Mises Yield Criterion Research Articles

Shear behavior of horizontal joints between precast panels

The objective of this study is to investigate the shear resisting capacity of precast wall-to-wall horizontal connection system by dowel action and shear friction. Three types of connection systems, which have varying embedment length in the upper wall panels, were investigated. The specimens were subjected to displacement-controlled lateral loading. The parameters investigated were the load–deformation relationship, ultimate load carrying capacity, ductility and energy dissipation. The experimental values were compared with the theoretical values of ultimate shear resisting capacity calculated from the Von Mises yield criteria, ductile bending failure due to the formation of plastic hinges and the shear friction hypothesis.

Analysis of non-Hertz contact stress and bearing capacity on meshing pairs in a real-time non-clearance precision ball transmission

Considering the friction on meshing pairs in a real-time non-clearance precision ball transmission, a modified meshing mechanical analysis model was established, and the normal meshing force and tangential friction acting on each meshing pair were calculated accurately via the contact stiffness coefficient method. The ball–tooth contact was equivalent to the contact model of an ellipsoid and semi-infinite elastic solid according to non-Hertzian theory, and the contact stress of meshing pairs was analyzed by the discrete convolution and fast Fourier transform (DC-FFT) technique. Furthermore, the bearing-capacity estimation method for a transmission system was established based on the Mises yield criterion. The results show that the tangential distribution force has a significant effect on the contact stress field of a meshing pair, with the maximum Mises equivalent stress being approximately 0.621 times the central contact pressure at different meshing positions. Moreover, the bearing capacity of the planetary plate is weaker than that of the center plate; hence, the bearing capacity of a transmission system should be determined by the planetary plate.

Yield behavior of polystyrene at strain rate 106/s under quasi-isentropic compression

The yield behaviors of polystyrene(PS) were researched by means of the technique of magnetically driven quasi-isentropic compression on compact pulsed power generator CQ-4 for its better applications in protection structure designs and plastic bonded explosives. The experimental wave profiles of PS under quasi-isentropic compression exhibit obvious inflection point at the interface velocity of 50 m/s between PS and LiF window, from which the isentropic elastic limit is inferred to be 0.39 GPa at strain rate of 1 × 106/s and strain of 0.06. Based on Von Mises or Tresca yield criterion under one-dimensional strain, the initial yield strength of PS is derived to be 0.186 GPa, about 4 times the value of 0.04 GPa under quasi-static compression. The hydrodynamic simulations were conducted to describe the dynamic response of PS including the Mie–Grüneisen equation of state (EOS) and Steinberg–Guinan strength model. The yield response of PS under quasi-isentropic compression can be described well in our simulations, which shows excellent agreement with the experimental data.

Blast loading of bumper shielded hybrid two-core Miura-ori/honeycomb core sandwich plates

We analyze transient elasto-plastic deformations of two-core sandwich plates with and without a bumper and subjected to blast loads with the objective of ascertaining the energy dissipated due to plastic deformations. The facesheets and the core are assumed to be made of a high strength steel modeled as an isotropic material that obeys the von Mises yield criterion with linear strain hardening. It is first shown that considering a material failure criterion and deleting failed elements does not noticeably affect the energy dissipated in a sandwich plate. Subsequent analyses of two-core structures with and without a blast shield ignore the material failure and assume facesheets to be perfectly bonded to the core. The nonlinear transient problems have been numerically analyzed with the commercial finite element software, ABAQUS/ Explicit. Four different two-core sandwich plates obtained by varying locations of the Miura-ori and honeycomb cores are considered. Results without a shield indicate that using a Miura-ori core beneath the topmost facesheet dissipates more energy for moderate blast loads, while a combination of a honeycomb and a Miura-ori core has the least facesheet deflections. The effects of using a blast shield or a bumper, at a fixed standoff distance from a honeycomb-Miura sandwich panel, is studied by ensuring that the shield and the sandwich structure combination has the same areal density as the sandwich panel without the shield. It is found that for a given blast load, using the shield significantly reduces the energy dissipated in the sandwich panel, the bottom facesheet maximum centroidal deflection and the maximum plastic strain in the cores when compared with equal-weight panels without a shield. For the same energy dissipation, the structure with a blast shield has approximately 42% less weight than that without the shield.

