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# von Mises yield criterion

About: von Mises yield criterion is a research topic. Over the lifetime, 4374 publications have been published within this topic receiving 82642 citations. The topic is also known as: Von Mises stress.

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TL;DR: In this article, a theory is suggested which describes the yielding and plastic flow of an anisotropic metal on a macroscopic scale and associated relations are then found between the stress and strain-increment tensors.

Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

3,426 citations

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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

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TL;DR: In this article, the authors investigated the yield behavior of two aluminium alloy foams (Alporas and Duocel) for a range of axisymmetric compressive stress states.

Abstract: The yield behaviour of two aluminium alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress, and evolve without corner formation. Two phenomenological isotropic constitutive models for the plastic behaviour are proposed. The first is based on a geometrically self-similar yield surface while the second is more complex and allows for a change in shape of the yield surface due to differential hardening along the hydrostatic and deviatoric axes. Good agreement is observed between the experimentally measured stress versus strain responses and the predictions of the models.

1,053 citations

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Alcoa

^{1}TL;DR: In this paper, a new six-component yield surface description for orthotropic materials is developed, which has the advantage of being relatively simple mathematically and yet is consistent with yield surfaces computed with polycrystal plasticity models.

940 citations