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The linear elastic analysis of cracked bodies, crack paths and some practical crack path examples

ENGINEERING FRACTURE MECHANICS 2016年 167卷 2-19页

作者： Pook, L. P. 21 Woodside Rd Sevenoaks TN13 3HF England

The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907. The stress intensity factor concept, introduced in 1957, developed rapidly in the 1960s, with widespread application to practical problems. Finite element analysis had a significant influence on the development of linear elastic fracture mechanics. Corner point singularities were investigated in the late 1970s, but a new field parameter is still needed to describe the stresses at surfaces. There are geometric constraints on permissible fatigue crack paths. Some case studies of fatigue crack paths in metallic materials are included. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： linear elastic analysis Stress intensity factors Corner point singularities Crack paths Finite element analysis

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The linear elastic analysis of cracked bodies and crack paths

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THEORETICAL AND APPLIED FRACTURE MECHANICS 2015年 79卷 34-50页

作者： Pook, L. P. 21 Woodside Rd Sevenoaks TN13 3HF England

The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. linear elastic fracture mechanics (LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. Finite element analysis had a significant influence on the development of LEFM. Corner point singularities were investigated in the late 1970s. It was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that the assumption that crack growth is in model leads to geometric constraints on permissible fatigue crack paths. Current open questions are. The need for a new field parameter, probably a singularity, to describe the stresses at surfaces. The use of strain energy density is promising. Adequate description of fatigue crack path stability. How best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. Development of an adequate plane strain fracture toughness testing standard. Some background information is given in appendices. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： linear elastic analysis Stress intensity factor Corner point singularity Crack path Finite element analysis

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Crack paths and the linear elastic analysis of cracked bodies

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FRATTURA ED INTEGRITA STRUTTURALE 2015年第34期9卷 150-159页

作者： Pook, L. P. 21 Woodside Road Sevenoaks TN13 3HF United Kingdom

The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. linear elastic fracture mechanics (LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. Finite element analysis had a significant influence on the development of LEFM. Corner point singularities were investigated in the late 1970s. It was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that the assumption that crack growth is in mode I leads to geometric constraints on permissible fatigue crack paths. Current open questions are. The need for a new field parameter, probably a singularity, to describe the stresses at surfaces. How best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. Adequate description of fatigue crack path stability.

关键词： linear elastic analysis Stress intensity factors Corner point singularities Crack paths Finite element analysis

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Exploring cracking resistance in modified asphalt mixtures through a comparative assessment of mechanical behavior and performance screening indicators

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CONSTRUCTION AND BUILDING MATERIALS 2025年 464卷

作者： Seitllari, Aksel Virginia Mil Inst 413 Letcher Ave Lexington VA 24450 USA

Fatigue cracking is a prevalent distress, affecting the service life of asphalt pavements. Traditional methods for assessing fatigue resistance can be complex and time-consuming, making it essential to implement more proactive approaches during the mix design and/or quality control process. Screening tests, such as the semi-circular bending (SCB) test with the Illinois flexibility index (FI) variant, have gained traction as a viable alternative. Despite its potential, the FI is often shown to exhibit high variability and lacks sensitivity to certain mix design variables. These limitations have prompted alternative data analysis methodologies and performance indices to evaluate the cracking potential of asphalt concrete. This study presents a comprehensive evaluation of cracking resistance derived from the SCB test results, where multiple performance indicators, including fracture energy (Gf), flexibility index (FI), cracking resistance index (CRI), toughness index (TI), fracture strain tolerance (FST), and Nflex factor, were adopted. Four polymer- modified, dense-graded asphalt mixtures, varying in aggregate types, gradations, and design gyrations, were tested. The efficacy of selected performance criteria to capture the cracking susceptibility of asphalt mixtures, focusing on consistency and reliability, was assessed. While useful for screening exercises, monotonic tests and associated performance indices often overlook critical behaviors, such as stress relaxation, highlighting the need for methods like cyclic loading tests and viscoelastic modeling to improve performance predictions of asphalt mixtures. Consequently, a comparative approach was initiated by benchmarking the results obtained against established fatigue characterization methods like the uniaxial tension/compression (T/C) fatigue test and viscoelastic continuum damage (VECD) analysis in a controlled laboratory environment. Results revealed varying degrees of correlation between SCB-based indicators a

关键词： Cracking resistance Fatigue assessment Performance indices Modified asphalt mixtures Viscoelastic continnum damage linear elastic analysis

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Numerical analysis of fixed-end hollow rectangular beam under uniformly distributed load

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STRUCTURES 2024年 70卷

作者： Haque, Md. Foisal Int Univ Business Agr & Technol Dept Civil Engn Dhaka 1230 Bangladesh GS Res & Design Dhaka 1230 Bangladesh

