Showing papers on "von Mises yield criterion published in 1970"

Longitudinal wave propagation on a traveling threadline—II

Abstract: The non-linear equations for wave propagation in both linear and non-linear materials are considered. An elastic shock condition is derived and the general solution for the linear elastic material is obtained by employing a von Mises type of transformation. The general non-linear elastic material is shown to have solutions of a non-linear ‘traveling wave’ character. A time to occurrence for the formation of discontinuities is obtained and compared with that of the Lax-Jeffrey theory. Solutions for both the Eulerian and Lagrangian equations are obtained.

A discrete element stress and displacement analysis of elastoplasticplates

Abstract: A displacement method of analysis for elastoplastie plates is presented with particular emphasis on accurate stress results. The Hencky-Nadai stress-strain law is assumed and a discretized potential energy function is formed using bicubic Hermite displacement functions. To achieve interelement continuous stress fields, bicubic spline constraints are introduced that produce interelement curvature continuity. The planar variation in material properties caused by plastic strains is approximated using additional nodes that uniformly subdivide the element planform into four quadrants. Integration of the strain energy through the plate thickness is accomplished using gaussian quadrature. Solutions of the nonlinear discretized equilibrium equations are obtained by energy minimization using the conjugate gradient algorithm. Results in the elastic range indicate the displacements converge with the fourth power of the grid size and the stresses converge with the grid size squared. These convergence rates were obtained with both bicubic Hermite and spline displacement functions. Elastoplastic results are presented that compare well with both deformation and incremental theory solutions. Stress results are also presented that demonstrate an elastic compressibility effect in elastoplastie plates.

EPAD, A Computer Program for the Elastic-Plastic Analysis of DOME Structures and Arbitrary Solids of Revolution Subjected to Unsymmetrical Loadings.

Abstract: : The EPAD computer program determines elastoplastic deformations, stresses, strains and plastic strains within solids of revolution of arbitrary shape subjected to arbitrary pressure and/or concentrated loads. All possible combinations of boundary conditions are permitted consistent with the theory of plasticity. The program is based on the finite element technique using the 'initial strain' approach to simulate the effect of plasticity in the incremental step-by-step method. Incremental stress-strain relationships are derived from the Prandtl-Reuss constitutive equations and the Von Mises yield criterion. Fourier analysis is utilized for the solution of unsymmetric loading conditions. A numerical procedure is developed for solving the coupled equilibrium equations. An iteration algorithm for improving convergence is presented. Numerical examples are compared with analytical results. Additionally, EPAD handles the detailed stress analysis of hemispherical or ellipsoidal thick walled dome structures due to a prescribed value of externally applied pressure. For specific dome geometry the program accepts simple descriptive dimensions and automatically generates all the necessary geometrical data. A capability is provided for convenient input of specialized axisymmetric and unsymmetric nonuniform pressure distribution when using the dome geometry option. (Author)

Application Of BEM To Elastoplastic ContactProblems

Abstract: In this paper, the contact between bodies with elastoplastic behaviour is studied. In order to solve the contact problem, a direct constraint technique is em- ployed. Friction between the bodies is taken into account, and the materials may have different elastoplastic properties. An initial strain BEM formulation is used to study the elastoplastic problem. The material is assumed to obey the Von Mises yield criterion with its associated flow rule. Two numerical examples are presented, to demonstrate the efficiency of the proposed method.

