Showing papers on "von Mises yield criterion published in 2008"
Book•
01 Jan 2008
TL;DR: In this article, the authors present a general numerical integration algorithm for elastoplastic constitutive equations, based on the von Mises model, which is used for the integration of the isotropically hardening deformation.
Abstract: Part One Basic concepts 1 Introduction 1.1 Aims and scope 1.2 Layout 1.3 General scheme of notation 2 ELEMENTS OF TENSOR ANALYSIS 2.1 Vectors 2.2 Second-order tensors 2.3 Higher-order tensors 2.4 Isotropic tensors 2.5 Differentiation 2.6 Linearisation of nonlinear problems 3 THERMODYNAMICS 3.1 Kinematics of deformation 3.2 Infinitesimal deformations 3.3 Forces. Stress Measures 3.4 Fundamental laws of thermodynamics 3.5 Constitutive theory 3.6 Weak equilibrium. The principle of virtual work 3.7 The quasi-static initial boundary value problem 4 The finite element method in quasi-static nonlinear solid mechanics 4.1 Displacement-based finite elements 4.2 Path-dependent materials. The incremental finite element procedure 4.3 Large strain formulation 4.4 Unstable equilibrium. The arc-length method 5 Overview of the program structure 5.1 Introduction 5.2 The main program 5.3 Data input and initialisation 5.4 The load incrementation loop. Overview 5.5 Material and element modularity 5.6 Elements. Implementation and management 5.7 Material models: implementation and management Part Two Small strains 6 The mathematical theory of plasticity 6.1 Phenomenological aspects 6.2 One-dimensional constitutive model 6.3 General elastoplastic constitutive model 6.4 Classical yield criteria 6.5 Plastic flow rules 6.6 Hardening laws 7 Finite elements in small-strain plasticity problems 7.1 Preliminary implementation aspects 7.2 General numerical integration algorithm for elastoplastic constitutive equations 7.3 Application: integration algorithm for the isotropically hardening von Mises model 7.4 The consistent tangent modulus 7.5 Numerical examples with the von Mises model 7.6 Further application: the von Mises model with nonlinear mixed hardening 8 Computations with other basic plasticity models 8.1 The Tresca model 8.2 The Mohr-Coulomb model 8.3 The Drucker-Prager model 8.4 Examples 9 Plane stress plasticity 9.1 The basic plane stress plasticity problem 9.2 Plane stress constraint at the Gauss point level 9.3 Plane stress constraint at the structural level 9.4 Plane stress-projected plasticity models 9.5 Numerical examples 9.6 Other stress-constrained states 10 Advanced plasticity models 10.1 A modified Cam-Clay model for soils 10.2 A capped Drucker-Prager model for geomaterials 10.3 Anisotropic plasticity: the Hill, Hoffman and Barlat-Lian models 11 Viscoplasticity 11.1 Viscoplasticity: phenomenological aspects 11.2 One-dimensional viscoplasticity model 11.3 A von Mises-based multidimensional model 11.4 General viscoplastic constitutive model 11.5 General numerical framework 11.6 Application: computational implementation of a von Mises-based model 11.7 Examples 12 Damage mechanics 12.1 Physical aspects of internal damage in solids 12.2 Continuum damage mechanics 12.3 Lemaitre's elastoplastic damage theory 12.4 A simplified version of Lemaitre's model 12.5 Gurson's void growth model 12.6 Further issues in damage modelling Part Three Large strains 13 Finite strain hyperelasticity 13.1 Hyperelasticity: basic concepts 13.2 Some particular models 13.3 Isotropic finite hyperelasticity in plane stress 13.4 Tangent moduli: the elasticity tensors 13.5 Application: Ogden material implementation 13.6 Numerical examples 13.7 Hyperelasticity with damage: the Mullins effect 14 Finite strain elastoplasticity 14.1 Finite strain elastoplasticity: a brief review 14.2 One-dimensional finite plasticity model 14.3 General hyperelastic-based multiplicative plasticity model 14.4 The general elastic predictor/return-mapping algorithm 14.5 The consistent spatial tangent modulus 14.6 Principal stress space-based implementation 14.7 Finite plasticity in plane stress 14.8 Finite viscoplasticity 14.9 Examples 14.10 Rate forms: hypoelastic-based plasticity models 14.11 Finite plasticity with kinematic hardening 15 Finite elements for large-strain incompressibility 15.1 The F-bar methodology 15.2 Enhanced assumed strain methods 15.3 Mixed u/p formulations 16 Anisotropic finite plasticity: Single crystals 16.1 Physical aspects 16.2 Plastic slip and the Schmid resolved shear stress 16.3 Single crystal simulation: a brief review 16.4 A