the partially-trained neural network in a central way in an iterative non-linear finite element analysis of the test specimen in order to extract approximate, but gradually improving, stress–strain information with which to train the neural network. An example is presented in which a simple neural network constitutive model of a T300/976 graphite/epoxy unidirectional lamina is trained, using the load–deflection response recorded during a destructive compressive test of a [(±45)6]S laminated structural plate containing an open hole. The results of a subsequent forward analysis are also presented, in which the trained material model is used to simulate the response of a compressively loaded [(±30)6]S structural laminate containing an open hole. Avenues for further improvement of the neural network model are also suggested. The proposed autoprogressive algorithm appears to have wide application in the general area of Non-Destructive Evaluation (NDE) and damage detection. Most NDE experiments can be viewed as structural tests and the proposed methodology can be used to determine certain damage indices, similar to the way in which constitutive models are determined.

Simulation of ductile crack growth using computational cells: numerical aspects

This study explores key computational issues that aAect analyses employing the computational cell methodology to predict crack growth in ductile metals caused by void growth and coalescence. These issues — computational load step size, procedures to remove cells with high porosity from the analysis, and the porosity for cell deletion — can adversely aAect predicted crack growth resistance (R) curves and/or hinder convergence of both local constitutive and global iterative computations. Strain increments generated by large computational load steps introduce errors in the predicted peak stress of computational cells and prevent convergence of stress updates for the Gurson‐Tvergaard constitutive model. An adaptive load control algorithm, which limits the maximum porosity over a load step, eliminates this problem. The delayed release of remaining forces in newly deleted cells elements elevates the stress triaxiality and thus artificially accelerates the rate of crack extension. The release of cell forces using a traction-separation model minimizes this eAect while maintaining good numerical convergence of the solutions. Crack growth analyses for a moderate strength steel demonstrate that critical porosity valuesOfEU between 0.1 and 0.2 show almost no eAect on predicted R-curves, while both larger and smaller values lead to low J‐Da curves. Finally, a parametric study indicates that specimens of low-hardening materials and specimens with high crack-front constraint show a stronger influence of large computational load steps and the delayed release of cell forces. Use of the adaptive load control algorithm and the traction-separation model with the controlling parameters described here, minimize numerical eAects on predicted R-curves. 7 2000 Elsevier Science Ltd. All rights reserved.

Refined 3D finite element modeling of partially-restrained connections including slip

This study presents an approach for refined parametric three-dimensional (3D) analysis of partially-restrained (PR) bolted steel beam-column connections. The models include the effects of slip by utilizing a general contact scheme. Non-linear 3D continuum elements are used for all parts of the connection and the contact conditions between all the components are explicitly recognized. A method for applying pretension in the bolts is introduced and verified. The effect of several geometrical and material parameters on the overall moment–rotation response of two connection configurations subject to static loading is studied. Models with parameters drawn from a previous experimental study of top and bottom seat angle connections are generated in order to compare the analyses with test results, with good prediction shown by the 3D refined models. The proposed 3D modeling approach is general and can be applied for accurate modeling of a wide range of other types of PR connections. A pronounced effect of slip and friction, between the connection components is shown with connections having thicker (stiffer) seat angles. This study demonstrates the effects of clamping through the bolts and contact between the components on the overall non-linear moment–rotation response. Equivalent moment–rotation responses of pull-test simulations are compared to FE model responses of full connections without web angles. The moment–rotation from the pull test is shown to be equivalent to that of the full FE model for small rotations. As the rotation increases a softer response is shown by the pull tests.  2002 Elsevier Science Ltd. All rights reserved.

