One of the most conspicuous phenomena in the Arctic Is the fracture of sea ice. It is scarcely po... more One of the most conspicuous phenomena in the Arctic Is the fracture of sea ice. It is scarcely possible to travel far without seeing a variety of fracture forms, produced both by natural processes and by human activity. At strain-rates below about 10−4 s−1, deformation is dominated by creep, but at higher strain-rates fracture is much more important. One of the reasons for this is the very low fracture toughness of ice. The movements of ice in contact with offshore structures often induce strain-rates well beyond the level at which fracture begins, and so offshore structures will often operate in the fracture regime, and it is fracture processes which will determine the design loads. We consider the different modes of repeated fracture that will occur, and classify them into distinct mechanisms of crushing, spalling, and radial and circumferential cracking. Experimental and field observations are plotted on a deformation mode map. A theoretical treatment of radial cracking confirms ...
An improved adaptive technique for the finite element formulation of limit analysis problems of s... more An improved adaptive technique for the finite element formulation of limit analysis problems of symmetrically loaded thin shells of revolution is presented. Bending, membrane behavior and changes of curvature are simulated by using an axisymmetrical thin shell element of three nodes associated with a new piecewise linear (PWL) yield surface. The results obtained show better upper bounds when compared to
Page 1. 8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computat... more Page 1. 8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 July 5, 2008 Venice, Italy DIRECT ...
... 轧制, eigenvector. sliding, thrush. texture, 天然气. 内燃机, natural gas. ic engine, t225ng. The Line... more ... 轧制, eigenvector. sliding, thrush. texture, 天然气. 内燃机, natural gas. ic engine, t225ng. The Linear Matching Method for shakedown and Limit Analyses Applied to Rolling and Sliding Point Contact Problems. 通过DOI定位原文. DOI：, 10.3166/rmpd.6.9-30. 作者 ：, HF Chen;ARS Ponter ...
In a previous paper (I)‡ an upper bound on the deformation of a creeping structure subject to con... more In a previous paper (I)‡ an upper bound on the deformation of a creeping structure subject to constant load was derived which remained valid until rupture occurred at the most highly strained point of the body. Here we show that this bound may be used to evaluate a lower bound to the time of initial rupture for a certain class of structures. The method suggests that for many structures simple design calculation of an approximate nature should be possible. Values of the rupture life, obtained using the prediction method, are shown to compare well with the results of experiments carried out on a number of structures.
ABSTRACT The paper derives minimum theorems that characterise the steady state cyclic state of a ... more ABSTRACT The paper derives minimum theorems that characterise the steady state cyclic state of a body subjected to cyclic load and temperature. The inelastic material behaviour is described by a convex flow potential. The model is chosen to provide an intermediary description between perfect plasticity, for which general minimum theorems are already known, and more complex and realistic creep constitutive relationships involving internal state variable. The results presented here provide generalisations of the upper and lower bound shakedown theorems and the general result of A. R. S. Ponter and H. Chen [ibid. 20, 539-553 (2001; Zbl 1002.74018)]. The linear matching method is also discussed and its role as a general programming method is clarified. This allows a discussion of the method as both a kinematic and an equilibrium method. Sufficient conditions for convergence are derived and are shown to correspond to realistic material creep properties only in the case of the kinematic method. This emphasises the view that the method exists as a useful computational tool only as an upper bound method. In an accompanying paper [the authors, ibid. 21, 899-914 (2002; Zbl 1027.74063)] the minimum theorems are applied to the evaluation of design related properties of the cyclic state of a creeping body.
ABSTRACT Although the shakedown theorems for perfect plasticity have been known since Koiter&... more ABSTRACT Although the shakedown theorems for perfect plasticity have been known since Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not appeared in the literature. In this paper a generalisation of the upper bound theorem is derived which reduces to the upper bound shakedown theorem in the limiting case when the load point approaches the shakedown boundary. The new theory is used to develop a method for identifying the ratchet limit for a class of loading histories through the sequential minimisation of two functionals. A programming method, based on the Elastic Compensation method for shakedown is then derived and convergence proven. Numerical examples of the application of the method to practical problems are discussed by us in an accompanying paper.
International Journal of Solids and Structures, 1976
ABSTRACT A method is described of evaluating the creep deformation rate of a body subject to comb... more ABSTRACT A method is described of evaluating the creep deformation rate of a body subject to combined static and dynamic loading. The method is applied to a beam problem and it is shown that the solution may be expressed in terms of a reference stress history which possesses both a static and a dynamic component, independent of material parameters. Experiments on lead beams are shown to correlate quite closely with predicted behaviour.
The paper considers the problem of a plate subjected to constant average in-plane stresses and te... more The paper considers the problem of a plate subjected to constant average in-plane stresses and temperature variations through the thickness of the plate. The material is described by a linear elastic/time-hardening viscous/perfectly plastic idealization. We show that the pertinent phenomenon which occurs due to a variable cyclic temperature history may be exhibited by computing bounding solutions which correspond to very fast and very slow cycling. This problem is typical of the situation which occurs in design of nuclear fuel cans and pressure vessels.
