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A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 380-396 doi: 10.1007/s11709-018-0471-9

摘要： In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.

关键词： phase field method FEniCS brittle fracture crack propagation variational theory of fracture

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Variational mode decomposition based modal parameter identification in civil engineering

Mingjie ZHANG, Fuyou XU

《结构与土木工程前沿（英文）》 2019年第13卷第5期页码 1082-1094 doi: 10.1007/s11709-019-0537-3

摘要： An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

关键词： modal parameter identification variational mode decomposition civil structure nonlinear system closely spaced modes

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Stability analysis of slopes with planar failure using variational calculus and numerical methods

Norly BELANDRIA, Roberto ÚCAR, Francisco M. LEÓN, Ferri HASSANI

《结构与土木工程前沿（英文）》 2020年第14卷第5期页码 1262-1273 doi: 10.1007/s11709-020-0657-9

摘要： This study investigates the technique of variational calculus applied to estimate the slope stability considering the mechanism of planar failure. The critical plane failure surface should be determined because it theoretically indicates the most unfavorable plane to be considered when stabilizing a slope to rectify the instability generated by several statistically possible planes. This generates integrals that can be solved by numerical methods, such as the Newton Cotes and the finite differences methods. Additionally, a system of nonlinear equations is obtained and solved. The surface of the critical planar failure is determined by applying the condition of transversality in mobile boundaries, for which various examples are provided. The number of slices is varied in one of the examples, while the surface of the critical planar failure is determined in the others. Results are compared using analytical methods through axis rotations. All the results obtained by considering normal stress, safety factors, and critical planar failure are nearly the same; however, in this research, a study is carried out for “ ” number of slices using programming methods. Sub-routines are important because they can be applied in slopes with different geometry, surcharge, interstitial pressure, and pseudo-static load.

关键词： slopes stability planar failure variational calculus numerical methods

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Mechanics analysis of thin-walled box continuous girder with variable cross-sections in considering effect of large deflection and shear lag

Yuji CHEN, Qizhi LUO,

《结构与土木工程前沿（英文）》 2009年第3卷第4期页码 352-356 doi: 10.1007/s11709-009-0057-7

摘要： In order to study the mechanics behavior of a thin-walled box continuous girder with variable cross-sections, using potential variation theories, considering the effect of shear lag of flange’s stress and the nonlinear geometry of vertical displacement, and evolving five generalized displacements with the spline function, the large deflection problem of the thin-walled box continuous girder with variable cross-section was transformed to a nonlinear algebraic equation, which was solved using the Newton-Raphon iterative method. The results of the calculation show that different shear lag warp functions to the cantilever, top and bottom plate should be taken to analyze the mechanics behavior of the thin-walled box continuous girder reliably. The thin-walled box continuous girder with variable cross-sections has more reasonable stress state and is more adaptable for the longitudinal change of internal forces than that with equal cross-sections. The effect of large deflection on the stress and displacement of the thin-walled box continuous girder with variable cross-sections depends on the values of the load.

关键词： thin-walled box girder with variable cross-sections potential variational theory shear lag large deflection problem

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Tests on impact effect of partial fracture at steel frame connections

CHEN Yiyi, BIAN Ruoning

《结构与土木工程前沿（英文）》 2008年第2卷第4期页码 295-301 doi: 10.1007/s11709-008-0049-z

摘要： Impact effect of sudden fracture at steel frame connections under severe earthquake or other extreme loads is presented in this paper. The relation of impulse caused by structural fracture to the release of inner force at the cracked location, the magnitude of the response to impact on the basis of one degree of freedom model, and the ratio of the peak value of response to natural period of the system are investigated. Two types of fracture tests were designed and carried out both on uniaxial steel bar tensioned and moment resistant steel frame model. It is proven that the response during the fracture process can be measured quite well using high-frequency data processing system. It is also revealed that the instant fracture of structural connection is characterized by progressive and partial fracture. Numerical evaluation of the impact effect of connection fracture is carried out.

