A Multiaxial Stochastic Constitutive Law for Concrete: Part I—Theoretical Development

1992 ◽  
Vol 59 (2) ◽  
pp. 283-288 ◽  
Author(s):  
A. Fafitis ◽  
Y. H. Won
Keyword(s):  
Three Dimensional ◽  
Complex Loading ◽  
Uniaxial Stress ◽  
Constitutive Law ◽  
Theoretical Development ◽  
Stress Strain ◽  
Shear Moduli ◽  
Space Truss ◽  
Dependent Behavior ◽  
Path Dependent

An incremental three-dimensional constitutive relation for concrete has been developed. The linear anisotropic and path-dependent behavior is modeled by updating the stiffness matrix at each load increment. The material is assumed incrementally elastic and the six elastic moduli E11, E12 .... E33 are expressed in terms of both the tangential hydrostatic and deviatoric stiffness whereas the three tangential shear moduli are expressed in terms of the deviatoric stiffness only. The hydrostatic and deviatoric stiffness are determined from uniaxial stress-strain relationships by employing the space truss concept. The unaxial stress-strain relationships are in a sense the stress-strain relationships of the members of the truss, and they were based on a rheological stochastic model developed earlier. The predictions of the model compare favorably with experimental data reported by various investigators. Complex loading paths are reproduced with acceptable accuracy as is demonstrated in the second part of this paper.

Simplified Second Stage Creep/Relaxation Analysis of Moderately Complex Spatially Three-Dimensional Piping Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 184-192 ◽  
Author(s):  
G. H. Workman ◽  
E. C. Rodabaugh
Keyword(s):  
Three Dimensional ◽  
Theoretical Development ◽  
Small Displacement ◽  
Piping System ◽  
Stress Strain ◽  
Curved Pipe ◽  
Thermal Change ◽  
Second Stage ◽  
Piping Systems ◽  
Applied Forces

An analysis technique for predicting the second stage creep/relaxation response of moderately complex spatially three-dimensional piping systems is presented herein. The theoretical development of this technique is based on two major assumptions. The first assumption is that at any time the behavior of the piping system can be associated with two components. One is an elastic component which is recoverable, and the other is a creep/relaxation component, which is not recoverable. The second major assumption, the simplifying assumption, is that the creep/relaxation strains due to axial, bending, and torsional loading can be decoupled and strains due to internal pressure can be neglected. Utilizing small displacement linear strain assumptions, the elastic stress-strain and creep/relaxation stress-strain rate laws can be integrated over the pipe’s cross section to yield generalized force-deformation relationships. The method of initial strains associated with the matrix displacement method of structural analysis is now applied to generate the solution of the creep/relaxation problem. This formulation utilizes two distinct types of piping elements. The first is a straight uniform pipe element and the second is a circularly curved pipe element, which incorporates both elastic and creep/relaxation flexibility factors. The end result of this formulation is a digital computer program capable of analyzing spatially three-dimensional piping systems under creep/relaxation conditions that can be represented by a series of straight or circularly curved pipe elements subjected to applied forces, displacements, and/or thermal change. An example analysis is included.

Three-Dimensional Effects of Solder Joints in Micro-Scale BGA Assembly

1999 ◽  
Vol 121 (4) ◽  
pp. 297-302 ◽  
Author(s):  
J. Zhu
Keyword(s):  
Finite Element ◽  
Creep Strain ◽  
Solder Joints ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Computational Time ◽  
Stress Strain ◽  
Micro Scale ◽  
Dimensional Effects ◽  
Solder Balls

Micro-scale BGA has attracted more and more interest due to their high performance/area ratio. This technology is especially important for mobile personal equipment, such as cellular phones and laptop computers. With the decrease of solder ball sizes, the reliability problem becomes the major concern for the package design, which requires more powerful tools to address this issue. Finite element method is a useful tool for packaging design and analysis. For some BGAs, the critical solder balls are sometimes not located at a symmetric plane and the deformations in three directions will affect the distribution of stress/strain in these solder balls. Therefore, a full three-dimensional analysis is necessary to address these effects. However, it is almost impossible to run a three-dimensional single finite element model to consider all design details even with simplified material properties, not to mention creep constitutive law. Therefore, the global/local modeling technique provides an alternate way, which can simplify the modeling work’ Significantly, reduce the computational time, and enhance the crucial information at critical locations. In this study, the global/local technique was used to study a micro-scale BGA assembly and to investigate the three-dimensional effects of stress/strain distribution inside the solder joints. It was found that the maximum creep strain is not located at the plane passing through the package center and solder joint axis. It was also found that the position of maximum creep strain will shift during first several cycles, but will stabilize after the fourth cycle. This result is also helpful in evaluating the reliability of the critical solder joints in micro-scale BGA assemblies.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

scholarly journals Rethinking student-teacher relationships in higher education: a multidimensional approach

2021 ◽  
Author(s):  
Roland Tormey
Keyword(s):  
Higher Education ◽  
Classroom Management ◽  
Student Teacher ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Theoretical Development ◽  
Multidimensional Model ◽  
Three Dimensional Model ◽  
Teacher Relationships ◽  
Student Teacher Relationships

AbstractStudent-teacher relationships play an important role in both teacher and student experiences in higher education and have been found to be linked to learning, classroom management, and to student absenteeism. Although historically conceptualised in terms of immediacy or distance and measured with reference to behaviours, the growing recognition of the role of emotions and of power—as well as the development of a range of multidimensional models of social relationships—all suggest it is time to re-evaluate how student-teacher relationships are understood. This paper develops a theoretical model of student-teacher affective relationships in higher education based on three dimensions: affection/warmth, attachment/safety, and assertion/power. The three-dimensional model was tested using the Classroom Affective Relationships Inventory (CARI) with data from 851 students. The data supported the use of this multidimensional model for student-teacher relationships with both two- and three-dimensional models of relationships being identified as appropriate. The theoretical development of a multidimensional model and the empirical development of an instrument with which to explore these dimensions has important implications for higher education teachers, administrators and researchers.