general continuum model of single crystals 16.5 A general integration algorithm 16.6 An algorithm for a planar double-slip model 16.7 The consistent spatial tangent modulus 16.8 Numerical examples 16.9 Viscoplastic single crystals Appendices A Isotropic functions of a symmetric tensor A.1 Isotropic scalar-valued functions A.1.1 Representation A.1.2 The derivative of anisotropic scalar function A.2 Isotropic tensor-valued functions A.2.1 Representation A.2.2 The derivative of anisotropic tensor function A.3 The two-dimensional case A.3.1 Tensor function derivative A.3.2 Plane strain and axisymmetric problems A.4 The three-dimensional case A.4.1 Function computation A.4.2 Computation of the function derivative A.5 A particular class of isotropic tensor functions A.5.1 Two dimensions A.5.2 Three dimensions A.6 Alternative procedures B The tensor exponential B.1 The tensor exponential function B.1.1 Some properties of the tensor exponential function B.1.2 Computation of the tensor exponential function B.2 The tensor exponential derivative B.2.1 Computer implementation B.3 Exponential map integrators B.3.1 The generalised exponential map midpoint rule C Linearisation of the virtual work C.1 Infinitesimal deformations C.2 Finite strains and deformations C.2.1 Material description C.2.2 Spatial description D Array notation for computations with tensors D.1 Second-order tensors D.2 Fourth-order tensors D.2.1 Operations with non-symmetric tensors References Index
1,077 citations
TL;DR: A maximum principal strain criterion can be defined a suitable candidate for the in vivo risk factor assessment on long bones by correctly identifying the level of failure risk and the location of fracture onset in all the modelled specimens.
343 citations
TL;DR: In this article, the combined effects of void shape and matrix anisotropy on the macroscopic response of ductile porous solids are investigated, and the overall anisotropic yield criterion, a limit analysis approach is used.
214 citations
TL;DR: In this article, a generalized yield criterion, based on the parabolic Drucker and Prager criterion, is proposed including the first invariant of the stress tensor as well as the second invariant and the third invariant for the deviatoric part of the tensor.
153 citations
TL;DR: In this article, the von Mises flow rule is used to predict the effect of residual stress on the contact pressure with and without residual stresses on the volume of interest measured during indentation experiments.
133 citations
TL;DR: In this paper, the authors investigate the influence of directional mesh bias on the results of failure simulations performed with isotropic and anisotropic damage models and compare the performance of the two models under shear with restricted or free volume expansion.
123 citations
TL;DR: In this article, the von Mises stress was made for each of the stems at designated locations as well as the displacement was recorded, and three materials were used to perform the analysis, they were; Cr-Co-Mo, Stainless Steel SS316L, and titanium alloy, Ti-6Al-4V.
84 citations
TL;DR: This work enhances a bi-layer fiber-matrix microstructural arterial model with softening and analyzes the arterial failure under internal pressure to illustrate the efficiency of the softening hyperelasticity approach on the problem of prediction of arterials failure.
83 citations
TL;DR: In this article, the failure behavior of reinforced concrete columns under eccentric compression was modeled with an elasto-plastic model using isotropic hardening and softening, and the reinforcement was described with an elastic-ideally plastic constitutive law by von Mises.
73 citations
TL;DR: In this article, a mesh-independent continuum damage model was proposed to predict the residual strength of adhesively bonded joints by introducing a displacement-based damage parameter into the constitutive equation of damaged materials.
72 citations
TL;DR: In this article, an experimental measurement of the plastic biaxial mechanical response for an aluminum alloy (AA5754-O) sheet metal is presented, and results show repeatable behavior (within quantified uncertainties) for U to 20%, PS to almost 15%, and BB to above 20% in-plane strains.
Journal Article•
TL;DR: The variation of the maximum von Mises stresses in jawbone was more sensitive to thread height than to thread width, and stress in cancellous bone is more likely to be influenced by thread parameters than stress in cortical bone.