关键词： structural fracture natural fracture progressive high-frequency

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Effect of fly ash replacement level on the fracture behavior of concrete

Mahdi AREZOUMANDI, Jeffery S. VOLZ

《结构与土木工程前沿（英文）》 2013年第7卷第4期页码 411-418 doi: 10.1007/s11709-013-0228-4

摘要： The production of portland cement–the key ingredient in concrete–generates a significant amount of carbon dioxide. However, due to its incredible versatility, availability, and relatively low cost, concrete is the most consumed manmade material on the planet. One method of reducing concrete’s contribution to greenhouse gas emissions is the use of fly ash to replace a significant amount of the cement. ?This study presents the results of an experimental investigation that evaluates effect of fly ash replacement level on the fracture energy of concrete. This study includes four mixes with 0%, 30%, 50%, and 70% fly ash as a cement replacement. This experimental program consisted of 32 fracture beams to study the fracture behavior of concrete. The experimental fracture energies were compared with the fracture energy provisions of different design codes and also different analytical equations. Furthermore, statistical data analyses (parametric and non-parametric) were performed to evaluate whether or not there is any statistically significant difference between the experimental fracture energies of different mixes. Results of these statistical tests show that the mix with higher level of fly ash replacement level has higher fracture energy.

关键词： concrete fracture energy fly ash

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Computational modeling of fracture in concrete: A review

Luthﬁ Muhammad Mauludin, Chahmi Oucif

《结构与土木工程前沿（英文）》 2020年第14卷第3期页码 586-598 doi: 10.1007/s11709-020-0573-z

摘要： This paper presents a review of fracture modeling of concrete. The complex material, such as concrete, has been widely used in construction industries and become trending issue in the last decades. Based on comprehensive literature review, there are two main approaches considered to-date of concrete fracture modeling, such as macroscopic and micromechanical models. The purpose of this review is to provide insight comparison from different techniques in modeling of fracture in concrete which are available. In the first section, an overview of fracture modeling in general is highlighted. Two different approaches both of macroscopic and micromechanical models will be reviewed. As heterogeneity of concrete material is major concern in micromechanical-based concrete modeling, one section will discuss this approach. Finally, the summary from all of reviewed techniques will be pointed out before the future perspective is given.

关键词： concrete fracture macroscopic micromechanical heterogeneity

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Computational modeling of fracture in capsule-based self-healing concrete: A 3D study

《结构与土木工程前沿（英文）》 2021年第15卷第6期页码 1337-1346 doi: 10.1007/s11709-021-0781-1

摘要： We present a three-dimensional (3D) numerical model to investigate complex fracture behavior using cohesive elements. An efficient packing algorithm is employed to create the mesoscale model of heterogeneous capsule-based self-healing concrete. Spherical aggregates are used and directly generated from specified size distributions with different volume fractions. Spherical capsules are also used and created based on a particular diameter, and wall thickness. Bilinear traction-separation laws of cohesive elements along the boundaries of the mortar matrix, aggregates, capsules, and their interfaces are pre-inserted to simulate crack initiation and propagation. These pre-inserted cohesive elements are also applied into the initial meshes of solid elements to account for fracture in the mortar matrix. Different realizations are carried out and statistically analyzed. The proposed model provides an effective tool for predicting the complex fracture response of capsule-based self-healing concrete at the meso-scale.

关键词： 3D fracture self-healing concrete spherical cohesive elements heterogeneous

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Evaluating the material strength from fracture angle under uniaxial loading

Jitang FAN

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 288-293 doi: 10.1007/s11709-018-0480-8

摘要： The most common experimental methods of measuring material strength are the uniaxial compressive and tensile tests. Generally, shearing fracture model occurs in both the tests. Compressive strength is higher than tensile strength for a material. Shearing fracture angle is smaller than 45° under uniaxial compression and greater than 45° under uniaxial tension. In this work, a unified relation of material strength under uniaxial compression and tension is developed by correlating the shearing fracture angle in theory. This constitutive relation is quantitatively illustrated by a function for analyzing the material strength from shear fracture angle. A computational simulation is conducted to validate this theoretical function. It is full of interest to give a scientific illustration for designing the high-strength materials and engineering structures.

关键词： strength fracture mechanics

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A dimensional analysis on asphalt binder fracture and fatigue cracking

Qian ZHAO, Zhoujing YE

《结构与土木工程前沿（英文）》 2018年第12卷第2期页码 201-206 doi: 10.1007/s11709-017-0402-1

摘要： Fracture and fatigue cracking in asphalt binder are two of most serious problems for pavement engineers. In this paper, we present a new comprehensive approach, which consists both of dimensional analysis using Buckingham Theorem and -integral analysis based on classic fracture mechanics, to evaluate the fracture and fatigue on asphalt binder. It is discovered that the dimensional analysis could provide a new perspective to analyze the asphalt fracture and fatigue cracking mechanism.