Bifurcation of elastic–plastic thick-walled cylindrical structures

This article presents theoretical analysis of the bifurcation behavior of metallic thick-walled cylindrical structures, extremely loaded by combined pressure and axial force. The analysis, which is based on the continuum theory, takes into account large elastic–plastic deformations and non-linear isotropic hardening. Bifurcation analysis investigates the uniqueness of the velocity field in the fundamental state, which adopts a constitutive law is based on the von Mises yield criterion. The solution successfully predicts load and deformation limits associated with the onset of bulging and buckling bifurcation of thick-walled cylindrical structures. The theoretical solution is validated by comparing the theoretically obtained results with those obtained independently using nonlinear finite element simulations utilizing the commercial FEA software Abaqus. As an example, the numerical solution is presented for a thick, relatively long cylinder. The results show that, for axially compressed long cylinders, axial deformations at column buckling increase with additional internal or external pressure. The results also explain and quantify the transition from axisymmetric bulging to column buckling bifurcation modes. It also explains the occurrence of non-symmetric (localized) bulging, which follows the axisymmetric bulging. The findings provide valuable information in the safety design of extremely loaded hollow cylindrical columns, thick-walled pressure vessels, piping and other cylindrical structures.

Effect of friction welding conditions on joint properties of austenitic stainless steel joints by friction stud welding

ABSTRACTThis study focuses on the opening mode of induction bends; this mode represents the deformation outside a bend. Bending experiments on induction bends are shown and the manner of failure of these bends was investigated. Ruptures occur at the intrados of the bends, which undergo tensile stress, and accompany the local reduction in wall thickness, i.e. necking that indicates strain localization. By implementing finite element analysis (FEA), it was shown that the rupture is dominated not by the fracture criterion of material but by the initiation of strain localization that is a deformation characteristic of the material. These ruptures are due to the rapid increase in local strain after the initiation of strain localization and suddenly reach the fracture criterion. For the evaluation of the deformability of the bends, a method based on FEA that can predict the displacement at the rupture is proposed. We show that the yield surface shape and the true stress–strain relationship after uniform elongation have to be defined on the basis of the actual properties of the bend material. The von Mises yield criterion, which is commonly used in cases of elastic–plastic FEA, could not predict the rupture and overestimated the deformability. In contrast, a yield surface obtained by performing tensile tests on a biaxial specimen could predict the rupture. The prediction of the rupture was accomplished by an inverse calibration method that determined the true stress–strain relationship after uniform elongation.

Model of Structured Emulsion Droplet Stability and Reconfigurability.

A model of internally structured emulsion droplets is presented that accounts for the traction forces generated by interfacial tension and the von Mises yield criterion of the internal supporting network. For symmetric droplets, the method calculates the total stress acting on a droplet locally, allowing droplet stability and location of failure to be predicted. It is not regions of high interfacial curvature that prompt droplet reconfiguration, rather regions transitioning from high to low curvature. The model enables the design of emulsion droplet response and reconfigurability to external triggers such as changes in surface tension (surfactant concentration) and temperature.

A simplified method for calculating surface stress of thick walled cylinder based on numerical calculation method

The maximum compound stress in the thick wall cylinder is usually the key factor that causes the thick wall cylinder to crack. The existing calculation method for stress–strain under thermo-mechanical impact in thick wall cylinder is suitable for stress analysis in the thermo-elastic range. However, the compound stress of the thick wall cylinder under the thermoplastic condition cannot be well analyzed. In this paper, a method to calculate the compound stress of the thick wall cylinder under the effect of thermal–mechanical impact is proposed, based on the finite difference method and the ideal elastic–plastic model and the Mises yield criterion. This method solves the problem of the compound stress calculation to the tube wall under the thermoplastic condition, which change as a result of the combined effect of thermo-mechanical impact. The compound stress in the wall close to the bore surface at different times during shooting is calculated, taking the firing process of a gun as an example. The calculation results well explain the cause of the formation of the crack and the distribution characteristics of the crack in the bore surface.

