### Browsing by Author "Martin, J B"

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- ItemOpen AccessA programming approach to the numerical analysis of elasto-plastic continua(1978) Dittmer, Colin Thomas; Martin, J BThe application of a kinematic minimum principle involving a continuous functional subject to inequality constraints is described for the incremental analysis of elasto-plastic continua. A simple algorithm is used for solution of the resulting mathematical programming problem. The formulation is presented for problems in plane stress, plane strain or axial symmetry, using triangular constant strain finite elements, and is extended to the use of cubic quadrilateral isoparametric elements for which a numerical integration technique is employed to account for elasto-plastic interfaces within elements. The material is assumed to obey the von Mises yield condition, and be either elastic-perfectly plastic or linear kinematic hardening. Computational details and solution techniques are described, and numerical examples compared with experimental and numerical results in the literature. Some assessment is made of the relative computational efficiency of the method.
- ItemOpen AccessBeam models for the hangingwall of deep, tabular excavations in stratified rock(1989) De Villiers, N A; Martin, J B; Bird, Wyndham WadhamIn the South African gold mining industry, mining is being conducted at depths of over 3 000 m below the surface. Severe fracturing and deformation of the rock occurs making it unlikely that stress analysis which treats the rock as a homogeneous elastic material will yield useful results about the behaviour around the excavation. The excavation, or stope, considered in this study is tabular. The stope occurs in stratified rock with bedding planes at approximately 1 m intervals. The height of the stope is about 1 m to 1.5 m and the length increases to over 100 m as mining progresses. Shear fractures initiate ahead of the advancing stope, which together with the bedding planes separate the rock into distinct blocks of relatively intact material. The stratified nature of the material in the hangingwall (or roof) of the excavation, and the lack of cohesion in the bedding planes, suggests that separation occurs along the bedding planes, with each layer supporting its own weight. The lowest of these layers is referred to as the "hangingwall beam". Stope closure occurs at a distance of around 30 to 40 m behind the stope face. This study focuses on the mechanics of the hangingwall beam with particular emphasis on the conditions for stable closure. In order to do this the stope is first analysed using a finite element model which treats the rock as a homogeneous elastic medium. By treating the hangingwall beam as a separate layer, 1 m thick, its behaviour is compared to that observed in practice. We find that the hangingwall beam does separate from the overlying rock, but that the axial stresses in the beam are tensile, thus contradicting the observed behaviour. In practice, compressive stresses exist in the hangingwall and footwall. It has been suggested that slip along the shear fractures generates the compressive stresses. In constructing a mathematical model of the hangingwall beam we consider the beam to be made up of blocks 1 m deep and 1 m long. The blocks are treated as a homogeneous elastic material. The behaviour of such a beam is different from that of a fully homogeneous beam, because of the possibility of the formation of hinges. By considering a range of simplified models of a beam composed of blocks, various questions regarding its stability can be addressed. These models consider beams of fixed span in which the weight is increased from zero to the full value. The largest unsupported halfspan which can be stably equilibrated is of the order of 31 m. The maximum stable deflection is 0. 4 m, and therefore additional support is required to allow closure to occur statically. The nature of a single supporting spring that will let down the beam in a limiting, stable manner is identified. Once closure has taken place, the hangingwall beam is stable. In order to obtain a realistic picture of the steady state configuration of the hangingwall beam, an analysis is performed which simulates the advancing stope face. The results show that the distance between the face and the point of closure is around 34 m which is in accord with the behaviour observed in practice. The results have shown that the model which treats the hangingwall as a beam composed of blocks provides useful information about the mechanics of the hangingwall.
- ItemOpen AccessConstitutive modelling and finite element analysis in geomechanics(1984) Resende, LuÃs Nuno da Costa; Martin, J BThe major objective of the work presented in this thesis was the development of a constitutive model for hard rock at high pressure. The model should capture the important features of material behaviour and should be soundly based on mechanical principles; furthermore it should be simple enough to permit implementation and use in large general purpose finite element codes. As a preliminary exercise, a state-of-the-art plasticity cap model was developed in order to provide a basis for comparison with the new model. Existing cap models were shown to exhibit certain inconsistencies associated with the suppression of a regime of potentially unstable behaviour; these inconsistencies were identified and eliminated in. the formulation which is presented in this thesis. The new rock model was based on internal damage concepts. The model is isotropic, and internal damage is measured by a scalar damage parameter. The properties of the material degrade as the damag~ parameter increases, and an evolution law governs the rate at which damage occurs. The damage model was calibrated against experimental results for Bushveld Norite, which is a very hard, brittle rock. The general form of the model, however, is suitable for application to soil and concrete. Both the plasticity cap model and the damage model were implemented into the finite element code NOSTRUM (developed by the Applied Mechanics Research Unit at the University of Cape Town). Solutions of a series of boundary value problems, including typical mining excavation problems, are presented to illustrate and compare the models.
