2D Plane Stress Model Research Articles

Soil-foundation interaction model for the assessment of tunnelling-induced damage to masonry buildings

Shallow tunnel construction inevitably causes local ground movements to occur. In an urban environment, these ground movements may cause damage to existing buildings on the ground surface. This paper describes a new, simplified, one-dimensional (1D) soil-foundation interaction model for use in damage assessment analyses of buildings that are at risk of tunnelling-induced damage. Simplified models of this sort facilitate efficient building risk assessments for urban infrastructure projects. The proposed soil-foundation interaction model is intended principally for buildings with traditional load-bearing masonry construction founded on embedded shallow foundations. A nonlinear Winkler model (incorporating shear and normal tractions acting on the foundation and the possibility of frictional sliding and gapping beneath the footing) is used to represent the soil-foundation interaction; the model also provides a means of specifying the tunnel-induced ground movements. The soil-foundation interaction model is demonstrated by combining it with a 2D plane stress model of a building facade; the combined model is shown to provide a close representation of the response of the facade to tunnel-induced ground movements, as computed with a corresponding 3D finite element model, but at a small fraction of the computational cost.

Phase-Field Fracture Modelling of Thin Monolithic and Laminated Glass Plates under Quasi-Static Bending

A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass plates, (ii) to assess the consequences of the dimensional reduction of the problem and mesh density and refinement, and (iii) to validate for quasi-static loading the time-/temperature-dependent material properties we derived recently for two commonly used polymer foils made of polyvinyl butyral or ethylene-vinyl acetate. As the nonlinear response prior to fracture, typical of the widely used Bourdin–Francfort–Marigo model, can lead to a significant overestimation of the response of thin plates under bending, the numerical study investigates two additional phase-field fracture models providing the linear elastic phase of the stress-strain diagram. The typical values of the critical fracture energy and tensile strength of glass lead to a phase-field length-scale parameter that is challenging to resolve in the numerical simulations. Therefore, we show how to determine the fracture energy concerning the applied dimensional reduction and the value of the length-scale parameter relative to the thickness of the plate. The comparison shows that the phase-field models provide very good agreement with the measured stresses and resistance of laminated glass, despite the fact that only one/two cracks are localised using the quasi-static analysis, whereas multiple cracks evolve during the experiment. It was also observed that the stiffness and resistance of the partially fractured laminated glass can be well approximated using a 2D plane-stress model with initially predefined cracks, which provides a better estimation than the one-glass-layer limit.

Modeling of RC shear walls strengthened by FRP composites

RC shear walls are considered one of the main lateral resisting members in buildings. In recent years, FRP has been widely utilized in order to strengthen and retrofit concrete structures. A number of experimental studies used CFRP sheets as an external bracing system for retrofitting of RC shear walls. It has been found that the common mode of failure is the debonding of the CFRP-concrete adhesive material. In this study, behavior of RC shear wall was investigated with three different micro models. The analysis included 2D model using plane stress element, 3D model using shell element and 3D model using solid element. To allow for the debonding mode of failure, the adhesive layer was modeled using cohesive surface-to-surface interaction model at 3D analysis model and node-to-node interaction method using Cartesian elastic-plastic connector element at 2D analysis model. The FE model results are validated comparing the experimental results in the literature. It is shown that the proposed FE model can predict the modes of failure due to debonding of CFRP and behavior of CFRP strengthened RC shear wall reasonably well. Additionally, using 2D plane stress model, many parameters on the behavior of the cohesive surfaces are investigated such as fracture energy, interfacial shear stress, partial bonding, proposed CFRP anchor location and using different bracing of CFRP strips. Using two anchors near end of each diagonal CFRP strips delay the end debonding and increase the ductility for RC shear walls.

