Showing papers on "von Mises yield criterion published in 1975"

The mechanical behaviour of polystyrene under pressure

Abstract: Tensile deformation of polystyrene carried out under pressure up to 4 kbar has shown that the pressure-transmitting fluid (silicon oil) acts as a stress crazing and cracking agent. Unsealed specimens showed a brittle-to-ductile transition at 2.95 kbar, while specimens sealed with Teflon tape and rubber showed the same transition at only 0.35 kbar. Analysis of the stress-strain curves for the sealed specimens indicated that the pressure dependency of the craze initiation stress differs from that of shear band initiation stress. The brittle-to-ductile transition occurs when the initiation stresses of both processes become equal. The principal stress for craze initiation showed almost no pressure dependency, suggesting that crazes initiate when the principal stress level of the tensile specimen reaches a critical value irrespective of the applied hydrostatic pressure. Similarly, no pressure dependency was observed for the principal ductile fracture stress. The pressure dependency of yield stress agreed well with a non-linear pressure dependent von Mises yield criterion.

The mechanical behavior of poly(methyl methacrylate) under pressure

Abstract: Tensile deformation of poly(methyl methacrylate) carried out under hydrostatic pressures up to 4 kbar has shown that the pressure-transmitting fluid (silicone oil) strongly affects the mechanical properties of this polymer. Unsealed specimens fractured in a brittle manner at almost the same strain of 5% in the whole pressure range examined, while specimens sealed with Teflon tape and rubber showed a brittle to ductile transition at only 0.25 kbar. At this pressure, the craze initiation and shear band initiation stresses were found to become equal. The pressure dependence of the shear band initiation stress could be expressed well with a “nonlinear” pressure-dependent von Mises criterion and the onset of the shear banding was proved to relate to the enthalpy energy density stored in the specimen. The combination of the nonlinear pressure-dependent von Mises criterion and the enthaply energy density concept enabled us to predict the pressure dependence of Young's modulus.

Maximum Likelihood Characterization of the Von Mises Distribution

Abstract: In 1918 von Mises discovered the circular probability distribution which now bears his name by studying the analogue on the circle of the Gaussian maximum likelihood characterization of the normal distribution on the line. Teicher [6] gave a specific condition on the density function for the Gaussian characterization to hold (see also Kagan, et al. [2], p, 411). It is shown in this paper that the same condition is sufficient for the von Mises characterization to be valid. The proof is based on Teicher’s approach, but the periodic nature of circular densities makes substantial modifications necessary. An extension to the hyperspherical case is also given.

Cracking Analysis of Reinforced Concrete Plates

Abstract: This paper develops an elastic-post elastic anlaysis for the response of reinforced plates of a tension-weak material such as concrete under small deflection theory limitations. The finite element displacement method of discretization is utilized, and a layered model is chosen to allow for different arrangements of reinforcing. As the load is progressively increased, cracking or crushing of the concrete layers and yielding of the steel layer can occur. New constitutive relations are derived to represent this behavior. Concrete is assumed to follow a maximum normal stress criterion in tension, and a von Mises criterion in compression. The steel is assumed to follow the von Mises criterion. Loading is applied incrementally as cracking and crushing occur progressively through the thickness and across the surface of the plate.

Bursting pressure of thick-walled cylinders subjected to internal and external pressures, axial load and torsion

Abstract: A finite-total-strain, incompressible, analytical solution is presented to predict load-deformation relations for loads from zero to failure for thick-walled cylinders subjected to internal pressure, external pressure, axial load and torsion. The solution assumes that the material is an isotropic hardening material that obeys the von Mises yield condition. The flow law incorporates the prandtl-Reuss stressstrain relations and a loading function represented by the tension true-stress vs. true-strain diagram. Poisson's ratio is assumed to be equal to one-half for both elastic and plastic strains. The difference between the strains given by the incompressible solution and the correct strains are calculated for one set of elastic loads; the strains given by the incompressible solution are then corrected based on the assumption that each correction is proportional to the increase in the given component of load. Good agreement is indicated between the corrected incompressible solution and data obtained from cylinders made of either SAE 1045 steel, OFHC copper, or aluminum alloy 1100.

