Nonlinear Analysis of Thin Fracture Specimens Using Solid, Isoparametric Finite Elements

This report examines the performance of various "solid" finite elements for the analysis of thin shell structures often encountered in nonlinear fracture mechanics studies. Such models require solid elements in the crack front region to capture strong through-thickness effects; modeling of the entire test specimen-structural element with solid elements then proves convenient. Unfortunately, the standard 8-node "brick" element with full integration exhibits strong shear-locking under bending deformations and thus overly stiff behavior. Three alternative elements are examined here: the 8-node element with single-point integration, the 8-node element with enhanced (incompatible) modes and the 20-node (quadratic) element. Element performance is assessed through analyses of a thin M(T) fracture specimen loaded in remote tension. This specimen generates strong compressive (T- )stresses parallel to the crack growth direction which leads to out-of-plane bending in the crack front region (triggered by a small normal force). The displacements obtained with a refined mesh of thin shell elements provide the reference solution for evaluation of the solid element performance. The analyses include large-displacement effects, but linear material response for simplicity, and are performed with Abaqus 5.6 and Warp3D. The results show clearly that both the 8-node element with enhanced modes and the 20-node element with conventional reduced integration provide solutions of accuracy comparable to the thin shell element. Mixed 8 and 20-node element meshes for ductile fracture analyses with transition elements to maintain displacement compatibility are demonstrated to provide an accurate and efficient modeling strategy.NASA-AMES Research CenterNASA-Langley Research CenterContract Nos. NCC 2-5126 and NAG 2-112

Recent Development in the Weibull Stress Model for Prediction of Cleavage Fracture in Ferritic Steels

This paper reviews recent developments in the Weibull stress model for prediction of cleavage fracture in ferritic steels. The procedure to calibrate the Weibull stress parameters builds upon the toughness scaling model between two crack configurations having different constraint levels and eliminates the recently discovered non-uniqueness that arises in calibrations using only fracture toughness data obtained under small scale yielding (SSY) conditions. The introduction of a non-zero threshold value for Weibull stress in the expression for cumulative failure probability is consistent with the experimental observations that there exists a minimum toughness value for cleavage fracture in ferritic steels, and brings numerical predictions of the scatter in fracture toughness data into better agreement with experiments. The calibrated model predicts accurately the toughness distributions for a variety of crack configurations including surface crack specimens subject to different combinations of bending tension

Theoretical and Software Considerations for General Dynamic Analysis Using Multilevel Substructured Models

An approach is presented for the dynamic analysis of complex structure sy~t'=!!!S using the finite element method and multilevel substructured models. The fixedinterface method is selected for substructure reduction because of its efficiency, accurac and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. Emphasis is placed on the implementation and performance of the method in a general purpose software system. Solution algorithms consistent with the chosen data structures are presented in detail. This study demonstrates that successful finite element software requires the use of software executives to supplement the algorithmic language. As modeling and analysis techniques become more complex, proportionally more implementation effort is spent on data and computer resource management. Executive systems are essential tools for these tasks. The complexity of the implementation of restart and reanalysis porcedures also illustrate the need for executive systems to support the non computational aspects of the software. The example problems show that significant computational efficiencies can be achieved through proper use of substructuring and reduction techniques without sacrificing solution accuracy. The unique restart and reanalysis capabilities developed in this study and the flexible procedures for multilevel substructured modeling allow analysts to achieve economical yet accurate analyses of complex structural systems

Finite Element Analysis of Concrete Fracture Specimens

The effects of the descending branch of the tensile stress-strain curve, fracture energy, grid refinement, and load-step size on the response of finite element models of notched concrete beams are studied. The width of the process zone and constraint of crack angles are investigated. Nonlinearity is 1 imited to cracking of the concrete. A limiting tensile stress criterion governs crack initiation. Concrete is represented as linear elastic prior to cracking. Cracks are modeled using a smeared representaion. The post-cracking behavior is controlled by the shape of the descending branch, fracture energy, crack angle, and element size. Unloading occurs at a slope equal to the i nitia 1 modulus of the material. load deflection curves and cracking patterns are used to evaluate the beam's response. Comparisons of the process zone size are made. All analyses are performed on a 200 x 200 x GOO mm concrete beam, with an initial notch length of 80 mm. The fracture energy, tensile strength, and shape of the descending branch interact to determine the stiffness and general behavior of the specimen. The width of the process zone has a negligible influence on the beam's response. The importance of proper crack orientation is demonstrated. The model is demonstrated to be objective with respect to grid refinement and load-step size

Thresholds, breakpoints, and nonlinearity in freshwaters as related to management.