Nonlinear behavior of pultruded FRP composites

Abstract Coupon tests are investigated and used to calibrate three-dimensional (3D) micromechanical models and to verify their prediction for the nonlinear elastic behavior of pultruded fiber reinforced plastic composites. The tested composite material system is made from E-glass/vinylester pultruded composite plate with both glass roving and continuous filament mat (CFM) layers. Tension, compression, and shear tests were performed, using off-axis coupons cut with different roving reinforcement orientations. The overall linear elastic properties are identified along with the nonlinear stress–strain behavior under in-plane multi-axial tension and compression loading. The tests were carried out for coupons with off-axis angles: 0, 15, 30,45, 60, and 90°, where each test was repeated three to five times. Finite element analyses are used to simulate the off-axis tests and examine the effects of coupon geometry, end-clamping condition, and off-axis orientation, on the spatial distribution of the axial strains at the center of the coupons. Lower initial elastic modulus and a softer nonlinear stress–strain responses were consistently observed in the tension tests compared to those in compression, for all off-axis (roving) orientations. The nonlinear behavior can be attributed to the relatively low overall fiber volume fractions (FVFs) in pultruded composites and the existence of manufacturing defects, such as voids and microcracks. It is also shown that the end-clamping effects for the tested geometry are relatively small at the center and allow extracting the nonlinear stress–strain response of the anisotropic material. The analytical part of this study includes two (3D) micromechanical models for the roving and CFM layers. Shear tests are used to calibrate the in situ nonlinear elastic properties of the matrix. Good prediction ability is shown by the proposed micromodels in capturing the stress–strain behavior in the off-axis tests.

Dynamic deformation characteristics of porcine aortic valve leaflet under normal and hypertensive conditions

Calcific aortic valve (AV) disease has a high prevalence in the United States, and hypertension is correlated to early onset of the disease. The cause of the disease is poorly understood, although biological and remodeling responses to mechanical forces, such as membrane tension, have been hypothesized to play a role. The mechanical behavior of the native AV has, therefore, been the focus of many recent studies. In the present study, the dynamic deformation characteristics of the AV leaflet and the effects of hypertension on leaflet deformation are quantified. Whole porcine aortic roots were trimmed and mounted in an in vitro pulsatile flow loop and subjected to normal (80/120 mmHg), hypertensive (120/160 mmHg), or severe hypertensive (150/190 mmHg) conditions. Local valve leaflet deformations were calculated with dual-camera photogrammetry method: by tracking the motion of markers placed on the AV leaflets in three dimensions and calculating their spatial deformations. The results demonstrate that, first, during diastole, high transvalvular pressure induces a stretch waveform which plateaus over the diastolic duration in both circumferential and radial directions. During systole, the leaflet stretches in the radial direction due to forward flow drag forces but compresses in the circumferential direction in a manner in agreement with Poissons effect. Second, average diastolic and systolic stretch ratios were quantified in the radial and circumferential directions in the base and belly region of the leaflet, and diastolic stretch was found to increase with increasing pressure conditions.

A fluid-structure interaction model of the aortic valve with coaptation and compliant aortic root

While aortic valve root compliance and leaflet coaptation have significant influence on valve closure, their implications have not yet been fully evaluated. The present study developed a full fluid–structure interaction (FSI) model that is able to cope with arbitrary coaptation between the leaflets of the aortic valve during the closing phase. Two simplifications were also evaluated for the simulation of the closing phase only. One employs an FSI model with a rigid root and the other uses a “dry” (without flow) model. Numerical tests were performed to verify the model. New metrics were defined to process the results in terms of leaflet coaptation area and contact pressure. The axial displacement of the leaflets, closure time and coaptation parameters were similar in the two FSI models, whereas the dry model, with imposed uniform load on the leaflets, produced larger coaptation area and contact pressure, larger axial displacement and faster closure time compared with the FSI model. The differences were up to 30% in the coaptation area, 55% in the contact pressure and 170% in the closure time. Consequently, an FSI model should be used to accurately resolve the kinematics of the aortic valve and leaflet coaptation details during the end-closing stage.

Aortic root numeric model: Annulus diameter prediction of effective height and coaptation in post–aortic valve repair

OBJECTIVE The aim of the present study was to determine the influence of the aortic annulus (AA) diameter in order to examine the performance metrics, such as maximum principal stress, strain energy density, coaptation area, and effective height in the aortic valve. METHODS Six cases of aortic roots with an AA diameter of 20 and 30 mm were numerically modeled. The coaptation height and area were calculated from 3-dimensional fluid structure interaction models of the aortic valve and root. The structural model included flexible cusps in a compliant aortic root with material properties similar to the physiologic values. The fluid dynamics model included blood hemodynamics under physiologic diastolic pressures of the left ventricle and ascending aorta. Furthermore, zero flow was assumed for effective height calculations, similar to clinical measurements. In these no-flow models, the cusps were loaded with a transvalvular pressure decrease. All other parameters were identical to the fluid structure interaction models. RESULTS The aortic valve models with an AA diameter range of 20 to 26 mm were fully closed, and those with an AA diameter range of 28 to 30 mm were only partially closed. Increasing the AA diameter from 20 to 30 mm decreased the averaged coaptation height and normalized cusp coaptation area from 3.3 to 0.3 mm and from 27% to 2.8%, respectively. Increasing the AA diameter from 20 to 30 mm decreased the effective height from 10.9 to 8.0 mm. CONCLUSIONS A decreased AA diameter increased the coaptation height and area, thereby improving the effective height during procedures, which could lead to increased coaptation and better valve performance.