Finite Element Analysis for evaluating liver tissue damage due to mechanical compression

The development of robotic-assisted minimally invasive surgery (RMIS) has resulted in increased research to improve surgeon training, proficiency and patient safety. Minimizing tissue damage is an essential consideration in RMIS. Various studies have reported the quantified tissue damage resulting from mechanical compression; however, most of them require bench work analysis, which limits their application in clinical conditions of RMIS. We present a new methodology based on nonlinear finite element (FE) analysis that can predict damage degree inside tissue. The effects of the boundary conditions and material property of the FE model on the simulated von Mises stress value and tissue damage were investigated. Four FE models were analyzed: two-dimensional (2D) plane strain model, 2D plane stress model, full three-dimensional (3D) model, and 3D thin membrane model. Nonlinear material properties of liver tissue used in the FEA were derived from previously reported in vivo and in vitro experiments.Our study showed that for integrated von Mises stress and tissue damage computations, the 3D thin membrane model yielded results closest to the full 3D analysis and required only 0.2% of the compute time. The results from 3D thin membrane and the full 3D models fell below plane-strain model and above the plane-stress model. Both stress and necrosis distributions were impacted by the material property of FE models. This study can guide engineers to design surgical instruments to improve patient safety. Additionally it is useful for improving the surgical simulator performance by reflecting more realistic tissue material property and displaying tissue damage severity.

철근 마디형상에 따른 부착특성에 관한 해석적 연구

기존의 많은 연구자들이 철근과 콘크리트 사이의 부착특성에 영향을 주는 다양한 변수에 대하여 연구해왔으며, 특히 최근에는 고강도철근의 등장과 더불어 부착강도의 증진을 위한 연구가 다수 진행 중이다. 철근과 콘크리트 사이의 부착특성은 두 이질재료 사이의 계면조건이 중요한 역할을 하게 되는데, 이 중에서 특히 철근의 마디형상은 계면조건에 가장 큰 영향을 미치게 된다. 본 연구에서는 철근과 콘크리트 사이의 부착거동을 분석할 수 있는 상용 비선형 유한요소프로그램을 사용하여 철근의 마디형상에 따른 부착특성에 대하여 연구하였다. 해석에 사용된 부착모델은 2차원 평면응력요소를 사용하였으며, 주요 해석변수로는 마디각, 마디높이, 마디간격 및 마디면적비이다. 해석결과, 마디각은 30~60도인 범위에서 부착력이 우수한 것으로 나타났으며, 마디높이는 일정구간까지는 부착강도가 증가하나 철근직경의 12%를 초과하면 전단파괴를 유발하여 오히려 부착강도가 감소되고, 마디간격에 대한 효과는 상대적으로 크지 않은 것으로 나타났다. 마디의 높이와 간격을 하나의 지표로 제시할 수 있는 마디면적비는 부착강도의 변화를 효과적으로 나타낼 수 있는 것으로 분석되었으며, 마디면적비는 0.15 이하에서 최대의 효율을 나타내는 것으로 분석되었다. 특히 대형마디(교차마디형상)를 가진 철근인 경우, 타 변수보다 우수한 효율을 나타내어 부착강도 증진효과가 커지는 것으로 평가되었다. Effects of various parameters on bond property between reinforcing bar and concrete are investigated in many researchers, and various study is on going to improve the bond strength. Properties of interface between reinforcement and concrete is important role in bond property. This study analyzed the interfacial bond mechanism between deformed bar and concrete by finite element analysis (FEA) to evaluate the effect of rib shape. The FEA model in this study is simplified 2D plane stress model. The variables of analysis are selected by rib angle, rib height, rib spacing and relative rib area. From the results of analysis, reinforcing bars with rib angle <TEX>$30{\sim}60^{\circ}$</TEX> showed better bond strength than the others. Bond strength ratio following to the rib height is proportionally increased up to the <TEX>$0.12d_b$</TEX>, but rib spacing has little effect on bond strength. The results also indicated that relative rib area can be efficiently represented the properties of deformed shape in reinforcing bars, and zigzagged rib height shape showed excellent bond strength increase.

