Showing papers on "von Mises yield criterion published in 2006"
TL;DR: In this article, a macroscopic orthotropic yield criterion, which can describe both the anisotropy of a material and the yielding asymmetry between tension and compression, is introduced.
650 citations
TL;DR: In this article, the authors investigated the effect of elastic-plastic normally loaded contact between a deformable sphere and a rigid flat on failure inception under perfect slip and full stick conditions for a wide range of the sphere mechanical properties.
184 citations
TL;DR: In this paper, the authors focus on a model in which shear localization is initiated through shear heating and use linear Maxwell viscoelastic with von Mises plasticity and an exponential dependence of viscosity on temperature.
Abstract: [1] Shear localization is a process of primary importance for the onset of subduction and the evolution of plate tectonics on Earth. In this paper we focus on a model in which shear localization is initiated through shear heating. The rheology employed is linear Maxwell viscoelastic with von Mises plasticity and an exponential dependence of viscosity on temperature. Dimensional analysis reveals that four nondimensional (0-D) parameters control the initiation of shear zones. The onset of shear localization is systematically studied with 0-D, 1-D, and 2-D numerical models, both under constant stress and under constant velocity boundary conditions. Mechanical phase diagrams demonstrate that six deformation modes exist under constant velocity boundary conditions. A constant stress boundary condition, on the other hand, exhibits only two deformation modes (localization or no localization). Scaling laws for the growth rate of temperature are computed for all deformation modes. Numerical and analytical solutions demonstrate that diffusion of heat may inhibit localization. Initial heterogeneities are required to initiate localization. The derived scaling laws are applied to Earth-like parameters. For a given heterogeneity size, stable (nonseismic) localization only occurs for a certain range of effective viscosities. Localization is inhibited if viscosity is smaller then a minimum threshold, which is a function of the heterogeneity size. The simplified rheological model is compared with a more realistic and more complex model of olivine that takes diffusion, power law, and Peierls creep into account. Good agreement exists between the models. The simplified model proposed in this study thus reproduces the main physics of ductile faulting. Two-dimensional late stage simulations of lithospheric-scale shear localization are presented that confirm the findings of the initial stage analysis.
157 citations
Journal Article•
TL;DR: It was concluded that abutment type has significant influence on the stress distribution in bone because of different load transfer mechanisms and the differences in size of the contact area between the abutments and implant.
Abstract: Purpose: The purpose of this study was to investigate the effect of 3 different abutment types on the stress distribution in bone with inclined loads using finite element analysis. Materials and Methods: The 1-body, internal-hex, and external-hex implant systems were modeled to study the effect of abutment type on stress distribution in bone. The bone model used in this study comprised compact and spongious bone assumed to be homogeneous, isotropic, and linearly elastic. Results: In the case of the 1-piece implant, the load was transferred evenly not only in the implant system but also in bone. However, the maximum Von Mises stress generated in bone with the 1-piece implant was always higher than that generated with the internal-hex implant, regardless of load angle inclination. In the case of the internal-hex implant, the contact condition with friction between abutment and implant in the tapered joints and at abutment neck reduced the effect of bending caused by horizontal component of inclined load. The maximum Von Mises stress in bone was the highest for the external-hex implant. Discussion: It was found that the internal-hex implant system generated the lowest maximum Von Mises stresses for all loading conditions because of reduction of the bending effect by sliding in the tapered joints between the implant and abutment. Conclusions: It was concluded that abutment type has significant influence on the stress distribution in bone because of different load transfer mechanisms and the differences in size of the contact area between the abutment and implant. (Basic Science) INT J ORAL MAXILLOFAC IMPLANTS 2006;21:195–202
117 citations
TL;DR: The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes.
