Continuous Variation Modelling within the Natural Stress-strain Space of Metallic Materials


In day-to-day engineering and industrial applications, plates/plate elements are required to withstand a wide range of in-plane and out-of-plane loading conditions. Under such conditions, the compressive buckling resistance becomes of primary concern to the designer. In particular, most engineering applications use moderately thick-to-thick plates thereby introducing intricacies in the approximation of the member’s buckling capacity. Consequently, it also increases the likelihood of inelastic buckling. As such, the elastic and inelastic buckling phenomena in metal plates has become a popular research area. Considerable amount of information regarding the latter is available as it has been analytically, empirically and numerically investigated for almost two centuries.

Current stress-strain models are mainly in the form of a power-law relationship, which expresses the strain as a function of the stresses. However, approximation of the true stress-true strain relationship of metallic materials using the simple power-law expressions has been observed to be inadequate for accurately predicting the stress-strain behavior beyond a limited strain range. Worse off, the more advanced stress-strain models are characterized by increased complexity due to requirement of a large number of constituent parameters.

In view of this, scientists at University of Alberta: Dr. Onyekachi Ndubuaku, Professor J.J. Roger Cheng, and Professor Samer Adeeb, in collaboration with Michael Martens at TransCanada Pipelines Ltd. and Dr. Xiaoben Liu at China University of Petroleum, developed a novel facile true stress-true strain equation with the capability to accurately approximate the stress-strain relationship of metallic materials over the full range of strains. Of crucial significance, their proposed model is characteristically unlike existing stress-strain models as it is essentially defined by a Product-Log function using two constitutive model parameters, and can capture a reasonable approximation of the yield plateau in the stress-strain curve. Their work is currently published in the research journal, Construction and Building Materials.

Briefly, the research method applied commenced with the characterization of material properties based on parameterization of the stress-strain curves using a simple and novel mathematical expression. Next, the researchers developed idealized stress-strain relationships using the proposed material mode. They then engaged in extensive parametric numerical analyses purposed to investigate the effect of the material stress-strain properties on the buckling capacity of flat plates.

The authors observed that for the stress-strain curves with a yield plateau, the results of the parametric study showed a minimal influence of the material properties on the buckling capacity of the plates whereas a significant effect of the strain-hardening properties was observed in plates with round-house curves. Additionally, the proposed stress-strain model was shown to be remarkably useful for capturing the relevant intricacies associated with material nonlinearity when predicting the buckling capacity and post-buckling behavior of uniformly-compressed flat plates.

In summary, Dr. Onyekachi Ndubuaku and his colleagues presented a simple finite element method that was successfully used to assess the effects of parametric variation of material stress-strain properties on the ultimate strength and strain capacity of simply-supported flat plates subjected to uniform axial compression. Altogether, the proposed stress-strain model proves to be very versatile in approximating the shape of the stress-strain curve over the entire range of strains, even for materials with a distinct yield point and yield plateau.

Continuous Variation Modelling within the Natural Stress-strain Space of Metallic Materials - Advances in Engineering

About the author

Dr. Onyekachi Ndubuaku is a recent graduate of the Department of Civil and Environmental Engineering at the University of Alberta (UofA) where he completed his Ph.D. studies in Structural Engineering. The research focus of his Ph.D. was on the effects of material stress-strain properties on the deformational capacity of onshore pipelines.

His research at the UofA involved developing and applying a novel material stress-strain characterization method, as well as conducting extensive parametric numerical analyses based on finite element discretization methodology, in order to generate a set of constitutive nonlinear regression equations for predicting the critical limit strain of both pressurized and unpressurized pipelines subjected to various loading conditions.

During the course of his Ph.D. studies, Dr. Ndubuaku was assigned the temporary role of a Principal Instructor for two undergraduate courses at the UofA: (1) Civil Engineering Analysis – which deals with the application of numerical methods to civil engineering problems, and (2) Introduction to Continuum Mechanics – which deals with the fundamental concepts and constitutive laws for stress, strain, and displacements in two and three dimensions, as well as strain energy, virtual work, and the theories of failure.

Prior to the commencement of his Ph.D. studies, Dr. Ndubuaku had gained more than six years’ experience working as a civil structural engineer on various residential, commercial, and industrial building design and construction projects. Through his working experience, he has acquired in-depth technical and practical knowledge of civil engineering design, structural analysis and project management. He also possesses two M.Sc. degrees; one in Structural Engineering from the University of Leeds, England and another in Subsea Engineering from the University of Aberdeen, Scotland.

He currently works as a Research Engineer for Alfa Upgrades Inc., a pipeline company based in Alberta, where he is involved in concept development, experimental validation, and field testing of a novel displacement buffering system for mitigating strain localization and local buckling in buried pipelines subjected to differential ground movement.

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About the author

Professor Samer Adeeb is a Professor in Civil and Environmental Engineering at the University of Alberta. He is an expert in finite element analysis for Structural Engineering applications.

He finished his Ph.D. at the University of Calgary in 2004, after which he worked for two and a half years in the Technical Support and Technology Management department at TransCanada Pipelines Inc. His role included managing and conducting various research involving new pipeline construction projects, and pipeline integrity. Some of the projects that he was involved in included alternate integrity validation, as well as analysis of dents, fatigue, cracks, corrosion, and their combined effects in pipelines. In addition, he was involved in research projects that investigated the mechanical behaviour of high strength steel pipes; in particular, strain based design of high strength steel pipes under combined internal pressure and lateral loading.

Professor Adeeb joined the University of Alberta in 2007. One of his research focus areas is computational mechanics applied to the pipeline industry. Currently, Professor Adeeb’s research projects are conducted in collaboration with various pipeline companies. In one research project, his team of students and researchers investigated the tensile strain capacity of pipelines wherein full-scale tests of pressurized 20-inch X52 pipes with initial circumferential flaws were tested under tensile loading.

In another project, Professor Adeeb’s team studied the combined effect of geometric imperfections and material properties on the mechanical response of high strength steel pipelines under combined loading. His team developed one of the first successful material models that is able to capture the material plastic anisotropy of high strength steel pipelines. This allowed proper investigation of the behaviour of high-strength steel under the combined effect of internal pressure and soil (lateral) loading.

Professor Adeeb is currently working on evaluating various pipeline analysis and design software, including investigating the “Bourdon Effect” in elbows on the stresses and strains developed in pipeline systems.

Google ScholarResearchGate , SCOPUS.


Onyekachi Ndubuaku, Xiaoben Liu, Michael Martens, J.J. Roger Cheng, Samer Adeeb. The effect of material stress-strain characteristics on the ultimate stress and critical buckling strain of flat plates subjected to uniform axial compression. Construction and Building Materials, volume 182 (2018) page 346–359.

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