Stress-strain curve of paper revisited

2012 ◽  
Vol 27 (2) ◽  
pp. 318-328 ◽  
Author(s):  
Svetlana Borodulina ◽  
Artem Kulachenko ◽  
Mikael Nygårds ◽  
Sylvain Galland
Keyword(s):  
Three Dimensional ◽  
Strain Curve ◽  
Failure Behavior ◽  
Three Dimensional Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Fiber Network ◽  
Bonding Parameters ◽  
Particle Level ◽  
The Impact

Abstract We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

scholarly journals Using Externally Bonded CFRP to Repair a PCCP with Broken Wires under Combined Loads

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kejie Zhai ◽  
Hongyuan Fang ◽  
Bing Fu ◽  
Fuming Wang ◽  
Benyue Hu
Keyword(s):  
Prestressed Concrete ◽  
Three Dimensional ◽  
Soil Pressure ◽  
Long Distance ◽  
Stress Strain ◽  
Wire Breakage ◽  
Water Pipelines ◽  
Externally Bonded ◽  
Prestressed Concrete Cylinder Pipe ◽  
Three Dimensional Finite Element

Prestressed concrete cylinder pipe (PCCP) is widely used for long-distance water pipelines throughout the world. However, prestressing wire breakage is the most common form of PCCP damage. For some pipelines that cannot be shut down, a new technique for in-service PCCP repair by externally bonding the pipe with layers of carbon fiber reinforced polymer (CFRP) was proposed. A set of three-dimensional finite element models of the repaired PCCP have been proposed and implemented in the ABAQUS software, which took into account the soil pressure, the weight of the PCCP, the weight of the water, and the hydrostatic pressure. The stress–strain features of the PCCP repaired with CFRP of various thicknesses were analyzed. The stress–strain features of different wire breakage rates for the repaired PCCP were also analyzed. The results showed that the strains and stresses decreased at the springline if the PCCP was repaired with CFRP, which improved the operation of the PCCP. It has been found that the wire breakage rates had a significant effect on the strains and stresses of each PCCP component, but CFRP failed to reach its potential tensile strength when other materials were broken.

Effect of Residual Stress or Plastic Deformation History on Fatigue Life Simulation of Pipeline Dents

2018 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Rick Wang
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Fatigue Life ◽  
Residual Stresses ◽  
Three Dimensional ◽  
Strain History ◽  
Deformation History ◽  
Stress Strain ◽  
Element Analysis ◽  
Fea Model

Mechanical dents often occur in transmission pipelines, and are recognized as one of major threats to pipeline integrity because of the potential fatigue failure due to cyclic pressures. With matured in-line-inspection (ILI) technology, mechanical dents can be identified from the ILI runs. Based on ILI measured dent profiles, finite element analysis (FEA) is commonly used to simulate stresses and strains in a dent, and to predict fatigue life of the dented pipeline. However, the dent profile defined by ILI data is a purely geometric shape without residual stresses nor plastic deformation history, and is different from its actual dent that contains residual stresses/strains due to dent creation and re-rounding. As a result, the FEA results of an ILI dent may not represent those of the actual dent, and may lead to inaccurate or incorrect results. To investigate the effect of residual stress or plastic deformation history on mechanics responses and fatigue life of an actual dent, three dent models are considered in this paper: (a) a true dent with residual stresses and dent formation history, (b) a purely geometric dent having the true dent profile with all stress/strain history removed from it, and (c) a purely geometric dent having an ILI defined dent profile with all stress/strain history removed from it. Using a three-dimensional FEA model, those three dents are simulated in the elastic-plastic conditions. The FEA results showed that the two geometric dents determine significantly different stresses and strains in comparison to those in the true dent, and overpredict the fatigue life or burst pressure of the true dent. On this basis, suggestions are made on how to use the ILI data to predict the dent fatigue life.

scholarly journals Numerical Analysis of the Perforated Steel Sheets Under Uni-Axial Tensile Force

Metals ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 632 ◽  
Author(s):  
Ahmed M. Sayed
Keyword(s):  
Load Capacity ◽  
Tensile Force ◽  
Three Dimensional ◽  
Tensile Load ◽  
Experimental Tests ◽  
Strain Engineering ◽  
Uniaxial Tensile ◽  
Fe Model ◽  
Stress Strain ◽  
Steel Sheets

The perforated steel sheets have many uses, so they should be studied under the influence of the uniaxial tensile load. The presence of these holes in the steel sheets certainly affects the mechanical properties. This paper aims at studying the behavior of the stress-strain engineering relationships of the perforated steel sheets. To achieve this, the three-dimensional finite element (FE) model is mainly designed to investigate the effect of this condition. Experimental tests were carried out on solid specimens to be used in the test of model accuracy of the FE simulation. Simulation testing shows that the FE modeling revealed the ability to calculate the stress-strain engineering relationships of perforated steel sheets. It can be concluded that the effect of a perforated rhombus shape is greater than the others, and perforated square shape has no effect on the stress-strain engineering relationships. The efficiency of the perforated staggered or linearly distribution shapes with the actual net area on the applied loads has the opposite effect, as it reduces the load capacity for all types of perforated shapes. Despite the decrease in load capacity, it improves the properties of the steel sheets.

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