A micromechanical constitutive framework for the nonlinear viscoelastic behavior of pultruded composite materials

Abstract This study introduces a new three-dimensional (3D) micromechanical modeling approach for the nonlinear viscoelastic behavior of pultruded composites. The studied pultruded composite system consists of vinylester matrix reinforced with E-glass roving and continuous filament mat (CFM) layers. Micromechanical models are introduced for the roving and CFM layers each having a unit-cell with four fiber and matrix subcells. In addition, a sublaminate model is used to provide for a nonlinear equivalent continuum of a layered medium with alternating roving and CFM layers. The roving layer consists of unidirectional fibers embedded in the matrix; it is idealized as doubly periodic array of fiber with square cross-sections. The CFM layer consists of relatively long, swirl, and randomly oriented filaments. This system is idealized using a weighted-average response of two simplified micromodels with fiber and matrix dominated responses. A new iterative procedure is introduced along with a recursive integration method for the Schapery nonlinear viscoelastic model used for the isotropic matrix subcells of the two micromodels. The fiber medium is considered as transversely isotropic and linear elastic. Incremental micromechanical formulations of the above three micromodels are geared towards the time integration scheme in the matrix phase. New iterative numerical algorithms with predictor–corrector type steps are derived and implemented for the micromodels in order to satisfy the fiber and matrix viscoelastic constitutive relations along with the micromechanical equations in the form of traction continuity and strain compatibility between the subcells. Experimental creep tests are performed with coupons cut from E-glass/vinylester pultruded plate to calibrate and predict the nonlinear viscoelastic response. Three sets of pultruded specimens having off-axis angles: 0°, 45°, and 90° were tested at room temperature under different applied compression stress levels.

A quantitative thermoelastic stress analysis method for pultruded composites

A non-contact Thermoelastic Stress Analysis (TSA) method is proposed to measure the sum of the direct strain components on the coated surface of thick pultruded composites. Traditionally, TSA methods are used to relate the change of surface temperature to the change of the first invariant of the stress. The proposed method takes advantage of the in-plane transversely isotropic surface layer and relates the measured temperature change to the sum of the surface strains because the latter are directly related to the first invariant of stress. Quantitative strain measurements using the TSA method are verified for multi-axial stress states by comparing the measured in-plane strain invariant in plate samples with a circular hole to those obtained from finite element (FE) simulations. Good comparisons are obtained when compared to the FE strain contours.

Cohesive Micromechanics: A New Approach for Progressive Damage Modeling in Laminated Composites:

A new cohesive micromechanical modeling framework is presented for the progressive damage analysis of laminated composite materials and structures. The cohesive micromechanics (CM) modeling approach is based on simplified 3D unit cell with incremental and damage formulations. The unidirectional CM model formulated in this paper is implemented in a local—global nonlinear damage modeling framework that recognizes the fiber and matrix constituents along with the cohesive interface/interphase subcells at the lower level. The cohesive elements are embedded between the fiber—fiber, fiber—matrix, and matrix—matrix subcells. Separate tension and compression traction-separation constitutive relations are used for the cohesive subcells in order to degrade the traction and internal resisting force across the plane between the two adjacent constituents. As a result, progressive damage modeling in the structural level can be achieved at the micromechanical level while maintaining the full advantage of using concurrent nonlinear micromechanical modeling prior and during damage progression spanning the entire structure. The proposed CM damage framework allows nonlinear anisotropic response, including strain softening, and damaged elastic loading/unloading behavior. Robust and efficient numerical stress correction algorithms have been also developed in order to satisfy the local traction continuity and strain compatibility of the micromechanical model. The effectiveness of the proposed modeling approach is demonstrated by predicting the response of composite plates with an open hole under tension and compression loading using available test results from the literature.