- ItemOpen AccessDeformation theory analysis of a dynamically loaded rigid-plastic cantilever(1980) Liebenberg, Franciscus Xavierius; Martin, J BTaya and Mura (1974) introduced a new thought into rigid-plastic approximate methods by presenting what was claimed to be an extension of Hamilton's Principle (normally considered to be restricted to conservative systems) to rigid-plastic structural dynamics. A comment by Professor A.R.S. Ponter, however, has led to the present study. Professor Ponter queried whether Taya and Mura had indeed extended Hamilton's Principle; it could equally well be interpreted that in the limited applications which they considered they had replaced the usual non-holonomic viscous rigid-plastic relation by a holonomic deformation theory or non-linear elastic relation. This interpretation can be made because Taya and Mura did not consider any applications in which unloading took place.
- ItemOpen AccessDevelopment of a constitutive model for a heaving clay from Rosebank(1993) Wiseman, K H; Martin, J B; Scheele, FHeaving clays are partially saturated soils composed of a high fraction of the montmorillonite clay mineral. When exposed to free water they undergo volumetric expansion, which often results in differential movements at the surface and damage to building structures founded on the clay. The economic consequences of such damage is severe. Heaving clay causes in excess of R100 million damage in South Africa each year, making it the country's most significant problem soil. The best method of dealing with a heaving clay is through appropriate design. This would be facilitated if methods such as finite element analysis were available to designers. The aim of this research project was to develop a constitutive model for an expansive clay which could be numerically implemented within the finite element method. A review of available literature on expansive clays showed that the heave strain that clay under an applied load will undergo can be expressed in terms of the parameters percent heave and heave pressure. These parameters are influenced by the degree of moisture changes experienced by the soil, and its dry density. Various different methods of establishing the percent heave and heave pressure have been proposed, but the values given by each differ due to the influence of different test stress paths on the results. More detailed examination of the effect of test stress path on the volume of heaving clays was therefore required to resolve the reasons for the differences in the test results, and to give a fuller understanding of the volumetric response of the material for the purposes of developing the constitutive model. Hence a series of laboratory tests was conducted on a clay from Rosebank in the Cape Province to investigate the effect of test stress path on the clay volume.
- ItemOpen AccessFinite element nonlinear stability analysis of framed structures(1985) McAdie, R L; Martin, J BThe development of efficient and accurate finite element modelling techniques for the routine analysis of elastic-plastic stability problems in frame structures is addressed. The necessary models, solution procedure and geometric algorithm used for nonlinear stability analysis of frames are presented. An available finite element code, NOSTRUM, which had the basic algorithms necessary to carry out nonlinear analysis was used as the starting point. The Timoshenko beam/frame elements with a layered representation of the cross-section, uniaxial elasticplastic constitutive models, different integration procedures and simplified large deformation geometric assumptions incorporated into NOSTRUM are discussed in detail. Numerical examples are given to validate the algorithms implemented and to provide the experience necessary to give guidelines for the adequate choice of discretization and numerical schemes to be used in routine nonlinear stability analysis of frame structures.
- ItemOpen AccessLarge deformation of rigid-viscoplastic cantilevers subjected to impulsive loading(1984) Trossbach, Rolf; Martin, J BThe problem of a ductile metal cantilever structure (not necessarily initially straight) subjected to dynamic loads leading to deformations of the order of the dimensions of the structure is considered. The material is treated as rigid-viscoplastic; in this idealisation elastic effects are ignored, and the dependence of the yield stress on the rate of strain is taken into account. The problem is first analysed as one of impulsive loading, using the concepts of the mode approximation technique. A new algorithm for the determination of mode shapes is presented for small displacement assumptions and then extended to incorporate geometric effects. An algorithm is given for the time integration of the motion in which the geometry of the st ructure is updated. Applications of the method are described for impulsive loading, and extended to a type of pipe-whip problem where the loading is a combination of an impulse and a pulse which acts in the direction of the tangent at the tip of the cantilever structure at each instant. Illustrative examples are presented which show that the algorithms can be used to give very good predictions of the displaced shape of the structures under consideration.