Finite element cyclic thermoplasticity analysis by the method of subvolumes

Abstract: The subject of this paper is the development of an analytical tool capable of economically evaluating the cyclic plasticity which occurs in areas of strain concentration resulting from the combination of both mechanical and thermal stresses. The techniques developed are capable of handling large excursions in temperatures with the associated variations in material properties, including plasticity. The techniques are capable of reproducing real cyclic material behavior including Bauschinger effect, cross-hardening and memory. These analytical techniques have been implemented in a time-sharing finite element computer program. Cyclic plasticity has been introduced into this program using incremental loading and an interative technique. The plasticity theory involved makes use of the von Mises yield criterion and the Prandtl-Reuss flow rule. The major portion of the developmental work in this effort was expended in the establishment of a temperature variable hardening rule and its finite element implementation. The plane stress, constant strain triangle is the finite element used in this work. The incremental plasticity solution is obtained by interatively revising and right-hand side of the system of finite element equations by the addition of a vector of plastic pseudo forces. The method of subvolumes is used to generate the vector of plastic pseudo forces such that real material cyclic plasticity behavior is mathematically reproduced. The effects of the plastic deformations are introduced into the system of finite element equations by considering them as load terms in much the same way as thermal expansions are usually treated. The nonlinear solution is then attained through solution of a series of elastic problems and by variation of the plastic load terms until the requirements of compatibility, equilibrium and the specified non-linear stress-strain relations are all met within a given tolerance.

Plasticity of ice and sand-ice systems

Abstract: The experimental deformation of ice and sand-ice systems is compared with predictions based upon plasticity theory. Properties of the materials were determined under various temperatures, confining pressures, and loading rates using conventional triaxial compression tests. Samples were indented at atmospheric pressure using flat punches and sharp wedges at two loading rates and calculated force-displacement relationships were determined for the Von Mises, coulomb, and parabolic yield conditions. Comparison of the results of the experiments with the computations indicates that the force-displacement relationships for ice and sand-ice samples can be approximated using plasticity theory. /AUTHOR/

Application of a von Mises transformation to a problem of non-linear one-dimensional electron plasma oscillations

Abstract: A von Mises transformation is applied to a non-linear boundary-value problem on electrostatic plasma oscillations. The results are found in good agreement with those of Davidson et al. (1968).

Inelastic Buckling of Plates Allowing for Shear Effects.

Abstract: : The inelastic buckling including the effects of transverse shear is analyzed for flat rectangular plates in uniform uniaxial compression. Using a hardening material obeying the von Mises yield condition, the problem is treated according to both the incremental and deformation theories of plasticity. The analysis is based on Shanley's concept of continuous loading. Using boundary conditions which permit separation of variables it becomes possible to solve the resulting ordinary differential equations by asymptotic approximations giving closed form expressions for the critical loads. The correction terms due to shear effects were obtained for infinitely long, and for square, simply supported plates, and for infinitely long ones, simply supported on three sides and free on one unloaded edge. The analysis presented is also suitable for sandwich plates. (Author)

Utilization of Cold Work in Cold-Formed Steel

Abstract: An analysis to predict the yield strength of corners in cold-formed steel structural members was presented by Karren in 1967. It is based on plastic theory, using isotropic power-law strain hardening with von Mises’ yield condition and plastic potential. The analysis and consequent design formulas are quite complicated. This paper presents an alterative elementary analysis; specific assumptions of isotropy, von Mises’ yield condition, and isotropic power-law strain hardening has been relaxed. The solution is specialized for the case of linear strain hardening, leading a simple and perspicuous design formula. The proposed formula gives practically the same result as existing code procedures.

An Elastic-Plastic Formulation for a Cylindrical Shell Finite Element

Abstract: Theme A N elastic-plastic formulation is presented for a curved ./^rectangular thin shell finite element. Elastic-perfectly plastic material behavior is assumed. The von Mises yield criterion is used to define the limit of plasticity. Plastic strain distributions and a distribution for an elastic-plastic boundary in the element are defined. Incremental stress-strain relations are developed for use in the plastic range. With this formulation and an incremental approach, yielding can be traced in a deforming shell and displacements, and stresses can be found at each increment of load.

On von mises directions

Abstract: In a previous paper [4], the author has derived the distribution of the length of the projection of a random unit vector inR n on the subspaceR m (1≦mň). The method used there is now applied to a direction defined by a unit vector of ann-dimensional hypersphere on the surface of which the probability element is given by then-dimensional von Mises distribution. The results obtained here include the previous results as a special case, since the random direction is a special case of von Mises direction.

The stability analysis of some shallow structures by the rzhanitsyn type creep law of the material

Abstract: The instability of von Mises truss and shallow sinusoidal arch is investigated either in symmetric or asymmetric buckling forms The constitutive equation of the material is assumed to be the general linear hereditary integral equation or the power series presentation of hereditary integrals in which the first considered equation forms the term of the first order In the linear material equation case the limit load value for asymptotically constant, stable state of equilibrium is analytically established and the relationship between load and critical time is numerically established In the case of non-linear material equation, only numerical treatment of the problem is outlined and demonstrated by an example