Abstract: The use of computational modelling in all areas of science and engineering has in recent years escalated to the point where it underpins much of current research. However, the distinction must be made between computer systems in which no knowledge of the underlying computer technology or computational theory is required and those areas of research where the mastery of computational techniques is of great value, almost essential, for final year undergraduates or masters students planning to pursue a career in research. Such a field of research in the latter category is continuum mechanics, and in particular non-linear material behaviour, which is the core topic of this book. The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes. Of particular interest is the guidance on how to create modules for use with the commercial system Abaqus for specific types of material behaviour. The book is in two parts, the first of which contains six chapters, starting with microplasticity, but predominantly on continuum plasticity. The first chapter on microplasticty gives a brief description of the grain structure of metals and the existence of slip systems within the grains. This provides an introduction to the concept of incompressibility during plastic deformation, the nature of plastic yield and the importance of the critically resolved shear stress on the slip planes (Schmid's law). Some knowledge of the notation commonly used to describe slip systems is assumed, which will be familiar to students of metallurgy, but anyone with a more general engineering background may need to undertake additional reading to understand the various descriptions. Any lack of knowledge in this area however, is of no disadvantage as it serves only as an introduction and the book moves on quickly to continuum plasticity. Chapter two introduces one of several yield criteria, that normally attributed to von Mises (though historians of mechanics might argue over who was first to develop the theory of yielding associated with strain energy density), and its two or three-dimensional representation as a yield surface. The expansion of the yield surface during plastic deformation, its translation due to kinematic hardening and the Bauschinger effect in reversed loading are described with a direct link to the material stress-strain curve. The assumption, that the increment of strain is normal to the yield surface, the normality principle, is introduced. Uniaxial loading of an elastic-plastic material is used as an example in which to develop expressions to describe increments in stress and strain. The full presentation of numerous expressions, tensors and matrices with a clear explanation of their development, is a recurring, and commendable, feature of the book, which provides an invaluable introduction for those new to the subject. The chapter moves on from time-independent behaviour to introduce viscoplasticity and creep. Chapter three takes the theories of deformation another stage further to consider the problems associated with large deformation in which an important concept is the separation of the phenomenon into material stretch and rotation. The latter is crucial to allow correct measures of strain and stress to be developed in which the effects of rigid body rotation do not contribute to these variables. Hence, the introduction of 'objective' measures for stress and strain. These are described with reference to deformation gradients, which are clearly explained; however, the introduction of displacement gradients passes with little comment, although velocity gradients appear later in the chapter. The interpretation of different strain measures, e.g. Green--Lagrange and Almansi, is covered briefly, followed by a description of the spin tensor and its use in developing the objective Jaumann rate of stress. It is tempting here to suggest that a more complete description should be given together with other measures of strain and stress, of which there are several, but there would be a danger of changing the book from an `introduction' to a more comprehensive text, and examples of such exist already. Chapter four begins the process of developing the plasticity theories into a form suitable for inclusion in the finite-element method. The starting point is Hamilton's principle for equilibrium of a dynamic system. A very brief introduction to the finite-element method is then given, followed by the finite-element equilibrium equations and a description of how they are incorporated into Hamilton's principle. A useful clarification is provided by comparing tensor notation and the form normally used in finite-element expressions, i.e. Voigt notation. The chapter concludes with a brief overview of implicit integration methods, i.e. tangent stiffness, initial tangent stiffness and Newton–Raphson. Chapter five deals with the more specialized topic of implicit and explicit integration of von Mises plasticity. One of the techniques described is the radial-return method which ensures that the stresses at the end of an increment of deformation always lie on the expanded yield surface. Although this method guarantees a solution it may not always be the most accurate for large deformation, this is one area where reference to alternative methods would have been a helpful addition. Chapter six continues with further detail of how the plasticity models may be incorporated into finite-element codes, with particular reference to the Abaqus package and the use of user-defined subroutines, introduced via a `UMAT' subroutine. This completes part I of the book. Part II focuses on plasticity models, each chapter dealing with a particular process or material model. For example, chapter seven deals with superplasticity, chapter eight with porous plasticity, chapter nine with creep and chapter ten with cyclic plasticity, creep and TMF. Examples of deep drawing, forming of titanium metal-matrix composites and creep damage are provided, together with further guidelines on the use of Abaqus to model these processes. Overall, the book is organised in a very logical and readable form. The use of simple one-dimensional examples, with full descriptions of tensors and vectors throughout the book, is particularly useful. It provides a good introduction to the topic, covering much of the theory and with applications to give a good grounding that can be taken further with more comprehensive advanced texts. An excellent starting point for anyone involved in research in computational plasticity.