Stability of tunnel in viscoelastic-plastic medium

Abstract: IN THIS PAPER STABILITY OF A CIRCULAR TUNNEL IN VISCOELASTIC-PLASTIC MEDIUM IS DISCUSSED ON THE BASIS OF THE THEORIES OF ELASTICITY, PLASTICITY AND VISCOELASTICITY. THE TUNNEL IS LOCATED AT A LARGE DEPTH UNDERNEATH THE HORIZONTAL GROUND SURFACE SO THAT THE TUNNEL CAN BE TREATED AS A HOLE IN AN INFINITE PLATE UNDER A UNIFORM LOADING CONDITION. FOR SIMPLICITY OF CALCULATION, THE MEDIUM IS ASSUMED TO BE HOMOGENEOUS AND ISOTROPIC ALTHOUGH THIS CONDITION IS NOT ALWAYS SATISFIED, AND ITS INITIAL STATE OF STRESSES BEFORE EXCAVATION OF THE TUNNEL IS CONSIDERED TO BE HYDROSTATIC. TIME-INDEPENDENT STRESS AND STRAIN DISTRIBUTIONS AROUND THE TUNNEL ARE CALCULATED BY ASSUMING A MODIFIED VON MISES YIELDING CRITERION, SO THAT THREE DIFFERENT REGIONS WITH RESPECT TO STATE OF STRESSES APPEAR IN GENERAL IN THE VICINITY OF THE TUNNEL. ALSO STUDIED WAS THE TIME-DEPENDENT BEHAVIOR OF THE TUNNEL. IF THE PRINCIPLE OF BOLTZMANN'S SUPERPOSITION IS VALID, PRESSURE ACTING ON A TUNNEL LINING, WHICH DOES NOT EXIST AT THE TIME-INDEPENDENT ANALYSIS, CAN BE OBTAINED BY SOLVING VOLTERRA'S INTEGRAL EQUATION OF THE SECOND KIND. ITS PRESSURE DEPENDS ON NOT ONLY RIGIDITY OF THE LINING AND MECHANICAL PROPERTIES OF SURROUNDING MEDIUM BUT ALSO WHEN THE LINING IS CONSTRUCTED. BY INTRODUCING A FAILURE CRITERION OF THE MEDIUM, THE OPTIMUM TIME OF LINING MAY BE EVALUATED. SOME NUMERICAL RESULTS ARE SHOWN IN ORDER TO DISCUSS INFLUENCES OF MECHANICAL PROPERTIES OF THE MEDIUM ON THE PRESSURE ACTING ON THE LINING. /AUTHOR/

Strength Analysis Of Buried Pipes Under Explosive Loads

Abstract: Three-dimensional FEM models concerned with the transient response and relevant strength analysis of buried structures due to blast explosions were proven extremely costly using conventional FEM codes. This is due to the required small time-step as well as the considerable extension of the problem domain that has to be chosen so long that no reflection is allowed from the artificial infinite soil boundaries before the maximum displacement (or Von Mises stress) amplitude of the structure is reached. In case of buried pipelines, the complexity increases because the length of the model should at least include the unknown wave length along the pipeline. To overcome this problem, a reduced model taking into consideration the decoupled incident P- SH- and SV-waves, has been developed. The new theory achieves a manageable conservative relationship between the strength of the buried pipeline and the allowable peak particle velocity. The proposed relationship is based on the criterion of either the hoop or Von-Mises stresses and it is given in terms of the allowable stress as a percentage of the Specified Minimum Yield Stress (SMYS) of the pipeline. An example is given for a buried high-pressured natural gas pipeline.

The tensile deformation of oriented polyvinyl chloride and oriented polyethylene.

Abstract: Polyvinyl chloride was oriented by hot drawing. The deformation was investigated under uniaxial tension at room temperature and at 50°C. The onset of yield was localised in deformation bands of which two kinds, referred to as type 1 and type 2, were observed. Type 2 bands formed before type 1 bands, but only type 1 bands developed into a running neck. The yield behaviour could be satisfactorily accounted for by a yield criterion based on the von Mises criterion, provided that a term representing an internal compressive stress in the molecular alignment direction was included. The internal stress was found to increase from zero with increasing prior extension ratio and birefringence, and was also equal to the true stress acting on the material during the initial hot drawing. The inclusion of a hydrostatic stress term in the criterion, the application to anisotropic materials of the Coulomb criterion and a critical strain form of the von Mises criterion are considered. Optical anisotropy changes are discussed in terms of an affine deformation model, which was found to apply for deformation at room temperature and 50°C, but not at 71°C and 90°C. The model has also been applied to the deformation, at 50°C, of oriented polyvinyl chloride, the molecular alignment of which was described by three different distribution functions. The agreement between theory and experiment was best for what is referred to as the Kuhn and Grun type 1 distribution. Stress whitening, which developed during hot stretching, is associated with changes in the room temperature deformation behaviour. There was a yield fracture transition at lambda[o] = 0° and a change in ductile fracture behavior at other values of lambda[o]. The ductile fracture direction in stress whitened material has been accounted for by a theory which proposed that the minimum energy was used in propagating the fracture. Two different kinds of type 1 bands were observed in oriented polyethylene. It is suggested that crystallinity may affect the position of the minimum yield stress.

