Mises Yield Criterion Research Articles

A micromechanical analysis of strain concentration tensor for elastoplastic medium containing aligned and misaligned pores

In this paper, making use of Eshelby tensor for the elastoplastic medium, will be presented an approach for the strain concentration tensor for materials that present spherical or spheroidal pores. The pores are embedded in a homogeneous isotropic matrix which presents an elastoplastic behavior, governed by the von Mises yield criterion and isotropic hardening. In this context, it will also be analyzed the behavior of a porous material through the influence of the extraction of the isotropic part of the anisotropic operator. The effective properties of the material in each incremental step are obtained through the micromechanical Mori-Tanaka's model. Through elastoplastic strain concentration tensor for aligned or misaligned pores, it was observed that the pore direction represents a greater influence on the elastoplastic behavior of the material studied than aspect ratio (length divided by pore diameter). This approach has the advantage of being easily incorporated into conventional mean-field homogenization (MFH) schemes for the case where inclusion stiffness is neglected and presents different geometries or directions in 3D space.

Inverse Finite Element Approach to Identify the Post-Necking Hardening Behavior of Polyamide 12 under Uniaxial Tension.

Finite-element (FE) simulations that go beyond the linear elastic limit of materials can aid the development of polymeric products such as stretch blow molded angioplasty balloons. The FE model requires the input of an appropriate elastoplastic material model. Up to the onset of necking, the identification of the hardening curve is well established. Subsequently, additional information such as the cross-section and the triaxial stress state inside the specimen is required. The present study aims to inversely identify the post-necking hardening behavior of the semi-crystalline polymer polyamide 12 (PA12) at different temperatures. Our approach uses structural FE simulations of a dog-bone tensile specimen in LS-DYNA with mesh sizes of 1 mm and 2 mm, respectively. The FE simulations are coupled with an optimization routine defined in LS-OPT to identify material properties matching the experimental behavior. A Von Mises yield criterion coupled with a user-defined hardening curve (HC) were considered. Up to the beginning of necking, the Hockett–Sherby hardening law achieved the best fit to the experimental HC. To fit the entire HC until fracture, an extension of the Hockett–Sherby law with power-law functions achieved an excellent fit. Comparing the simulation and the experiment, the following coefficient of determination could be achieved: Group I: > 0.9743; Group II: > 0.9653; Group III: > 0.9927. Using an inverse approach, we were able to determine the deformation behavior of PA12 under uniaxial tension for different temperatures and mathematically describe the HC.

Theoretical prediction of cross-sectional deformation of circular thin-walled tube in large elastic–plastic deformation stage under lateral compression

The present paper focusing on the most important energy absorbing system of the circular thin-walled tubes or shells under lateral compression between two rigid plates, which is also a basic mechanical issue, studies the cross-sectional deformation in terms of the compressive force applying to the tube in the large elastic–plastic deformation stage during the lateral compressive process by both theoretical as well as finite element analysis (FEA) methods. Firstly a FEA simulation for the thin-walled tube’s lateral compressive process between two parallel plates is carried out to analyze the mechanical response and deformation characteristics, and then it is validated by tube’s lateral compressive experiment using digital image processing technology. Following the simulation results, some assumptions are proposed for theoretical derivation. Secondly focusing on the large elastic–plastic deformation stage (Stage II, in this paper), the compressive deformation of thin-walled tubes is divided into elastic and plastic regions according to the von Mises yield criterion. In elastic region the linear strain–displacement relations of shell theory and Hooke’s stress–strain relations are employed, and in plastic region the nonlinear large strain–displacement relations of doubly-curved shell theory and the power hardening rule are employed. Then considering both geometric and material nonlinearities, the equilibrium equation, which is a complicate integral equation with the variable upper limit, is derived using the principle of virtual work. It is solved by expanding the integrand as a set of polynomials power series. Then the predicted cross-sectional deformation in terms of the compressive force can be obtained by the iterative method. Finally some lateral compressive simulations involving various tubes with different geometric parameters are carried out, and the theoretical model is validated by comparison of the cross-sectional profiles predicted by theoretical model with those obtained by the simulations as well as other methods. At the same time, the applicable conditions of this model are discussed. This paper will play a positive role in studying the cross-sectional deformation for various shells under lateral compression in different application areas.

Analysis of Side-Wall Wrinkling in Deep Drawing Processes

Wrinkling, developed due to compressive instability, is one of the main failure modes in deep drawing processes. Depending on the die geometry and blank holder force, it can be observed as flange wrinkling and/or side-wall wrinkling. In this study, side-wall wrinkling in cylindrical cup drawing process is investigated by using different constitutive models that are formed by using CPB06ex2, Hill’48, BBC2008-8p and BBC2008-16p yield criteria with isotropic hardening, and von Mises yield criterion with isotropic, kinematic and combined hardening. Numerical simulations are performed by implementing CPB06ex2, BBC2008-8p and BBC2008-16p models to a commercial finite element code through user subroutines. AA5042-H2 aluminium alloy is selected as a sheet material with 0.2083 mm thickness. In order to verify the developed models, the experimental results of the previous works for wrinkling profile and punch force evolution are employed. The results are compared and presented for the considered yield criteria.