114 citations
TL;DR: The results of the FEM analyses have allowed us to conclude that fibreglass-reinforced composite distributes stress better than titanium alloy or stainless steel and as much radicular dentin as possible should be preserved.
Abstract: Clinicians are opting ever more frequently for restorative materials which have an elastic modulus similar to that of dentin when reconstructing endodontically treated teeth. Metallic posts, which are capable of causing dangerous and non-homogenous stresses in root dentin, are slowly being abandoned. Ideal posts may be those made of various types of fibre (carbon, mineral and glass) and which are adhesively luted into the canal. Among the different methods for evaluating the mechanical behaviour of posts in root canals (progressive loads and photo-elastic technique) the finite element method (FEM) presents many advantages. The aim of this paper is to evaluate, utilizing three-dimensional analysis of the finite elements, what the effect of material rigidity, depth of insertion and post diameter could be on the stress distribution in the different components of the single tooth-post-core reconstruction unit. The results of the FEM analyses, expressed as the distribution of Von Mises stress values, has allowed us to conclude that (i) fibreglass-reinforced composite distributes stress better than titanium alloy or stainless steel; (ii) fibreglass-reinforced composite posts should be inserted as deeply as possible (but maintaining 5-6 mm of gutta-percha apical seal); (iii) fibreglass-reinforced composite post diameter does not affect stress distribution, therefore, as much radicular dentin as possible should be preserved.
108 citations
TL;DR: In this article, a multiaxial yield criterion, referred to as the average shear stress yield (ASSY) criterion for isotropic hardening materials, is developed in order to predict the burst pressure of a pipeline at plastic collapse.
107 citations
TL;DR: A semi-analytical thermo-elastic-plastic contact model has been recently developed and presented in a companion paper as discussed by the authors, where a return-mapping algorithm with an elastic predictor/plastic corrector scheme and a von Mises criterion is now used, which improves the plasticity loop.
Abstract: A semi-analytical thermo-elastic-plastic contact model has been recently developed and presented in a companion paper. The main advantage of this approach over the classical finite element method (FEM) is the treatment of transient problems with the use of fine meshing and the possibility of studying the effect of a surface defect on the surface deflection as well as on subsurface stress state. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and a von Mises criterion is now used, which improves the plasticity loop. This improvement in the numerical algorithm increases the computing speed significantly and shows a much better convergence and accuracy. The contact model is validated through a comparison with the FEM results of Kogut and Etsion (2002, J. Appl. Mech., 69, pp. 657–662) which correspond to the axisymmetric contact between an elastic-perfectly plastic sphere and a rigid flat. A model for wear prediction based on the material removal during cyclic loading is then proposed. Results are presented, first, for initially smooth surfaces and, second, for rough surfaces. The effects of surface shear stress and hardening law are underlined.
101 citations
TL;DR: The three-dimensional FEA model study found that the cement with elastic modulus similar to that of dentin could reinforce weakened root and reduce the stress in dentin, and may be a better choice for the restoration of weakened roots in clinical practice.