The first quantitative analysis of the forward flow in frictionless rolling contact, firstly disc... more The first quantitative analysis of the forward flow in frictionless rolling contact, firstly discovered experimentally by Crook [Proc. Inst. Mech. Eng. London 171 (1957) 187], was conducted by Merwin [Plastic deformation of surfaces in rolling, Ph.D. Dissertation, Cambridge University, UK, 1962] who attempted to model the ratchetting phenomenon in excess of shakedown (the cumulative forward flow due to continuous shear strain increase observed in experiments) as a function of load using a simple perfect plasticity model and a simplified solution to the elasto-plastic problem. However, later FEM analysis [J. Appl. Mech., Trans. ASME 52 (1985) 67, 75] and more refined calculations still based on perfect plasticity but using distributed dislocations [J. Mech. Phys. Solids 33 (1987) 61], found that the ratchet rate was much higher than what measured in experiments, showing the Merwin's approximate solution method was not effective. However, later analysis have concentrated on sophis...
Computer Methods in Applied Mechanics and Engineering, Nov 1, 2005
ABSTRACT An extension of the linear matching method for shakedown is given here for the Drucker–P... more ABSTRACT An extension of the linear matching method for shakedown is given here for the Drucker–Prager yield condition as an approximation to the Mohr Coulomb slip condition for geotechnical materials. For this yield condition, the established criterion for the application of the method are not satisfied. We here describe adaptations of the method that yields converged solutions. The method is applied to a simple indentation problem as well as 3D rolling contact problem for both an associated and a non-associated flow rules. The developed method is appropriate for the design analysis associated with road pavements and railways foundations.
ABSTRACT Some structural situations encountered in the design of the liquid metal fast breeder re... more ABSTRACT Some structural situations encountered in the design of the liquid metal fast breeder reactor (LMFBR) can be reduced to problems where an element of material is subjected to a constant primary load and a cyclic secondary strain. Three simple material models are used to calculate the amount of primary plastic strain accumulated in this type of problem. The analyses lead to closed form solutions that overestimate the amount of strain accumulated in experiments performed by Lebey et al. (2)† to model these situations.
ABSTRACT This paper examines the thermodynamic structure of constitutive relationships for a comp... more ABSTRACT This paper examines the thermodynamic structure of constitutive relationships for a composite material which consists of n isotropic plastically deforming elements. It is demonstrated that the macroscopic response requires n scalar state variables and n - 1 second order tensor state variables. Deformation bounds for structures subjected to cyclic loading are developed and a two component system is analysed in detail.
One of the most conspicuous phenomena in the Arctic Is the fracture of sea ice. It is scarcely po... more One of the most conspicuous phenomena in the Arctic Is the fracture of sea ice. It is scarcely possible to travel far without seeing a variety of fracture forms, produced both by natural processes and by human activity. At strain-rates below about 10−4 s−1, deformation is dominated by creep, but at higher strain-rates fracture is much more important. One of the reasons for this is the very low fracture toughness of ice. The movements of ice in contact with offshore structures often induce strain-rates well beyond the level at which fracture begins, and so offshore structures will often operate in the fracture regime, and it is fracture processes which will determine the design loads. We consider the different modes of repeated fracture that will occur, and classify them into distinct mechanisms of crushing, spalling, and radial and circumferential cracking. Experimental and field observations are plotted on a deformation mode map. A theoretical treatment of radial cracking confirms ...
An improved adaptive technique for the finite element formulation of limit analysis problems of s... more An improved adaptive technique for the finite element formulation of limit analysis problems of symmetrically loaded thin shells of revolution is presented. Bending, membrane behavior and changes of curvature are simulated by using an axisymmetrical thin shell element of three nodes associated with a new piecewise linear (PWL) yield surface. The results obtained show better upper bounds when compared to
Page 1. 8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computat... more Page 1. 8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 July 5, 2008 Venice, Italy DIRECT ...
... 轧制, eigenvector. sliding, thrush. texture, 天然气. 内燃机, natural gas. ic engine, t225ng. The Line... more ... 轧制, eigenvector. sliding, thrush. texture, 天然气. 内燃机, natural gas. ic engine, t225ng. The Linear Matching Method for shakedown and Limit Analyses Applied to Rolling and Sliding Point Contact Problems. 通过DOI定位原文. DOI：, 10.3166/rmpd.6.9-30. 作者 ：, HF Chen;ARS Ponter ...
In a previous paper (I)‡ an upper bound on the deformation of a creeping structure subject to con... more In a previous paper (I)‡ an upper bound on the deformation of a creeping structure subject to constant load was derived which remained valid until rupture occurred at the most highly strained point of the body. Here we show that this bound may be used to evaluate a lower bound to the time of initial rupture for a certain class of structures. The method suggests that for many structures simple design calculation of an approximate nature should be possible. Values of the rupture life, obtained using the prediction method, are shown to compare well with the results of experiments carried out on a number of structures.