Bulging of Isotropic Materials

There is a large body of literature on both the techniques for bulge testing and experimental results for various metallic materials (see the book of Banabic [1]). Generally, the experimental data for isotropic materials are interpreted using the von Mises yield criterion [2]. In this paper, we investigate the role played by the third invariant of the stress deviator, on the response under bulging of isotropic materials that have the same mechanical response in tension and compression. To this end, we use the yield criterion developed by Cazacu [3] and our implementation of this model in the F.E. code Abaqus [4]. For isotropic materials, this yield criterion involves a unique parameter, denoted ; in the case when it reduces to the von Mises yield criterion while for it involves dependence on . The results of F.E. simulations of bulge tests for isotropic materials characterized by various values of the parameterput into evidence new aspects concerning the stress states experienced by the respective materials under bulging.

On the Effect of the Tension-Compression Ratio on Forming of Isotropic Materials

It is generally believed that the choice of the yield criterion used to describe the plastic behaviour of isotropic metallic materials does not affect much the accuracy of the predictions of forming operations. For this reason, the von Mises yield criterion is widely used for modelling their plastic behaviour. However, according to the von Mises yield criterion, the ratio between the yield stresses in tension and compression is always 1.0. Nevertheless, materials can present same asymmetry, i.e. a strength differential (SD) effect. In this work, the yield criterion proposed by Cazacu et al. [1], is adopted to describe the mechanical behaviour of isotropic materials, with different levels of tension-compression asymmetry. Numerical simulations of the deep drawing of a cylindrical cup were performed considering these different virtual isotropic materials, in order to evaluate its impact on the thickness distribution and cup height. The analysis of the stress and strain paths, for material points initially located in the flange is performed, enabling the correlation between the thickness distributions predicted and the plastic strain ratios obtained analytically, using the yield function and the normality rule. The results show that even small changes in the tension-compression stress ratio can influence the strains distribution, in isotropic materials.

Investigation of plastic and slipping regions at the edge of an adhered complete contact of elastically dissimilar materials

Slipping and yielding at a sharp edge in an adhered and complete contact problem is studied. Eigenvalue problem is formed and eigen-solutions are obtained. Stress distribution in the vicinity of the sharp edge is analyzed using the singular terms of the stress equations. Generalized stress intensity factors, KI and KII are evaluated using a simple finite element analysis. Von Mises yield criterion is applied to observe the boundary of the plastic region on the contact surface. Ratio of the shear to normal stresses is compared with the coefficient of friction to estimate the slip region. With using those analysis method, analyzed is a contact between a cracked pellet and a cladding tube of a nuclear fuel rod, made of uranium dioxide and zirconium alloy, respectively, as an example problem. Under the average contact stress of 10 MPa, the contact length of 10 mm, and 0.3 ≤ μ ≤ 0.7, the size of the plastic region is found extremely tiny (order of 10-6 mm) in the cladding tube. Whereas, the size of the slip region in the vicinity of the contact edge dramatically changes (order of 1.0 ∼ 10-8 mm). The effect of material dissimilarity is investigated for the condition of xp = xs. The result is displayed in the Dundurs parallelogram domain, (α,β).

Modeling and Simulation of the Mechanical Properties of Reinforced Fuel Cell Membranes