Abstract: Background It is very difficult and relatively unpredictable to preserve and restore severely weakened pulpless roots. To provide much needed benefit basis for clinical practice, this study was carried out to analyze the stress distribution in weakened roots restored with different cements in combination with titanium alloy posts. Finite element analysis (FEA) was employed in the study. Methods A pseudo three-dimensional model of a maxillary central incisor with flared root canal, theoretically restored with titanium alloy posts in combination with different cements, was established. The analysis was performed by use of ANSYS software. The tooth was assumed to be isotropic, homogenous and elastic. A load of 100 N at an angle of 45 degrees to the longitudinal axis was applied at the palatal surface of the crown. The distributions of stresses in weakened roots filled with cements of different elastic modulus were analyzed by the three-dimensional FEA model. Results Several stress trends were observed when the stress cloud atlas obtained in the study was analyzed. With the increase of the elastic modulus of cements from 1.8 GPa to 22.4 GPa, the stress values in dentin decreased from 39.58 MPa to 31.43 MPa and from 24.51 MPa to 20.76 MPa (respectively, for maximum principle stress values and Von Mises stress values). When Panavia F and zinc phosphate cement were used, the stress peak values in dentin were very small with no significant difference observed, and the Von Mises stress values were 20.87 MPa and 20.76 MPa respectively. On the other hand, maximum principle stress value and Von Mises stress value in cement layer increased with the increase of the elastic modulus of cements. Conclusions The result of this study demonstrated that elastic modulus was indeed one of the important parameters to evaluate property of the cements. Our three-dimensional FEA model study also found that the cement with elastic modulus similar to that of dentin could reinforce weakened root and reduce the stress in dentin. Thus, it may be a better choice for the restoration of weakened roots in clinical practice.
100 citations
TL;DR: In this article, a three-dimensional finite element analysis (FEA) model is developed to study the effects of three parameters (cutting depth, support length, and pretightening load) on the maximum normal stress and von Mises stress in the region where the edge chipping initiates.
Abstract: Rotary ultrasonic machining (RUM) is one of the machining processes for advanced ceramics. Edge chipping (or chamfer), commonly observed in RUM of ceramic materials, not only compromises geometric accuracy but also possibly causes an increase in machining cost. In this paper, a three-dimensional finite element analysis (FEA) model is developed to study the effects of three parameters (cutting depth, support length, and pretightening load) on the maximum normal stress and von Mises stress in the region where the edge chipping initiates. Two failure criteria (the maximum normal stress criterion and von Mises stress criterion) were used to predict the relation between the edge chipping thickness and the support length. Furthermore, a solution to reduce the edge chipping is proposed based upon the FEA simulations and verified by experiments.
94 citations
TL;DR: In this article, a detailed study on the stress-based forming limit criterion (FLSD) during linear and complex strain paths is developed by applying several combinations of different constitutive equations on the required plastic calculation.
TL;DR: In this paper, a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials is presented, which combines von Mises plasticity with volumetric plastic expansion as induced by the growth of voids and defects in metals.
Abstract: This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.
TL;DR: In this paper, the 3D shell theory is employed in order to provide a new perspective to earthquake-induced strains in long cylindrical underground structures, when soil-structure interaction can be ignored.
TL;DR: In this paper, the material constants of AISI 52100 steel (62 HRc) were determined for both the Internal State Variable (ISV) plasticity model and the conventional Johnson-Cook (JC) model.
Abstract: Work materials experience large strains, high strain rates, high temperatures, and complex loading histories in machining. The problem of how to accurately model dynamic material behavior, including the adiabatic effect is essential to understand a hard machining process. Several conventional constitutive models have often been used to approximate flow stress in machining analysis and simulations. The empirical or semi-empirical conventional models lack mechanisms for incorporating isotropic/kinematic hardening, recovery, and loading history effects. In this study, the material constants of AISI 52100 steel (62 HRc) were determined for both the Internal State Variable (ISV) plasticity model and the conventional Johnson-Cook (JC) model. The material constants were obtained by fitting the ISV and JC models using nonlinear least square methods to same baseline test data at different strains, strain rates, and temperatures. Both models are capable of modeling strain hardening and thermal softening phenomena. However, the ISV model can also accommodate the adiabatic and recovery effects, while the JC model is isothermal. Based on the method of design of experiment, FEA simulations and corresponding cutting tests were performed using the cutting tool with a 20 deg chamfer angle. The predicted chip morphology using the ISV model is consistent with the measured chips, while the JC model is not. The predicted temperatures can be qualitatively verified by the subsurface microstructure. In addition, the ISV model gave larger subsurface von Mises stress, plastic strain, and temperature compared with those by the JC model.