The purpose of using opening in the reinforced concrete (RC) rectangular beam is the reduction of self-weight, cost, displacement, and strain. Therefore, this research performs linear elastic finite element analysis by using ETABS for fixed-ended RC hollow and solid rectangular beams under uniformly distributed loadings with variable beam lengths, compressive strengths, and opening *** solid and hollow beams are considered to be a 2-nodded line element for the numerical analysis. The maximum range of validation result in case of hollow beam is found to be (3.9 to 7.9) %, which may indicate good accuracy of numerical analysis. The 50 x 50 mm opening size is suitable for 300 x 300 mm RC rectangular beam because of showing the positive normalized deflection of (0-1.45) % and lower strain rates (i.e. 0.13 % and 0.17 %) to compare the solid beam. This research may help professional engineers to use suitable opening size for design and construction works. Although, there is a scope to enhance this research in future by performing nonlinear analysis.

关键词： Finite Element-Based Software ETABS Hollow and solid rectangular beams linear elastic analysis Suitable opening size Uniformly distributed load

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Numerically predicting deflections of mat-sand interaction model under gravity loadings

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DISCOVER MATERIALS 2024年第1期4卷 1-10页

作者： Haque, Md. Foisal Ashraf, Nure Chalkder, Jahidul Islam Musa, Abu Salem Int Univ Business Agr & Technol Dept Civil Engn Dhaka 1230 Bangladesh

This research proposes a novel mat-sand interaction model to evaluate limiting values of sand elastic modulus and super-imposed gravity load for a specific mat thickness to control vertical deflection of mat by using BNBC 2020 prescribed allowable deflection limit. For this reason, the linear elastic analysis is performed by using finite element-based software ETABS v.18.1.1, whereas the impact of sand on the mat is transferred by springs. The difference in results between present and previous studies is obtained to be 1.76%, which may indicate good accuracy of verification of the proposed model with the field study data. The difference in mat vertical deflections between two consecutive sand elastic moduli is obtained to be 7.1%, and it is found to be 32.8% in the case of the mat thickness variations. So, the difference in the case of the sand elastic modulus is reduced by 78.4% compared to the mat thickness. The limiting value of imposed gravity load is found to be 60 kPa for 150 mm mat thickness with a range of sand elastic modulus of (5-25) MPa. Similarly, it is obtained to be 120 kPa in the case of the 200 mm mat thickness for 5 MPa elastic modulus of sand. These findings may help engineers to select suitable mat thickness with corresponding sand elastic modulus and super-structure gravity load.

关键词： linear elastic analysis Mat thickness Sand elastic modulus Super-imposed gravity load Vertical deflection of mat

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Latest findings on the behaviour factor q for the seismic design of URM buildings

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BULLETIN OF EARTHQUAKE ENGINEERING 2022年第11期20卷 5797-5848页

作者： Morandi, P. Butenweg, C. Breis, K. Beyer, K. Magenes, G. Euctr Fdn Dept Bldg & Infrastruct Pavia Italy SDA Engn GmbH Aachen Germany Studio Calvi Pavia Italy Ecole Polytech Fed Lausanne EPFL Sch Architectural Civil & Environm Engn ENAC Earthquake Engn & Struct Dynam EESD CH-1015 Lausanne Switzerland Univ Pavia Dept Civil Engn & Architecture Pavia Italy

Recent earthquakes as the 2012 Emilia earthquake sequence showed that recently built unreinforced masonry (URM) buildings behaved much better than expected and sustained, despite the maximum PGA values ranged between 0.20-0.30 g, either minor damage or structural damage that is deemed repairable. Especially low-rise residential and commercial masonry buildings with a code-conforming seismic design and detailing behaved in general very well without substantial damages. The low damage grades of modern masonry buildings that was observed during this earthquake series highlighted again that codified design procedures based on linear analysis can be rather conservative. Although advances in simulation tools make nonlinear calculation methods more readily accessible to designers, linear analyses will still be the standard design method for years to come. The present paper aims to improve the linear seismic design method by providing a proper definition of the q-factor of URM buildings. These q-factors are derived for low-rise URM buildings with rigid diaphragms which represent recent construction practise in low to moderate seismic areas of Italy and Germany. The behaviour factor components for deformation and energy dissipation capacity and for overstrength due to the redistribution of forces are derived by means of pushover analyses. Furthermore, considerations on the behaviour factor component due to other sources of overstrength in masonry buildings are presented. As a result of the investigations, rationally based values of the behaviour factor q to be used in linear analyses in the range of 2.0-3.0 are proposed.