Nonlinear ecological responses to anthropogenic forcing are common, and in some cases, the ecosystem responds by assuming a new stable state. This article is an overview and serves as the introduction to several articles in this BRIDGES cluster that are directed toward managers interested in dealing with nonlinear responses in freshwaters, particularly streams. A threshold or breakpoint occurs where the system responds rapidly to a relatively small change in a driver. The existence of a threshold can signal a change in system configuration to an alternative stable state, although such a change does not occur with all thresholds. In general, a mechanistic understanding of ecological dynamics is required to predict thresholds, where they will occur, and if they are associated with the occurrence of alternative stable states. Thresholds are difficult to predict, although a variety of univariate methods has been used to indicate thresholds in ecological data. When we applied several methods to one type of response variable, the resulting threshold values varied 3-fold, indicating that more research on detection methods is necessary. Numerous case studies suggest that the threshold concept is important in all ecosystems. Managers should be aware that human actions might result in undesirable rapid changes and potentially an unwanted alternative stable state, and that recovery from that state might require far more resources and time than avoiding entering the state in the first place would have required. Given the difficulties in predicting thresholds and alternative states, the precautionary approach to ecosystem management is probably the most prudent

Grid Size Effects With Smeared Cracking in Finite Element Analysis of Reinforced Concrete

The effects of modeling parameters on the response of finite element representations of reinforced concrete members are examined. Convergence of load-deflection curves and cracking patterns is studied. Nonlinear behavior is limited to cracking of the concrete and yielding of the reinforcement. The ''smeared" crack representation is governed by a limiting tensile stress criterion. Concrete is treated as linear elastic in compression. Reinforcement has a bilinear stress-strain curve. Constant strain bar elements and rectangular isoparametric elements model the steel and the concrete, respectively. Analyses are performed for flexural members with span-to-depth ratios of 12-1, 5-l and 2-1, under both a uniformly distributed load and a concentrated load at midspan, using a minimum of three variations in grid refinement. Load-deflection curves exhibit convergence with grid refinement. Concrete tensile s tr eng th has a negligible influence on response for the members studied. Load increment size affects the response only in unstable regions of the load deflection curve and does not affect the stiff ness or the post-yield response

Nitrate removal in stream ecosystems measured by 15N addition experiments: Total uptake

We measured uptake length of 15NO3− in 72 streams in eight regions across the United States and Puerto Rico to develop quantitative predictive models on controls of NO3− uptake length. As part of the Lotic Intersite Nitrogen eXperiment II project, we chose nine streams in each region corresponding to natural (reference), suburban-urban, and agricultural land uses. Study streams spanned a range of human land use to maximize variation in NO3− concentration, geomorphology, and metabolism. We tested a causal model predicting controls on NO3− uptake length using structural equation modeling. The model included concomitant measurements of ecosystem metabolism, hydraulic parameters, and nitrogen concentration. We compared this structural equation model to multiple regression models which included additional biotic, catchment, and riparian variables. The structural equation model explained 79% of the variation in log uptake length (SWtot). Uptake length increased with specific discharge (Q/w) and increasing NO3− concentrations, showing a loss in removal efficiency in streams with high NO3− concentration. Uptake lengths shortened with increasing gross primary production, suggesting autotrophic assimilation dominated NO3− removal. The fraction of catchment area as agriculture and suburban-urban land use weakly predicted NO3− uptake in bivariate regression, and did improve prediction in a set of multiple regression models. Adding land use to the structural equation model showed that land use indirectly affected NO3− uptake lengths via directly increasing both gross primary production and NO3− concentration. Gross primary production shortened SWtot, while increasing NO3− lengthened SWtot resulting in no net effect of land use on NO3− removal

Nitrate removal in stream ecosystems measured by 15N addition experiments: Denitrification

We measured denitrification rates using a field 15NO3− tracer-addition approach in a large, cross-site study of nitrate uptake in reference, agricultural, and suburban-urban streams. We measured denitrification rates in 49 of 72 streams studied. Uptake length due to denitrification (SWdenn) ranged from 89 m to 184 km (median of 9050 m) and there were no significant differences among regions or land-use categories, likely because of the wide range of conditions within each region and land use. N2 production rates far exceeded N2O production rates in all streams. The fraction of total NO3− removal from water due to denitrification ranged from 0.5% to 100% among streams (median of 16%), and was related to NH4+ concentration and ecosystem respiration rate (ER). Multivariate approaches showed that the most important factors controlling SWden were specific discharge (discharge / width) and NO3− concentration (positive effects), and ER and transient storage zones (negative effects). The relationship between areal denitrification rate (Uden) and NO3− concentration indicated a partial saturation effect. A power function with an exponent of 0.5 described this relationship better than a Michaelis-Menten equation. Although Uden increased with increasing NO3− concentration, the efficiency of NO3− removal from water via denitrification declined, resulting in a smaller proportion of streamwater NO3− load removed over a given length of stream. Regional differences in stream denitrification rates were small relative to the proximate factors of NO3− concentration and ecosystem respiration rate, and land use was an important but indirect control on denitrification in streams, primarily via its effect on NO3− concentration