TL;DR: In this paper, the authors evaluated the mechanical stress in reconstruction plates and the screw-bone interface used in bridging a mandibular angle defect by means of the finite element method (FEM).
Abstract: SUMMARY Introduction The objective of the present study was to evaluate the mechanical stress in reconstruction plates and the screw–plate–bone interface used in bridging a mandibular angle defect by means of the finite element method (FEM). The influence of plate geometry as well as the configuration and the diameter of the screws on the mechanical stress distribution was to be determined at the same time and was used as the basis for developing suggestions to optimize the design of the reconstruction plates. Material Based on the geometrical data of a human mandible, an angle defect bridged by a titanium reconstruction plate was generated and exposed to chewing force. First a reconstruction plate was tightly fixed with M2.7 titanium screws. Then, plate design, screw configuration and screw diameter were varied. The mechanical stress was calculated according to von Mises stress hypothesis. Results In the standard reconstruction plate, the result of the finite element analysis revealed stress resulting from the simulated functional loadings which far exceeded the strengths of the components. Possible clinical consequences could be a fatigue fracture of the plate itself, gradual loosening of the osteosynthesis screws and loss of bone. The stress can be reduced to less than half by increasing the diameter of the screw threads 1.5 fold. Conclusion Maximizing the interface between bone and reconstruction plate had a favourable effect. As a consequence of the large interface and a triangular or square configuration of the screws, the stresses could be substantially reduced, the plate could be made thinner and thus better adapted to the mandible. As a preliminary result, the newly designed reconstruction plate could be thinned in areas subject to less mechanical stress.
TL;DR: In this paper, a 3D finite element simulation of a rigid Rockwell C indenter scratching a TiN/Ti-6Al-4V coating/substrate system is presented.
TL;DR: Wang et al. as discussed by the authors developed a multiaxial yield theory for isotropic hardening materials, based on an average shear stress criterion (ASSC), which can well correlate the stress-strain relations for both initial yield and subsequent yield states.
Abstract: It is known that the Tresca yield theory predicts a lower bound of burst pressure, whereas the von Mises yield theory provides an upper bound of burst pressure of pipelines. To accurately predict the burst pressure, the present authors [1] recently developed a new multiaxial yield theory for isotropic hardening materials, based on an average shear stress criterion (ASSC). Extensive classic experiments showed that the ASSC criterion can well correlate the stress-strain relations for both initial yield and subsequent yield states. Based on the ASSC yield theory, a new theoretical solution of the burst pressure of pipelines at plastic collapse is developed as a function of pipe geometry, material hardening exponent, and ultimate tensile strength. This solution is then validated by experimental data for various pipeline steels. The ASSC yield theory is further applied to accurately determine actual burst pressure using available finite element software like ABAQUS, which currently adopts the von Mises yield criterion and the associate flow rule for isotropic elastic-plastic analysis. Four burst failure criteria: the Mises equivalent stress criterion, the maximum principal stress criterion, the Mises equivalent strain criterion and the maximum tensile strain criterion are developed as functions of the ultimate tensile stress and the strain hardening exponent. Application demonstrates that the proposed failure criteria in conjunction with ABAQUS numerical analysis can accurately determine burst pressure of pipelines.Copyright © 2006 by ASME
TL;DR: In this article, a model for multiple repeated loading and unloading of an elastic-plastic sphere and a rigid flat is presented to cover a wide range of loading conditions far beyond the elastic limit.
TL;DR: In this paper, a phenomenological yield function is developed to characterize the initial yield behavior of the closed cell polymeric foam under a full range of loading conditions, which is a linear combination of non-quadratic functions of the relative principal stresses and the second invariant of the deviatoric stress tensor.
TL;DR: In this paper, the von Mises yield criterion with its associated flow rule is assumed to model the plastic behavior of elastoplastic undrained clays and an explicit finite element scheme is used to efficiently perform a large number of loading increments and to simplify the treatment of contact.