- ItemOpen AccessA model for the time dependent behaviour of rock joints(1989) Camp, Nicholas Julian; Martin, J B; Bird, Wyndham WadhamThis thesis is a theoretical investigation into the time-dependent behaviour of rock joints. Much of the research work that has been conducted to date in the area of finite element analysis has been involved with the development of special elements to deal with these discontinuities. A comprehensive literature survey is undertaken highlighting some of the significant contributions to the modelling of joints. It is then shown how internal variables can be used to model discontinuities in the rock mass. A finite element formulation is described resulting in a system of equations which can easily be adapted to cope with various constitutive behaviours on the discontinuities. In particular, a viscoplastic relationship; which uses a homogeneous, hyperbolic yield function is adopted. The viscoplastic relationship can be used for both time-dependent (creep) or quasi-static (elasto-plastic) problems. Time-dependent behaviour requires a time integration scheme and therefore a generalised explicit/implicit scheme is chosen. The resulting numerical algorithms are all implemented in the finite element program, NOSTRUM. Various examples are presented to illustrate certain features of both the formulation and the numerical algorithm. Jointed rock beams and a jointed infinite rock mass are modelled assuming plane strain conditions. Reasons are proposed to explain the predicted behaviour. The results of the analysis shows that the internal variable formulation successfully models time-dependent joint movements in a continuous media. The method gives good, qualitative results which agree with observations in deep level mines. It is recommended that quantitative mine observations be used to calibrate the model so that usable predictions of joint movement can be made. This would enable any new developments to be implemented in the model. Further work on implicit methods might allow greater modelling flexibility by reducing computer run times.
- ItemOpen AccessNumerical investigation of the edge profile in hot-rolling(1992) Veale, John; Mercer, Colin Douglas; Martin, J BDuring the hot-rolling of aluminium ingot into sheet, the material elongates in the rolling direction as it is reduced vertically. The spread which occurs in the lateral direction during the multiple pass schedules used in industry is minimal. However, the deformation on these edges is important. During the initial passes a concave profile develops - the material near the surfaces spreads outward while the material at the centre moves inward. The concave profile can lead to defects in the final product; these are the 'roll over' of material from the edges to the top and bottom surfaces, the fold over of material in the centre of the edge, and the formation of vertical edge cracks. To remove these the edges are trimmed at the end of the process. Research work in this area was motivated by the possibility of identifying means of reducing the amount of material that needs to be trimmed. The objectives of this thesis are to develop techniques of simulating the rolling, and to use these to investigate the deformation mechanisms which lead to the concave edge profile. Models of the rolling were developed using the general purpose, non-linear finite element code ABAQUS. To reproduce the edge profiles accurately requires large three-dimensional models, for which the explicit dynamic method was found to be the most suitable. The results of the analyses were used to investigate the mechanisms which lead to the concave edge profile. In the roll-gap the work-load arches through the ingot; and for roll passes with small reductions a stress pattern occurs which leads to the concave edge profile. In this pattern the stresses of highest magnitude at the surfaces are compressive stresses in the vertical direction, while in the centre of the ingot they are orientated in the rolling direction and are tensile. Thus deformation occurs by vertical compression near the surfaces, and by stretching in the rolling direction at the centre. At the edges the material is not constrained laterally; and due to the Poisson effect, the material spreads outward near the surfaces, and moves inward at the centre. The effect of certain variables on the edge profile were investigated with the modelling. The friction between the work-rolls and the ingot was found to have significant influence on the amount of lateral surface spread. Work hardening, strain rate and temperature effects in the material lead to variations in the yield stress through the height of the ingot. These effects were included in the modelling and were found to affect the shape of the profile, but to a lesser extent than the friction.
- ItemOpen AccessThe numerical modelling of transformation induced plasticity in the deep drawing of stainless steel(1994) Ward, John Douglas Bain; Martin, J BSheet metal forming processes are an important part of many manufacturing operations today. The numerical simulation of these processes has become an important aspect in the design of the processes and in the understanding of the material forming itself. This thesis document describes the development and formulation of a material model which was used in the numerical simulation of deep drawing problems. The purpose of the material model was to predict the formation of martensite during the plastic straining of metastable austenitic stainless steel and the effect of the martensite formation on the plasticity of the steel. The model was developed from existing work as a modified von Mises isotropic hardening elastic-plastic algorithm. The algorithm was implemented as the subroutine UMAT in the finite element program ABAQUS. Finite element simulations employing the material model were performed on two axisymmetric deep drawing examples. The finite element analysis was performed as a coupled displacement-temperature analysis. The simulations produced results which predicted the distribution of various material state variables such as the volume fraction of martensite, plastic strain, yield stress and temperature in the formed component. The results were consistent with what is intuitively expected from the physics of the problem. They were able to explain phenomena observed in physical tests such as the location of failures in the formed components and the occurrence of delayed cracking. It is concluded that the model was successful in providing qualitative information on the distribution of martensite in components formed by deep drawing. These predictions were for a broad range of stainless steel behaviour. However, extensions to the model are required to be able to make accurate quantitative predictions on the formation of martensite in specific materials.