A coupled elastic-plastic damage model for the mechanical behavior of three-dimensional (3D) braided composites

A coupled elastic-plastic damage model is developed to describe the non-linear mechanical behavior of three-dimensional (3D) braided composites. In this model, the fiber breakage, inter-fiber fracture and matrix fracture are considered in the level of the fiber bundle and matrix. The onset and propagation of fiber bundle failure mechanisms are elastic and brittle, which is accounted for elastic damage model, and the elastic-plastic damage model used to describe the degradation of matrix is non-linear with progressive damage and inelastic strains. A set of internal variables are introduced to characterize the damage states of the fiber bundle and matrix and as a subsequence the degradation of the material stiffness. The damage initiation and propagation criteria are based on the Hashin criteria for the fiber bundle and the von Mises yield criterion for the matrix. The proposed damage model is implemented in the non-linear finite element analysis code ABAQUS using a user-subroutine UMAT to determine the response behavior of 3D braided composites under quasi-static loading, and the numerical predictions are compared with experimental data. The results predicted by the proposed model agree well with the experiment.

Structural Design Optimization of Multi-layer Spherical Pressure Vessels: A Metaheuristic Approach

This study addresses the optimum design problem of multi-layer spherical pressure vessels based on von Mises yield criterion. In order to compute the structural responses under internal pressure, analytical solutions for one-, two-, and three-layer spherical pressure vessels are provided. A population-based metaheuristic algorithm is reformulated for optimum material selection as well as thickness optimization of multi-layer spherical pressure vessels. Furthermore, in order to enhance the computational efficiency of the optimization algorithm, upper bound strategy is also integrated with the algorithm for reducing the total number of structural response evaluations during the optimization iterations. The performance of the algorithm is investigated through weight and cost minimization of one-, two- and three-layer spherical pressure vessels and the results are presented in detail. The obtained numerical results, based on different internal pressures as well as vessel sizes, indicate the usefulness and efficiency of the employed methodology in optimum design of multi-layer spherical pressure vessels.

The analysis of reinforced concrete slabs strengthened by composite fabrics by the finite element method

The finite element method of calculation of reinforced concrete slabs strengthened with composite fabrics based on carbon fibers, implemented in the PRINS program, is considered. The method is designed for analyzing the stress-strain state of reinforced concrete structures when cracks in concrete and plastic deformations in the reinforcement arise. The calculation is carried out in increments, and at each stage of loading a variable stiffness matrix is used. Its constant part represents the stiffness matrix at the beginning of the loading stage, and the variable one is calculated taking into account the stress-strain state at the end of the current iteration. The variable part of the stiffness matrix, multiplied by the displacement vector found at the previous iteration, is transferred to the right side of the equation system and is considered to be an additional load. When cracks occur or when plastic strains appear, the stresses are corrected in accordance with the specified deformation diagrams. Therefore, at the end of the loading step the equilibrium conditions are checked. If necessary, the external and internal forces are balanced. When considering plastic deformations in concrete and reinforcement, the theory of plastic flow and the Huber - Mises yield criterion, modified taking into account the experimental studies of Kupfer et al., are used. An example of the reinforced concrete slab analysis with different variants of strengthening by composite and without strengthening is given. The results of the calculation are analyzed. The possibility of studying the stress-strain state throughout the entire path of loading of reinforced concrete slabs up to destruction is shown.

A Simple Model for Elastic‐Plastic Contact of Granular Geomaterials

We propose a simple elastic‐plastic contact model by considering the interaction of two spheres in the normal direction, for use in discrete element method (DEM) simulations of geomaterials. This model has been developed by using the finite element method (FEM) and nonlinear fitting methods, in the form of power‐law relation of the dimensionless normal force and displacement. Only four parameters are needed for each loading‐unloading contact process between two spheres, which are relevant to material properties evaluated by FEM simulations. Within the given range of material properties, those four parameters can be quickly accessed by interpolating the data appended or by regression functions supplied. Instead of the Von Mises (V‐M) yield criterion, the Drucker–Prager (D‐P) criterion is used to describe the yield behavior of contacting spheres in this model. The D‐P criterion takes the effects of confining pressure, the intermediate principal stress, and strain rate into consideration; thus, this model can be used for DEM simulation of geomaterials as well as other granular materials with pressure sensitivity.