ABSTRACT The paper derives minimum theorems that characterise the steady state cyclic state of a ... more ABSTRACT The paper derives minimum theorems that characterise the steady state cyclic state of a body subjected to cyclic load and temperature. The inelastic material behaviour is described by a convex flow potential. The model is chosen to provide an intermediary description between perfect plasticity, for which general minimum theorems are already known, and more complex and realistic creep constitutive relationships involving internal state variable. The results presented here provide generalisations of the upper and lower bound shakedown theorems and the general result of A. R. S. Ponter and H. Chen [ibid. 20, 539-553 (2001; Zbl 1002.74018)]. The linear matching method is also discussed and its role as a general programming method is clarified. This allows a discussion of the method as both a kinematic and an equilibrium method. Sufficient conditions for convergence are derived and are shown to correspond to realistic material creep properties only in the case of the kinematic method. This emphasises the view that the method exists as a useful computational tool only as an upper bound method. In an accompanying paper [the authors, ibid. 21, 899-914 (2002; Zbl 1027.74063)] the minimum theorems are applied to the evaluation of design related properties of the cyclic state of a creeping body.
ABSTRACT Although the shakedown theorems for perfect plasticity have been known since Koiter&... more ABSTRACT Although the shakedown theorems for perfect plasticity have been known since Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not appeared in the literature. In this paper a generalisation of the upper bound theorem is derived which reduces to the upper bound shakedown theorem in the limiting case when the load point approaches the shakedown boundary. The new theory is used to develop a method for identifying the ratchet limit for a class of loading histories through the sequential minimisation of two functionals. A programming method, based on the Elastic Compensation method for shakedown is then derived and convergence proven. Numerical examples of the application of the method to practical problems are discussed by us in an accompanying paper.
International Journal of Solids and Structures, 1976
ABSTRACT A method is described of evaluating the creep deformation rate of a body subject to comb... more ABSTRACT A method is described of evaluating the creep deformation rate of a body subject to combined static and dynamic loading. The method is applied to a beam problem and it is shown that the solution may be expressed in terms of a reference stress history which possesses both a static and a dynamic component, independent of material parameters. Experiments on lead beams are shown to correlate quite closely with predicted behaviour.
The paper considers the problem of a plate subjected to constant average in-plane stresses and te... more The paper considers the problem of a plate subjected to constant average in-plane stresses and temperature variations through the thickness of the plate. The material is described by a linear elastic/time-hardening viscous/perfectly plastic idealization. We show that the pertinent phenomenon which occurs due to a variable cyclic temperature history may be exhibited by computing bounding solutions which correspond to very fast and very slow cycling. This problem is typical of the situation which occurs in design of nuclear fuel cans and pressure vessels.
The first quantitative analysis of the forward flow in frictionless rolling contact, firstly disc... more The first quantitative analysis of the forward flow in frictionless rolling contact, firstly discovered experimentally by Crook [Proc. Inst. Mech. Eng. London 171 (1957) 187], was conducted by Merwin [Plastic deformation of surfaces in rolling, Ph.D. Dissertation, Cambridge University, UK, 1962] who attempted to model the ratchetting phenomenon in excess of shakedown (the cumulative forward flow due to continuous shear strain increase observed in experiments) as a function of load using a simple perfect plasticity model and a simplified solution to the elasto-plastic problem. However, later FEM analysis [J. Appl. Mech., Trans. ASME 52 (1985) 67, 75] and more refined calculations still based on perfect plasticity but using distributed dislocations [J. Mech. Phys. Solids 33 (1987) 61], found that the ratchet rate was much higher than what measured in experiments, showing the Merwin's approximate solution method was not effective. However, later analysis have concentrated on sophis...
Computer Methods in Applied Mechanics and Engineering, Nov 1, 2005
ABSTRACT An extension of the linear matching method for shakedown is given here for the Drucker–P... more ABSTRACT An extension of the linear matching method for shakedown is given here for the Drucker–Prager yield condition as an approximation to the Mohr Coulomb slip condition for geotechnical materials. For this yield condition, the established criterion for the application of the method are not satisfied. We here describe adaptations of the method that yields converged solutions. The method is applied to a simple indentation problem as well as 3D rolling contact problem for both an associated and a non-associated flow rules. The developed method is appropriate for the design analysis associated with road pavements and railways foundations.
ABSTRACT Some structural situations encountered in the design of the liquid metal fast breeder re... more ABSTRACT Some structural situations encountered in the design of the liquid metal fast breeder reactor (LMFBR) can be reduced to problems where an element of material is subjected to a constant primary load and a cyclic secondary strain. Three simple material models are used to calculate the amount of primary plastic strain accumulated in this type of problem. The analyses lead to closed form solutions that overestimate the amount of strain accumulated in experiments performed by Lebey et al. (2)† to model these situations.
ABSTRACT This paper examines the thermodynamic structure of constitutive relationships for a comp... more ABSTRACT This paper examines the thermodynamic structure of constitutive relationships for a composite material which consists of n isotropic plastically deforming elements. It is demonstrated that the macroscopic response requires n scalar state variables and n - 1 second order tensor state variables. Deformation bounds for structures subjected to cyclic loading are developed and a two component system is analysed in detail.
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Papers by Alan Ponter