Experimental and analytical study of the structural response of segmental tunnel linings based on an in situ loading test. Part 2: Numerical simulation

The numerical simulation of the in situ test described in the part 1 of the paper is performed by means of two different approaches: a 2D plane stress model and a 3D shell elements model. A consistent modeling of the tunnel behavior is achieved through the proper simulation of the main phenomena involved on the structural response of the lining: (1) the steel fiber reinforced concrete (SFRC) post-cracking behavior, (2) the detailed behavior of the joints between segments and (3) the ground–structure interaction. The origin and the effects of all these phenomena and the modeling techniques employed to simulate them are carefully described and discussed. Finally, the results obtained are compared with the experimental evidences, showing the excellent accuracy achieved in terms of displacements, joints closures and crack patterns.

Numerical and Experimental Analysis of Crack Closure

The fatigue life of metallic materials is strongly influenced by crack closure effects. Finite element (FE) methods allow the study of crack closure with great detail and can provide valuable information about phenomena occurring in the bulk of the material. In this work the distribution of stresses through the thickness of a cracked specimen has been studied using 3D FE simulations. It was found that the transition between the interior of the specimen (plane strain) and the surface (plane stress) differs from that predicted by 2D plane stress models. In addition, an attempt is presented to experimentally validate the results at the surface level. For this purpose full-field image correlation technique was utilized. This allowed direct comparison between the displacement field predicted by the numerical simulations and the experimental results measured by digital image correlation.

Finite-element modelling of contemporary and palaeo-intraplate stress using ABAQUS™

Knowledge of the contemporaneous and palaeo-orientation of maximum horizontal compressive stress ( S Hmax) in the Earth's crust is important for the exploration and recovery of hydrocarbons and also provides insights into the mechanisms driving plate motion and intra-plate seismicity. To date, most approaches for modelling intraplate stress orientations have been based on applying forces to homogeneous elastic plates. However, real tectonic plates consist of oceanic and continental lithosphere, including sedimentary basins, fold belts and cratons with large differences in elastic properties. We have used the finite-element method as implemented in the software package ABAQUS™ along with the optimisation software Nimrod/O to model the orientations and magnitudes of S Hmax over the Indo-Australian plate for the present and the Miocene. An elastic 2D plane stress model incorporating realistic mechanical properties for the Australian continent was used consisting of 24,400 elements, providing a resolution of 0.2° in both latitude and longitude. In general, modelled S Hmax directions correlate well with observed contemporary stress indicator data and reactivation histories over the NW Shelf and Bass Strait regions of the Australian continent, where Tertiary tectonic reactivation through time is best documented. Large perturbations in S Hmax orientation over the Australian continent are shown to occur in and around regions of heterogeneous material properties.

Modelling the Contemporary and Palaeo Stress Field of Australia using Finite-Element Modelling with Automatic Optimisation

Knowledge of the contemporary and palaeo-orientation of maximum horizontal compressive stress (Sh^) in the Earth's crust is important for the exploration and recovery of hydrocarbons, and provides insights into the mechanisms driving plate motion. To date, most approaches for modelling intraplate stress orientations have been based on applying forces to homogeneous elastic plates. However, real tectonic plates consist of oceanic and continental lithosphere, including sedimentary basins, fold belts, and cratons with large differences in elastic parameters. We have used the finite-element method, as implemented in the software package ABAQUS along with the automatic optimisation software Nimrod/O, to model the orientations and magnitudes of SHmax over the Indo-Australian plate for the present and the Miocene. An elastic 2D plane-stress model incorporating realistic mechanical parameters for the Australian continent was used, consisting of 24 400 elements, providing a resolution of 0.2̊ in both latitude and longitude. In general, modelled SHmax directions correlate well with observed contemporary stress indicator data and reactivation histories over the Northwest Shelf and Bass Strait regions of the Australian continent, where Tertiary tectonic reactivation through time is best documented. Large perturbations in SHmax orientation over the Australian continent are shown to occur in and around regions of heterogeneous material parameters.