The dynamic orthotropic dugdale model

Abstract: : The problem of ductile fracture in anisotropic solids is an important engineering problem. In this report the Dugdale model is assumed, that is, the yielded zone is replaced by a constant yield stress. A solution is presented for an orthotropic dynamic solid. The solution was obtained by the complex variable approach. Stress functions which must satisfy a generalized bi-harmonic equation are represented in terms of two analytic functions of two different complex variables. In this way boundary value problems can be reduced to problems of complex function theory. The yield stress is assumed to follow a Von Mises' yield criterion which was adapted to the orthotropic dynamic case. It was found that the plastic zone is given by the same relation as in the isotropic-static case. Any orthotropic dynamic parameter may be obtained from the corresponding isotropic dynamic parameter by simply multiplying the orthotropic parameter by a coefficient. A limit on yielding along the line of the crack and therefore a limit on the anisotropy and velocity are derived. (Author)

Analysis of Elasto-Plastic Thermal Stresses by the Finite Element Method

Abstract: Hereunder is presented a procedure to analyze elasto-plastic thermal stresses by the finite element method. On the finite element analysis of thermal stresses, the equivalent load matrix due to thermal expansion is employed, as the so-called external load matrix. The stiffness matrix in the plastic region is constructed according to Yamada's [Dp] matrix, which is derived from Prandtl-Reuss equation and von Mises yield criterion. A modified Marcal's method gives appropriate stiffness to the element adjacent to the elasto-plastic interface.Attension is to be focused on the analysis of thermal residual stresses. The steps in calculation of the residual stresses are as follows:(1) The elasto-plastic stresses and strains will be determined.(2) The plastic strains will be estimated.(3) The residual stresses will be calculated so as to compensate the remaining plastic strains in the body.Numerical calculation was made of the thermal residual stresses in a cylindrical bar induced by the partial induction quenching. The temperature distribution in the heating and cooling processes was determined by means of the finite difference method. The residual stresses induced in the present case are found to be resultant of two kinds of plastic deformation; one made during the initial heating and the other during the subsequent cooling.The method of calculating the residual stresses by such a technique is applicable to repeated loading.

Thickness Optimisation Of A Bi-stratumStructure

Abstract: This paper deals with the thickness optimisation of layers of a bi-stratum composite structure having infinite lateral dimensions. The composite is considered as a one-dimensional structure. Using a direct integration of the behaviour equation an analytical solution can be obtained without expensive calculation time. This approach is based on the techniques which are applied to acoustic analysis of multi-layer structures and can be extended to calculate a general composite laminate structure. The advantage of such a method is a short calculation time. The objective of this paper is to minimise the Von Mises stress in average with respect to the position of the interface between two layers. The analytical solution is obtained in a similar way as for analysis problem. This analytical solution is compared with the numerical results obtained by using the finite element system ANSYS. A very good correlation between analytical and numerical solutions is observed.

A Contribution to Creep Fracture under Combined Stress System

Abstract: An analytical investigation was conducted on the creep fracture of thin-walled cylinders subjected to combined tension and internal pressure, and the results were analyzed on the basis of the large strain theory. The experimental results on a 0.14% carbon steel at the test temperature of 500 °C proved the validity of the large strain theory combined with the von Mises criterion, and the time to rupture estimated by the large strain theory was in good agreement with the experimental results.

Non-conforming BEM Discretisation In FrictionalElastoplastic Contact Problems

Abstract: In this paper, elastoplastic contact problems with friction are solved by BEM, using non conforming discretisation. The contact conditions are directly enforced by relating tractions and displacements at every node of the contact zone with a point on the opposite surface. An ini- tial strain BEM formulation is used to study the elastoplastic problem. The material is assumed to obey the Von Mises yield criterion with its associated flow rule. A numerical application is presented, and the results are compared to those obtained by the use of conforming discretisation.