Abstract: This paper presents a numerical technique for the analysis of the cone penetration test by means of the commercial finite element code ABAQUS. The von Mises yield criterion with its associated flow rule is assumed to model the plastic behaviour of elastoplastic undrained clays. An explicit finite element scheme is used to efficiently perform a large number of loading increments and to simplify the treatment of contact. An Arbitrary Langrangian–Eulerian (ALE) scheme is adopted to preserve the quality of mesh throughout the numerical simulation. A volumetric weighting algorithm adjusts the relative positions of nodes after each loading increment. This prevents mesh over distortion and allows the simulation to run continuously. The variation of the cone resistance is examined in relation to various parameters such as the in situ stress state, shaft and cone face roughness, and the material strength when steady state conditions have been reached. The trends of these variations are highlighted and compared with those found by other researchers. This technique can be extended to analyse the plastic behaviour of elastoplastic sands often modelled using either the Drucker–Prager yield criterion or a critical state model.
TL;DR: In this article, a new exponential-based integration algorithm for associative von-Mises plasticity with linear isotropic and kinematic hardening is proposed, which follows the ones presented by the authors in previous papers.
Abstract: SUMMARY In this communication we propose a new exponential-based integration algorithm for associative von-Mises plasticity with linear isotropic and kinematic hardening, which follows the ones presented by the authors in previous papers. In the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential-based schemes and, in particular, we address the yield consistency, exactness under proportional loading, accuracy and stability of the methods. In the second part of the contribution, we show a detailed numerical comparison between the new exponential-based method and two classical radial return map methods, based on backward Euler and midpoint integration rules, respectively. The developed tests include pointwise stress–strain loading histories, iso-error maps and global boundary value problems. The theoretical and numerical results reveal the optimal properties of the proposed scheme. Copyright 2006 John Wiley & Sons, Ltd.
TL;DR: In this paper, a cantilever assembly subjected to heating at its fixed end, which resembles the welding of a sheet metal is considered, and a control volume approach is introduced for numerical solution of heat transfer equations while the finite element method is adopted for stress field predictions.
TL;DR: In this paper, the analysis of stress and strain data acquired with the finite element method and with tests that used post-yielding strain gages bonded onto the external surface of pipes that suffered thickness metal loss and that had been loaded with internal pressure was presented.
Abstract: This paper presents the analysis of stress and strain data acquired with the finite element method and with tests that used post-yielding strain gages bonded onto the external surface of pipes that suffered thickness metal loss and that had been loaded with internal pressure. These metal loss areas were produced by three different processes: actual internal corrosion, careful machining of external patches by spark-erosion, and milling of internal or external patches to simulate limited or extensive strip corrosion defects with depths up to 70% of the pipe’s thickness. Results show that: (1) the extensive longitudinal internal or external defect areas behave as extensive strips with a high degree of freedom to deform elastically and plastically in the circumferential and thickness directions, and (2) large restraints are offered to the longitudinal strains by the non-corroded thick walls parallel to the strip. Using the above experimental observation, a simple mathematical model was developed to predict the burst pressure of pipes with longitudinal extensive and reasonably constant depths of metal loss. This model employed thin-pipe-strength-of-material equations associated to a bulging correction factor, the material’s uniaxial ultimate strength and the von Mises criterion. The onset of plastic collapse predicted by the simple model was successfully compared with results determined from actual hydrostatic tests that were carried out with full scale pipe specimens and from finite element results generated by the use of a commercial program. The developed model was also helpful in showing that the yield and burst behaviors of new or corroded pipeline specimens under laboratory test conditions can be directly compared and extended to the yield and burst behaviors of buried pipeline in field operation.
TL;DR: In this paper, the von Mises equivalent stress and strain were fitted by the Ramberg-Osgood relationship for multiaxial fatigue tests on 63Sn-37Pb solder specimens under proportional and non-proportional axial/torsional loading.
TL;DR: The deformation behavior of polyoxymethylene has been studied in plane strain compression at temperatures from 120°C up to 165°C and in uniaxial tension and simple shear at 160°C for strain rates from 10−4 to 1 s−1 as mentioned in this paper.