Abstract: Purpose: To evaluate continuous and simultaneous variations of thread height and width for an experimental screw-type implant. Materials and Methods: A finite element model of an implant with a Vshaped thread was created. The range of thread height was set at 0.20 to 0.60 mm, and the range of thread width was set at 0.10 to 0.40 mm. Forces of 100 N and 50 N were applied along the implant axis (AX) and an angle of 45 degrees in a buccolingual direction (45-degree BL), respectively. The maximum von Mises stresses in jawbone were evaluated, and the sensitivity of the stress in jawbone to the variables was also evaluated. Results: Under AX load, the maximum von Mises stresses in cortical and cancellous bones increased by 4.3% and 63.0%, respectively, as thread parameters changed. Under 45-degree BL load, maximum von Mises stresses in cortical and cancellous bones increased by 19.3% and 118.0%, respectively. When thread height was from 0.34 to 0.50 mm and thread width was 0.18 to 0.30 mm, the tangent slope of the maximum von Mises stress response curve ranged from –1 to 1. The variation of the maximum von Mises stresses in jawbone was more sensitive to thread height than to thread width. Conclusions: Stress in cancellous bone is more likely to be influenced by thread parameters than stress in cortical bone. A 45-degree BL force is more likely to be influenced by thread parameters than an axial force. A thread height of 0.34 to 0.50 mm and a thread width of 0.18 to 0.30 mm is optimal from a biomechanical point of view. In the design of a screw-type implant, thread height is more important than thread width for the reduction of stress within the bone. INT J ORAL MAXILLOFAC IMPLANTS 2008;23:65–74
TL;DR: In this article, the effects of strain rate, temperature and sheet thickness on the yield locus of magnesium alloy (AZ31) sheets with different sheet thickness (0.5 and 0.8mm) were experimentally investigated.
TL;DR: In this paper, a method to analyze pavements under cyclic, in particular, rolling contact loading is presented, in which repeated sliding/rolling line contact as well as repeated stationary contact are considered.
Abstract: SUMMARY Based on the lower-bound shakedown theorem by Melan, a method to analyse pavements under cyclic, in particular, rolling contact loading is presented. Repeated sliding/rolling line contact as well as repeated stationary contact is considered. The material is assumed to be rate-independent elastic–plastic. As yield conditions, the rounded Mohr–Coulomb and von Mises yield criteria are used, assuming associated flow rules. The proposed numerical method is based on finite elements, and the inherent optimization problem to determine the shakedown factors is solved using the interior-point method. Several numerical results are presented and compared with the existing results in literatures. Copyright q 2008 John Wiley & Sons, Ltd.
TL;DR: A study of the effect of Poisson's ratio on the stationary mode I crack tip fields in amorphous alloys is conducted in this article, where a Mohr-Coulomb based constitutive model is used to account for pressure sensitivity of plastic flow as well as the localization of plastic strain into discrete shear bands.
TL;DR: In this paper, the authors investigated the dependency of the fracture locus on the stress triaxiality ratio and found that there is an exponential dependency on the fracture location on the ratio of the von Mises equivalent stress.
TL;DR: In this article, the authors used finite element method (FEM) to simulate deformation behavior of high-density polyethylene (HDPE) when subjected to tensile loading, either without or with the presence of pre-cracks.
TL;DR: In this paper, the authors reported the application of this ML sensing technique to stress concentration analysis on an aluminium plate and the comparison with a theoretical calculation demonstrated that the ML intensity of SAO sensing film correlates linearly with von Mises stress on metal surface and the observed real-time ML images quantitatively reflect stress concentration.
Abstract: Dynamic visualization of stress distribution even due to a small deformation has been realized by coating the surface of the test object of metal with a upgrade mechanoluminescence (ML) material of SrAl2O4:Eu (SAO). In this paper we report the application of this ML sensing technique to stress concentration analysis on an aluminium plate. And the comparison with a theoretical calculation demonstrated that the ML intensity of SAO sensing film correlates linearly with von Mises stress on metal surface and the observed real-time ML images quantitatively reflect stress concentration.
TL;DR: In this paper, a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code, which is applied to a unit volume element of a metal-ceramic composite with proportional loading.
TL;DR: In this paper, the effects of mechanical and thermal surface loadings on deformation of elastic-plastic semi-infinite medium were analyzed simultaneously by using the finite element method.
TL;DR: In this article, a solution based on a Lennard-Jones potential in combination with the von Mises yield criterion was proposed to solve the jump-in phenomenon in the presence of adhesion.