An improved 2D model for bonded composite joints

A growing number of structural applications and repairs require strong adhesively bonded joints between composite parts. The viability of the finite elements method (FEM) for the design and analysis of such joints has been shown by several researchers (Composites 13(1982) 29, mechanics and mechanisms of damage in composites and multi-materials, ESIS11, Mechanical Engineering Publications, London, 1991, Structural adhesive joints in engineering, Elsevier Applied science Publishers, Amsterdam, 1984). Most of the proposed plane stress models for adhesively bonded joints have traditionally relied on effective lamina properties for the composite adherends because one of the primary goals was the study of adhesive stresses and failure criteria (J. Adhes. 42 (1993)). Such work has also been usually carried out on mainframe computers. However, with the rapid developments in computing, commercial FE codes now exists for PC applications. These present new possibilities, namely the construction of models which are closer in their approximation to the structures they represent. Within this context, a new 2D plane stress approach has been developed which allows ply-by-ply modelling of composite adherends in a joint. It is a development of the traditional 2D plane stress model used by several authors such as Siener (Compos. Mater.: Testing Des. 10 (1992) 444) in investigating of composite repair joints. This paper reports the application of this new approach to the modelling of scarf joints between composite adherends under tensile loading. Various scarf angles were investigated and ultimate joint failure predicted. The results of the analysis were compared to the experimental results published by Adkins and Pipes (Proceedings of the Fourth Japan–US Conference on Composite Materials, 1988, pp. 845–854). The main aim of work was to develop a model which could provided more information than conventional models. The new approach offers the prospect of accurately modelling more realistic joints because, through the retention of the laminated nature of the composite adherends, scope now exists for the application of more physically based failure criteria. This work has shown that it is possible to model adhesively bonded composite joints using an improved 2D plane stress model which retains the laminated nature of the composite adherends. There was good agreement between the predicted failure loads and the experimental results for 3.0°, 6.2° and 9.2° scarf joints. These predictions are dependent on the type of failure criteria used. For the composite adherends, the maximum stress criterion faired better in predicting the 3.0° scarf joint strength.

An improved 2D model for bonded composite joints

A growing number of structural applications and repairs require strong adhesively bonded joints between composite parts. The viability of the finite elements method (FEM) for the design and analysis of such joints has been shown by several researchers (Composites 13(1982) 29, mechanics and mechanisms of damage in composites and multi-materials, ESIS11, Mechanical Engineering Publications, London, 1991, Structural adhesive joints in engineering, Elsevier Applied science Publishers, Amsterdam, 1984). Most of the proposed plane stress models for adhesively bonded joints have traditionally relied on effective lamina properties for the composite adherends because one of the primary goals was the study of adhesive stresses and failure criteria (J. Adhes. 42 (1993)). Such work has also been usually carried out on mainframe computers. However, with the rapid developments in computing, commercial FE codes now exists for PC applications. These present new possibilities, namely the construction of models which are closer in their approximation to the structures they represent. Within this context, a new 2D plane stress approach has been developed which allows ply-by-ply modelling of composite adherends in a joint. It is a development of the traditional 2D plane stress model used by several authors such as Siener (Compos. Mater.: Testing Des. 10 (1992) 444) in investigating of composite repair joints. This paper reports the application of this new approach to the modelling of scarf joints between composite adherends under tensile loading. Various scarf angles were investigated and ultimate joint failure predicted. The results of the analysis were compared to the experimental results published by Adkins and Pipes (Proceedings of the Fourth Japan–US Conference on Composite Materials, 1988, pp. 845–854). The main aim of work was to develop a model which could provided more information than conventional models. The new approach offers the prospect of accurately modelling more realistic joints because, through the retention of the laminated nature of the composite adherends, scope now exists for the application of more physically based failure criteria. This work has shown that it is possible to model adhesively bonded composite joints using an improved 2D plane stress model which retains the laminated nature of the composite adherends. There was good agreement between the predicted failure loads and the experimental results for 3.0°, 6.2° and 9.2° scarf joints. These predictions are dependent on the type of failure criteria used. For the composite adherends, the maximum stress criterion faired better in predicting the 3.0° scarf joint strength.