Explanation the difference in destructed areas simulated using various failure criteria by the wave dynamics analysis

Recent researches have shown that the damaged areas, calculated using various failure criteria for materials with complex heterogeneous structure are not always consistent with physical experiments and with each other. In this paper, we compare two failure criteria, i.e. the principal stress criterion and the von Mises yield criterion. Also, we compare two models of destruction formation, i.e. the model of fractures and sand model. Using the wave dynamics analysis, we explain the difference in the calculated zones of destruction. We indicate what differences in elastic wave phenomena cause the difference in the calculated fracture zones. We assume that further study of the connection between wave phenomena and destruction of materials will allow to develop more precise failure criteria. To carry out the research, we applied numerical modeling of spatial dynamic elastic wave processes in a nuclear power plant and enclosing rocks. We use the grid-characteristic method on combined regular and structural hexahedral grids to describe the complex shape of the dome of the nuclear power plant with minimal computational costs. Moreover, in this work, we consider an approach for calculating the contribution of dynamic elastic wave phenomena to seismic stability of facilities. This technique can be especially useful in the development and testing of seismic insulation of buildings. We propose a failure formation model that takes into account the contribution of static loads and dynamic loads separately.

Effect of the yield stresses in uniaxial tension and pure shear on the size of the plastic zone near a crack

In this paper, we make use of complex potentials for the problem of an elliptic hole subject to far field uniaxial tension to obtain the elastic stress distribution in the vicinity of a crack. Unlike the classical Westergaard stress distribution, the new stress field obtained is not axisymmetric in the crack plane. Using this new elastic stress field, it is possible to assess the effect of the particularities of yielding on the extent of the plastic zone near a crack. Analysis is done considering yielding governed by von Mises, Tresca, and Drucker yield criterion, respectively. It is demonstrated that the ratio between the yield stresses in uniaxial tension and pure shear of a material has a great influence on the size of the plastic zone around the crack. Specifically, the larger this ratio the larger is the plastic zone. Finite-element calculations confirm the theoretical predictions. Moreover, we derive new analytic relations between the length of the plastic zone, measured from the crack tip in the crack plane, and the external applied load for the case when yielding is governed by the von Mises and Tresca criterion, respectively.

A multisurface model for gradient‐enhanced damage coupled to finite plasticity

AbstractA gradient‐enhanced damage formulation is coupled to isotropic plasticity in the framework of finite strains. Within the finite element method, an additional field variable representing nonlocal damage is introduced and linked to its local counterpart in order to allow a standard local formulation at the material point level. The onset of damage and plasticity is governed by damage and yield criteria respectively. This multisurface approach requires the determination of the two Lagrange multipliers. By using logarithmic strains, a formulation in principal axes in combination with a von Mises yield criterion is implemented. The damage functions are defined by means of exponential functions in order to avoid further constraints on the local damage variable. The model is able to capture a wide range of material responses, ranging from brittle to ductile damage and plasticitiy dominated behaviour. The mesh independence of the model is shown by means of representative finite element examples. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Instability and axisymmetric bifurcation of elastic-plastic thick-walled cylindrical pressure vessels

This article presents a theoretical and numerical investigation of the instability and bifurcation of metallic thick-walled cylindrical pressure vessels loaded by combinations of large pressure and axial force. A general bifurcation theory is developed considering elastic-plastic material behavior with non-linear isotropic hardening. The constitutive law is based on applying the von Mises yield criterion in association with the normality rule. Instability limit loads and deformations are obtained and compared with those associated with axisymmetric bifurcation. The developed theory is validated by comparing the theoretically obtained results with those obtained numerically using nonlinear finite element simulations. It is shown that axisymmetric bifurcation occurs at descending loads after the instability limit has been reached. The unstable regular deformation, which continues under descending loads prior to bifurcation, is more evident in shorter cylinders where the delay of bifurcation after instability depends on the loading combination. While in some cases, bifurcation immediately follows instability, leading to catastrophic failure, in some other cases axisymmetric bifurcation is delayed so much that it does not occur at all, even after extremely large unstable regular deformations have developed under descending loads, which provides the opportunity for further energy absorption through unstable, albeit regular plastic deformations. This investigation addresses and provides a solution for a long-standing unresolved problem. The findings provide valuable information in the safety design of extremely loaded pressure vessels.