- ItemOpen AccessNumerical simulation of the casting process(1989) Bowles_HC; Martin, J BThe increasingly competitive market for cast products has required the development of higher quality and lower cost products. Although conventional process development techniques have improved, the cost and time associated to process development needs to be reduced. A faster and more cost-effective development method is required. Numerical modelling techniques provide a means by which casting design and process parameters can be optimized with minimum use of prototypes. This thesis reviews the current state of the art in solidification modelling. A typical casting problem is modelled, and the numerical results compared against measured temperatures. further work is required to from this investigation it is concluded that obtain, and accurately model the material properties and complex radiation behaviour within the fibrous insulation.
- ItemOpen AccessNumerical simulation of the plastics injection moulding process(1994) De Kock, Willem Johan; Martin, J B; Reddy, B DayaThe Hele-Shaw formulation is widely used for the simulation of the injection moulding process. The influence of the Hele-Shaw approximations is, however, unknown. A two-dimensional numerical model based on the Hele-Shaw formulation, and a model based on the Navier-Stokes equations without the Hele-Shaw approximations were developed. The solutions obtained with these two approaches were compared to investigate the influence of the Hele-Shaw approximations on the simulation of the injection moulding process. Weakly compressible, non-Newtonian flow of an amorphous polymer melt under non-isothermal conditions were simulated using constitutive equations generalized to non-Newtonian materials. The finite volume method, which is a very powerful method yet easy to use, was used to discretize the governing equations as compared to finite element methods used in most other reported models. The influence of the Hele-Shaw approximations on the solutions of specific flow cases was determined by comparing the solutions obtained with the model based on the Hele-Shaw formulation and the model based on the Navier-Stokes equations. Parametric studies were done to compare the solutions of the two numerical models for a wider range of flow cases. The following conclusions were made as a consequence of this study: Numerical models to simulate the injection moulding process can be simplified and the computer time required to solve these models can be reduced by using the Hele-Shaw formulation instead of solving the full Navier-Stokes equations. Numerical models based on the Hele-Shaw formulation are well suited to simulate the injection moulding process when the geometries and flow conditions fall within certain limits. These limits are determined by the combined effect of the geometry and the flow conditions represented by the Reynolds number. The simplicity of the finite volume method used in the generalized Hele-Shaw model makes it an attractive model to use for injection moulding simulations.
- ItemOpen AccessThe performance of high speed reciprocating polymer seals in water(1991) Barnes, Jonathan James; Martin, J BThe elastohydrodynamic lubrication of polymeric piston seals in a water powered rockdrill has been modelled in this thesis. Current seal designs, consist of an Ultra High Molecular Weight Polyethylene (UHMWPE) ring, energised to remain in contact with the reciprocating piston, using a nitrile rubber o-ring. The design of the seals is such that they do not facilitate the formation of a lubricating film, and the high contact stresses at the seal face due to the seal pressure cause excessive wear of the seals. The elastohydrodynamic model is based on a numerical algorithm in which the elasticity equations for the seal deflection and the one dimensional lubrication equation have been solved simultaneously. The polymeric ring has been simplified due to its axisymmetry, and modelled in cross section as an elastic beam resting on a spring base, while the deformation of the o-ring has been considered independently since the moduli of the two materials differs by nearly two orders of magnitude. The o-ring was modelled using the non-linear Mooney-Rivlin constitutive equation implemented in the finite element code ABAQUS. With this model, the contact stresses existing between the o-ring and the back of the polymer seal have been determined for a range of o-ring squeezes and rubber hardnesses. The resultant lubrication and o-ring forces acting on the rectangular polymer seal have been used in a finite difference formulation of the seal (or beam on a spring base) to determine the seal deflection above the piston.
- ItemOpen AccessThe permanent deformation of circular cylindrical shells subjected to internal explosive loading(1978) Upsher, Stanley Minnaar; Martin, J BThis work describes what is primarily an investigation into methods for estimating the maximum permanent deformation of a circular cylindrical shell subjected to internal explosive loadings. A complete rigid-plastic analysis of the transient response is performed. Subsequently the effects of material properties are included. Finally the theoretical predictions are compared with the experimental results obtained from a series of tests on aluminium shell specimens.
- ItemOpen AccessA programming approach to the numerical analysis of elasto-plastic continua(1978) Dittmer, Colin Thomas; Martin, J BThe application of a kinematic minimum principle involving a continuous functional subject to inequality constraints is described for the incremental analysis of elasto-plastic continua. A simple algorithm is used for solution of the resulting mathematical programming problem. The formulation is presented for problems in plane stress, plane strain or axial symmetry, using triangular constant strain finite elements, and is extended to the use of cubic quadrilateral isoparametric elements for which a numerical integration technique is employed to account for elasto-plastic interfaces within elements. The material is assumed to obey the von Mises yield condition, and be either elastic-perfectly plastic or linear kinematic hardening. Computational details and solution techniques are described, and numerical examples compared with experimental and numerical results in the literature. Some assessment is made of the relative computational efficiency of the method.