Abstract: Approach between two deformable microbodies in the presence of adhesion is sometimes accompanied by discontinuous change of the surface profile at the narrow region near their summits (jump-in phenomenon). Previous studies of adhesive spherical contact showed that neck formation during jump-in always involves onset of local plastic yield near the edge of the contact zone. The current paper reveals that pure elastic jump-in is also feasible. The solution is based on a Lennard-Jones potential in combination with the von Mises yield criterion. The theoretical strength rather than the engineering yield strength of the material is used and the sufficient condition for jump-in induced onset of plastic yield under this extreme strength is discussed.
TL;DR: In this article, the authors consider the regularity of weak solutions to evolution variational inequalities arising from the flow theory of plasticity with isotropic and kinematic hardening and derive a Morrey condition for the stress velocities and the strains up to the boundary.
Abstract: We consider the regularity of weak solutions to evolution variational inequalities arising from the flow theory of plasticity with isotropic and kinematic hardening. The (linear) elasticity tensor is allowed to have discontinuities. We derive a Morrey condition for the stress velocities and the strains (not the strain velocity!) up to the boundary. In the case of two space dimensions we conclude the Holder continuity of the displacements.
TL;DR: In this paper, a high-cycle fatigue life model for structures subjected to variable amplitude multiaxial loading is presented, which is characterized by the choice of a damage factor related to the accumulated mesoscopic plastic strain per stabilised cycle, and the use of a mesoscopic mechanical behaviour taking into account the fatigue mechanisms such as plasticity and void growth.
Abstract: A high-cycle fatigue life model for structures subjected to variable amplitude multiaxial loading is presented in this paper. It treats any kind of repeated blocks of variable amplitude multiaxial loading without using a cycle counting method. This model based on a mesoscopic approach is characterized by the following features: (i) the choice of a damage factor related to the accumulated mesoscopic plastic strain per stabilised cycle; (ii) the use of a mesoscopic mechanical behaviour taking into account the fatigue mechanisms such as plasticity and void growth. This behaviour is a von Mises elastoplastic model with linear kinematic hardening and hydrostatic stress dependent yield stress. The fatigue life model has six parameters identified with one SN curve and two fatigue limits. In-phase and out-of-phase experimental tests from the literature are simulated. The predicted fatigue lives are compared to experimental ones.
TL;DR: In this paper, a quadratic extension of a recently proposed mixed finite element method of the kinematic approach is applied to obtain precise solutions to a forming problem with Gurson and Drucker-Prager materials.
TL;DR: In this paper, Leblond et al. provided an external estimate of the yield surface of an arbitrary (non-spheroidal) ellipsoid made of ideal-plastic von Mises material and containing a confocal elliptipsoidal void, under conditions of homogeneous boundary strain rate.
TL;DR: In this article, the failure analysis of simply supported, isotropic, square plates is addressed, focusing on minimum failure load amplitudes and failure locations, and von Mises equivalent stress along the plate thickness is also addressed.
Abstract: The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations. von Mises’ equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 (thin plates) and as low as 2 (very thick plates). Results are obtained via several 2D plate models. Classical theories (CTs) and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories (HOTs), HOTsd models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed: by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.
TL;DR: In this article, a wide set of simple hyperelastic-plastic isotropic models not restricted to quadratic elastic behavior can be constructed by relaxing the classical decomposition amplitude/direction by the sum of spectral quantities.
TL;DR: In this paper, the yield behavior of commercial homopolymer polypropylene modified by elastomeric metallocene-catalyzed polyolefin blends was investigated by carrying out uniaxial tension, uniaaxial compression, plane strain compression, and simple shear mechanical tests.
Abstract: The yield behavior of commercial homopolymer polypropylene modified by elastomeric metallocene-catalyzed polyolefin blends was investigated by carrying out uniaxial tension, uniaxial compression, plane strain compression, and simple shear mechanical tests. Investigation was performed using specimens machined from isotropic compression molded plates. The onset of yielding was determined by means of the residual strain method. Experimental data was fitted according to the two most popular yield criteria in the polymer field—modified Tresca and modified Von Mises criteria. Both criteria provided reasonable predictions of the yield onset locus despite the tendency of polymers to develop crazes under positive hydrostatic pressure. A generalized yield locus based on the modified Von Mises criterion and the Lazzeri and Bucknall relationship was constructed for PP/POE blends. In addition, for one blend composition the effect of the polypropylene matrix crystalline morphology—altered by thermal annealing—was investigated. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.
TL;DR: In this paper, a closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition, which is governed by the non-linear von Mises criterion.
Abstract: The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.