Mechanical modelling and simulation analyses of stress distribution and material failure for vanadium redox flow battery

During the operation of vanadium redox flow battery, the cell stack can suffer from electrolyte leakage and material failure that significantly affect the overall performance of the battery, provided that the stack is improperly designed and assembled. In order to manufacture more reliable battery stacks without undergoing electrolyte leakage and mechanical failure, the stress distributions on all key components of the stack need to be known. In this study, three-dimensional mechanical models are developed to perform simulation analyses on stress distribution for the cell stacks. Stress distributions on key cell components under specified sealing gasket designs, assembling forces and number of cells in a stack are investigated for the single cell and multi-cell stacks, while potential material failure and damage for the stack components are also analyzed in accordance with maximum stress criterion and von Mises yield criterion depending on the material of the components. Simulations results successfully demonstrate the stress distribution and magnitude in specified stack design and assembly condition, and highlight the importance of mechanical analyses in developing flow battery stacks with superior sealing and mechanical performance for long-term use.

Effective elastic–plastic response of two-phase composite materials of aligned spheroids under uniaxial loading

In this study the incremental elastic–plastic double-inclusion model previously developed for two-phase particulate composites of spherical particles is extended to two-phase particulate composites of aligned spheroidal particles. The study is limited to the effective elastic–plastic response under uniaxial loading of composites consisting of purely elastic particles and elastic–plastic matrix of the von Mises yield criterion with isotropic strain hardening. The incremental elastic–plastic double-inclusion model is formulated through the use of the matrix tangent moduli, and evaluated by comparison of the model predictions with the exact results of the direct approach using representative volume elements containing many particles, and with available experimental results. It is shown that the incremental elastic–plastic double-inclusion formulation gives good prediction of the effective elastic–plastic response of two-phase composites of aligned spheroidal particles under uniaxial loading at moderate particle volume fractions. A unique feature of the present study is that during elastic–plastic deformation the composite matrix is treated as a two-phase material consisting of both an elastic and a plastic region.

Accelerated proximal gradient method for elastoplastic analysis with von Mises yield criterion

It is known that, under certain conditions, the quasi-static incremental analysis problem of elastoplastic structures with the von Mises yield criterion can be formulated as a second-order cone programming (SOCP) problem, which can be solved with a primal-dual interior-point method. Alternatively, this paper proposes to solve an equivalent unconstrained nonsmooth convex optimization problem, which has a form similar to a class of regularized least-square problems, known as group LASSO. We propose an accelerated proximal gradient method with an adaptive restart scheme for solving this unconstrained optimization problem. The algorithm is easy to implement, and free from numerical solution of linear equations unlike conventional methods in computational mechanics. Numerical experiments suggest that the presented algorithm outperforms a standard solver that implements a primal-dual interior-point method for conic optimization.

Effect of Computational Parameters on Springback Prediction by Numerical Simulation

Elastic recovery of the material, called springback, is one of the problems in sheet metal forming of drawpieces, especially with a complex shape. The springback can be influenced by various technological, geometrical, and material parameters. In this paper the results of experimental testing and numerical study are presented. The experiments are conducted on DC04 steel sheets, commonly used in the automotive industry. The numerical analysis of V-die air bending tests is carried out with the finite element method (FEM)-based ABAQUS/Standard 2016 program. A quadratic Hill anisotropic yield criterion is compared with an isotropic material described by the von Mises yield criterion. The effect of a number of integration points and integration rules on the springback amount and computation time is also considered. Two integration rules available in ABAQUS: the Gauss’ integration rule and Simpson’s integration rule are considered. The effect of sample orientation according to the sheet rolling direction and friction contact behaviour on the prediction of springback is also analysed. It is observed that the width of the sample bend in the V-bending test influences the stress-state in the cross-section of the sample. Different stress-states in the sample bend of the V-shaped die cause that the sheet undergoes springback in different planes. Friction contact phenomena slightly influences the springback behaviour.