关键词： Unreinforced masonry buildings Modern constructions Seismic design linear elastic analysis Behaviour factor q Codified procedures

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In-Situ Plate Load Test Measurements of Stress Distribution Properties for Coarse Unbound Granular Materials

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Transportation Geotechnics 2025年 52卷

作者： Hannasvik, Lisa Tronhuus Mork, Helge Evensen, Ragnar Johansen, Johnny M. Hoff, Inge Kierstein, René Department of Civil and Environmental Engineering Norwegian University of Science and Technology Trondheim 7491 Norway ViaNova Trondheim AS Trondheim 7037 Norway Veidekke Entreprenør AS Oslo 0278 Norway ViaNova AS Sandvika 1337 Norway

A field test was conducted to study in-situ stress distribution of coarse crushed rock (CR) materials. The existing literature on CR materials with upper sieve size > 90 mm is very limited, and there is a need to characterize these materials and validate the application of existing theory and models for unbound granular materials. The objective of this paper is to compare plate loading test (PLT) measurements on two CR subbase materials, and to analyze and compare computed and measured vertical stresses below subbase layers of these materials: open-graded CR 22/125 mm and dense-graded CR 0/125 mm. Earth pressure cells (EPCs) were installed to measure vertical stress at 0.6 m depth, σ_0.6, during static PLTs with 300 mm plate diameter. The ratio of σ_0.6 to the average stress at the surface, σ₀, was compared with outputs from Boussinesq's theory and multilayer nonlinear analyses in KENPAVE. The average σ_0.6 for all loading levels during the second cycle of PLT was 41% higher for CR 22/125 as compared to CR 0/125. The average ratio Δσ_0.6/Δσ₀ for EPC measurements were 12.4% and 9.7% for CR 22/125 and CR 0/125, respectively. Based on Boussinesq's theory, Δσ_0.6/Δσ₀ was 8.7%. Computed with KENPAVE, the average Δσ_0.6/Δσ₀ was 5.4% for both sections. The EPC measurements indicate better load distribution properties for dense-graded as compared to open-graded CR. These findings could be applied for empiric design systems by differentiating the load distribution parameters of such materials. Furthermore, the results indicate a need to validate the application of analytical or mechanistic-empirical pavement design tools for pavement structures comprising coarse CR materials. © 2025

关键词： Coarse unbound granular materials Dense-graded aggregates Earth pressure cell linear elastic analysis Load distribution Nonlinear elastic analysis Open-graded aggregates

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An accurate and efficient scheme for linear and nonlinear analyses based on a gradient-weighted technique

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INTERNATIONAL JOURNAL OF NON-linear MECHANICS 2018年 105卷 9-19页

作者： Liu, Pengwei Cui, Xiangyang Wang, Gang Wang, Zhuo Chen, Lei Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Mississippi State Univ Dept Mech Engn Mississippi State MS 39762 USA Hebei Univ Technol Sch Mech Engn Tianjin 300130 Peoples R China

An accurate and efficient gradient weighted finite element method (GW-FEM) is developed for linear elastic, free vibration and material nonlinear analyses. The new approach is based on the triangular and tetrahedral elements that can be generated automatically for any complicated geometries in 2D and 3D spaces. Shepard interpolation technique (SIT) is used to formulate the weighted gradient field considering the effect of the element itself and its adjacent elements sharing common edges (2D) or faces (3D). Due to the simple formulations, the SIT is easily implemented and coded in constructing the weighted gradient field. Both of the linear elastic and work hardening-based elastic-plastic material models are incorporated in the GW-FEM for the linear and nonlinear analyses. The GW-FEM is then coupled with the total strain theory and projection method to solve the nonlinear elastic-plastic problem. Our numerical examples, including both of benchmark and practical engineering cases, reveal that GW-FEM provides superior performance in accuracy and efficiency, compared to the standard finite element method.

关键词： Gradient-weighted technique Finite element method linear elastic analysis Free vibration analysis elastic-plastic analysis

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Simplified procedure for the estimation of local inelastic deformation demands for seismic performance assessment of buildings

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2017年第3期46卷 491-514页

作者： Araujo, Miguel Castro, Jose Miguel Univ Porto Dept Civil Engn Fac Engn Oporto Portugal

The implementation of performance-based design and assessment procedures in seismic codes leads to the need for an accurate estimation of local component demands. According to Part 3 of Eurocode 8 safety checks should be always conducted in terms of plastic rotations, even when linear elastic methods of analysis are used. This paper demonstrates that linear analysis fails to predict inelastic deformation demands at the member level. Therefore, a simplified procedure that allows for the estimation of beam inelastic deformation demands using linear elastic methods of analysis in a simple and conservative way is presented herein. A number of moment-resisting steel frames designed according to different criteria and exhibiting different column-to-beam strength ratios were analysed and used for the derivation of the proposed procedure. A comparative study between alternative methods of quantifying inelastic deformation demands using linear analysis is also carried out. The results obtained allow concluding about the efficiency and conservativeness of the proposed procedure which makes it attractive to be employed in engineering practice. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： chord rotations Part 3 of Eurocode 8 assessment of existing steel buildingschord rotations linear elastic analysis

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