TL;DR: In this article, two extensions of the classical fiber bundle model are presented to study the creep rupture of heterogeneous materials and the shear failure of glued interfaces of solid blocks, where the fibres of a parallel bundle present time dependent behaviour under an external load and fail when the deformation exceeds their local breaking threshold.
Abstract: We present two extensions of the classical fibre bundle model to study the creep rupture of heterogeneous materials and the shear failure of glued interfaces of solid blocks. To model creep rupture, we assume that the fibres of a parallel bundle present time dependent behaviour under an external load and fail when the deformation exceeds their local breaking threshold. Assuming global load sharing among fibres, analytical and numerical calculations showed that there exists a critical load below which only partial failure occurs while above which the system fails globally after a finite time. Approaching the critical point from both sides the system exhibits scaling behaviour which implies that creep rupture is analogous to continuous phase transitions. To describe interfacial failure, we model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. In the framework of global load sharing, we obtain analytically the macroscopic constitutive behaviour of the system and describe the microscopic process of the progressive failure of the interface.
TL;DR: In this article, a topology optimization framework is proposed to design the material distribution of functionally graded structures considering mechanical stress constraints, where the problem of minimizing the volumetric density of a material phase subjected to a global stress constraint is considered.
Abstract: This work describes a topology optimization framework to design the material distribution of functionally graded structures considering mechanical stress constraints. The problem of interest consists in minimizing the volumetric density of a material phase subjected to a global stress constraint. Due to the existence of microstructure, the micro-level stress is considered, which is computed by means of a mechanical concentration factor using a p-norm of the Von Mises stress criterium (applied to the micro-level stress). Because a 0–1 (void–solid) material distribution is not being sought, the singularity phenomenon of stress constraint does not occur as long as the material at any point of the medium does not vanish and it varies smoothly between material 1 and material 2. To design a smoothly graded material distribution, a material model based on a non-linear interpolation of the Hashin–Strikhman upper and lower bounds is considered. Consistently with the framework adopted here in, the so-called ‘continuous approximation of material distribution’ approach is employed, which considers a continuous distribution of the design variable inside the finite element. As examples, the designs of functionally graded disks subjected to centrifugal body force are presented. The method generates smooth material distributions, which are able to satisfy the stress constraint. Copyright © 2006 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors present a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects, based on multi-component forms of kinematic and isotropic hardening variables in conjunction with von Mises yield criterion.
TL;DR: In this paper, a cold rolling model based on asperity flattening and von Mises homogenous deformation for mixed regime is developed, the variations of the yield stress with strain and strain rate are considered in this model.
TL;DR: In this article, the authors examined the yielding and fracture behavior of Zr57.4Cu16.4Ni8.2Ta8Al10 composites with a small volume fraction (∼4 pct) of ductile crystalline particles under quasi-static uniaxial tension and compression, consistent with a von Mises yield criterion.
Abstract: We have examined the yielding and fracture behavior of Zr57.4Cu16.4Ni8.2Ta8Al10 metallic-glass-matrix composites with a small volume fraction (∼4 pct) of ductile crystalline particles under quasi-static uniaxial tension and compression and dynamic uniaxial compression. The yield stress of the composite is the same for quasi-static tension and compression, consistent with a von Mises yield criterion. The measured average angle between the shear bands and the loading axis in quasi-static compression is 47±2 deg, significantly larger than the value of ∼42 deg typically reported for single-phase metallic glasses. Finite element modeling (FEM) shows that the measured value is consistent with both the von Mises criterion (48±4 deg) and the Mohr-Coulomb criterion (46±5 deg). The fracture surface angles, however, are 41±1 deg (compression) and 54±2 deg (tension), in good agreement with observations of single-phase metallic glasses. At low strain rates ( 100 s−1), the failure stress decreases with increasing strain rate, which again is similar to the behavior of single-phase glasses. These results indicate that while the presence of the particles has a significant effect on the yield behavior of the composites, the fracture behavior is largely governed by the properties and behavior of the amorphous matrix.