关键词： Dimensional analysis asphalt fracture fatigue cracking

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Experimental research on ductile fracture criterion in metal forming

Song YU, Weiming FENG

《机械工程前沿（英文）》 2011年第6卷第3期页码 308-311 doi: 10.1007/s11465-011-0233-z

摘要：

Ductile fracture criterion is key limitation parameter in material forming. Accuracy predicting surface and internal failure in plastic deformation process affects on the technology design of workpiece and die greatly. Tension, compression, torsion and shearing test on 45# steel are utilized for providing the experimental values of the critical values at fracture, and 11 widely used ductile fracture criterion are selected to simulate the physical experiments and their relative accuracy for predicting and quantifying fracture initiation sites are investigated. The comparing results show that metal forming process under high triaxiality can be estimated successively using both Normalized Cockcroft-latham and the Brozzo ductile fracture criteria, but the Ayada and general Rice-Tracey model work very well for the low triaxiality cases.

关键词： ductile fracture criteria metal forming process material experiment stress triaxiality

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Hybrid deep learning model for risk prediction of fracture in patients with diabetes and osteoporosis

《医学前沿（英文）》 2022年第16卷第3期页码 496-506 doi: 10.1007/s11684-021-0828-7

摘要： The fracture risk of patients with diabetes is higher than those of patients without diabetes due to hyperglycemia, usage of diabetes drugs, changes in insulin levels, and excretion, and this risk begins as early as adolescence. Many factors including demographic data (such as age, height, weight, and gender), medical history (such as smoking, drinking, and menopause), and examination (such as bone mineral density, blood routine, and urine routine) may be related to bone metabolism in patients with diabetes. However, most of the existing methods are qualitative assessments and do not consider the interactions of the physiological factors of humans. In addition, the fracture risk of patients with diabetes and osteoporosis has not been further studied previously. In this paper, a hybrid model combining XGBoost with deep neural network is used to predict the fracture risk of patients with diabetes and osteoporosis, and investigate the effect of patients’ physiological factors on fracture risk. A total of 147 raw input features are considered in our model. The presented model is compared with several benchmarks based on various metrics to prove its effectiveness. Moreover, the top 18 influencing factors of fracture risks of patients with diabetes are determined.

关键词： XGBoost deep neural network healthcare risk prediction

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A concise review about fracture assessments of brittle solids with V-notches

Hsien-Yang YEH, Bin YANG

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 478-485 doi: 10.1007/s11709-019-0520-z

摘要：

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used.

关键词： fracture assessment brittle solids V-notches review

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Measurement of dynamic fracture toughness and failure behavior for explosive mock materials

Pengwan CHEN, Zhongbin ZHOU, Shaopeng MA, Qinwei MA, Fenglei HUANG

《机械工程前沿（英文）》 2011年第6卷第3期页码 292-295 doi: 10.1007/s11465-011-0237-8

摘要：

In this work, a pre-cracked semi-circular shaped explosive simulant was loaded using a split Hopkinson pressure bar (SHPB). A high-speed camera was used to capture the deformation and fracture process of the specimen in situ. The digital images were processed using the digital image correlation (DIC) method. Next, full displacement and strain fields were obtained. The displacement vector field shows that the specimen fractured under tensile stress action. The strain field can be used to predict the crack propagation. Results show that the method of combined DIC and SHPB is effective to study the dynamic deformation and fracture behavior of explosive simulants. In addition, the specimen was loaded using a drop weight. The fracture toughness of the specimen was preliminary measured.

关键词： digital image correlation polymer bonded explosive simulant split Hopkinson pressure bar (SHPB) semicircular bending test deformation fracture toughness

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A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture

Yongchang CAI, Hehua ZHU, Xiaoying ZHUANG

《结构与土木工程前沿（英文）》 2013年第7卷第4期页码 369-378 doi: 10.1007/s11709-013-0222-x

摘要： In the framework of finite element meshes, a novel continuous/discontinuous deformation analysis (CDDA) method is proposed in this paper for modeling of crack problems. In the present CDDA, simple polynomial interpolations are defined at the deformable block elements, and a link element is employed to connect the adjacent block elements. The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures. The SIFs (stress intensity factors) for various types of cracks, such as kinked cracks or curved cracks, can be easily computed in the CDDA by using the virtual crack extension technique (VCET). Both the formulation and implementation of the VCET in CDDA are simple and straightforward. Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes, and can automatically simulate the crack propagation without degrading accuracy.

关键词： fracture crack propagation deformable block continuous/discontinuous deformation analysis (CDDA)