Polymer electrolyte fuel cells (PEFCs) have gained popularity over internal combustion engines due to their zero CO2 emission, low working temperature, and high efficiency. However, transportation markets generally require high durability and reliability, which remains a significant challenge for PEFC developers. For instance, the thin, ion-conducting membranes used in PEFCs must be able to withstand both chemical and mechanical stresses during dynamic operation. Reinforced membranes even still there are durability challenges that remain even though it is more robust. These membranes have limited mechanical strength, and micro-cracks may allow hydrogen permeation and cause ultimate fuel cell failure. Dynamic stresses caused by temperature and humidity cycles are causing micro-cracks to form and propagate. Because the membrane is constrained by the other parts of the membrane-electrode assembly (MEA), any change in temperature and humidity can create swelling strain and thermal strain in the membrane, resulting in residual stress [1]. The first step in understanding this damaging phenomenon is to simulate the membrane's visco-elastic and visco-plastic behavior while taking temperature, humidity, and strain rate into account. The objective of the present work is to develop such a constitutive mechanical model for mechanically reinforced membranes, which are commonly used in modern PEFCs.Khorasany et al. [2] developed a fatigue lifetime model based on the elastic-plastic constitutive method and Smith-Watson-Topper (SWT) fatigue equilibrium for conventional, non-reinforced fuel cell membranes. In the present work, for strains below the yield point, the linear elasticity by Hooke's law has been considered and the visco-elastic and visco-plastic behaviors of the membrane have been neglected, but for every temperature and humidity, the related Young’s modulus and Poisson’s ratio have been obtained from prior experiments, and for plastic yield response, the Von Mises yield criterion has been selected. Khattra et al. [3] used the G’Sell-Jonas theory for the constitutive model of a non-reinforced membrane, which can only be employed for tensile stresses, while in this study, a generalized G’Sell-Jonas approach; equation 1, has been developed for the reinforced membrane that can also be used for compressive stresses that are common during in-situ fuel cell conditions. This phenomenological theory accounts for the effects of temperature, humidity, and strain rate on membrane mechanical properties and, when combined with thermal and swelling strains, provides a comprehensive model of membrane behavior for both ex-situ and in-situ conditions. For the reinforced membrane, tensile stress-strain tests in two principal in-plane directions have been done that showed its isotropic behavior and, therefore, provide input data for the parameters of the proposed generalized G’Sell-Jonas model. σ(ε,T,H)generalized G'Sell-Jonas=step(ε)K(T,H)(1-e-w(H)abs(ε))eh(H)ε^2 (1) step(ε)=+1 ε≥0, -1 ε<0 In the above equations, K, w, and h are empirical parameters dependent on temperature (T) and humidity (H), and ε is strain. Elastic modeling based on Von-Mises has been studied for constitutive models with stresses below 1 MPa, while isotropic work hardening based on the generalized G'Sell-Jonas theory has been considered for higher stresses in order to follow plastic behavior. In elastic mode, the membrane's Young’s modulus is calculated using a function of humidity and temperature derived from tensile tests. Tensile tests under four environmental conditions and two strain rates in two principal in-plane directions, as well as fatigue tests for extracting S-N curves for this membrane, have been obtained using dynamic mechanical analysis (DMA).Based on Figure 1, the mechanical strength of this isotropic reinforced membrane decreases with increasing temperature and humidity, but the effect of temperature is greater. Because of the viscoelastic nature of the membrane, by increasing the strain rate, the membrane stiffness has been increased too. In the fatigue tests done in DMA, the force track is 150% (= ×100%), R-value = , and frequency is 10 Hz.FEM modeling based on G’Sell-Jonas’s theory shows a strong agreement with the experiments that has been illustrated in Figure 1. The fatigue lifetime distribution based on generalized G’Sell-Jonas’s theory and SWT parameters extracted from Khorasany’s paper [2] have been simulated that reveals when the maximum stress in fatigue cycles is more than 17-18 MPa, a huge drop in fatigue lifetime is observed. Acknowledgments Funding for this research has been provided by AVL Fuel Cell Canada and Mitacs. References Alavijeh, A.S., et al., Effect of hygral swelling and shrinkage on mechanical durability of fuel cell membranes. Journal of Power Sources, 2019. 427: p. 207-214.Khorasany, R.M., et al., Mechanical degradation of fuel cell membranes under fatigue fracture tests. Journal of Power Sources, 2015. 274: p. 1208-1216.Khattra, N.S., et al., Residual fatigue life modeling of fuel cell membranes. Journal of Power Sources, 2020. 477: p. 228714. Figure 1

Shear band formation in porous thin-walled tubes subjected to dynamic torsion

In this paper, we have performed 3D finite element calculations of thin-walled tubes subjected to dynamic twisting to investigate the effect of porous microstructure on the formation of shear localization bands under simple shear conditions. For that purpose, we have incorporated into the finite element model the porous microstructures of four different additive manufactured metals – aluminium alloy AlSi10Mg, stainless steel 316L, titanium alloy Ti6Al4V and Inconel 718 – for which the void volume fraction varies from ≈0.001% to ≈2%, and the voids size between ≈6μm and ≈110μm (Marvi-Mashhadi et al., 2021). For each microstructure, we have created up to 10 realizations varying the spatial location of the voids and the distribution of voids size. The matrix material is elastic/plastic, with yielding defined by the von Mises yield criterion and associated flow rule. The yield stress evolution is considered to be dependent on strain, strain rate and temperature, with parameters corresponding to Titanium and HY-100 Steel, taken from Molinari (1997) and Batra and Kim (1990), respectively. Moreover, we have assumed the deformation process to be adiabatic. The calculations have been performed for shear strain rates ranging from 100s−1 to 10000s−1. To the authors’ knowledge, this is the first study ever that simulates dynamic torsion testing of porous materials with actual representation of voids, providing new results which bring to light the influence of porosity on dynamic shear banding under simple shearing. Namely, the numerical calculations have shown that both the location of the shear band and the critical strain leading to the shear band formation depend on the spatial and size distribution of the voids in the specimen, evidencing the influence of material defects on the localization pattern. Notably, the shear band nucleation strain decreases with both the void volume fraction in the specimen and the size of the voids, the size of the largest pore being the main microstructural feature controlling the loss of load carrying capacity of the specimen. In addition, we have carried out a parametric analysis varying the temperature and strain rate sensitivities of the material, and the loading rate. For the strain rates investigated, increasing the loading speed leads to a mild decrease of the shear strain leading to shear band formation, while the strain rate sensitivity is shown to stabilize material behavior and delay localization. Moreover, the numerical results have made apparent that for the hardening materials considered, thermal softening is essential to trigger the shear band formation, so that the porous microstructure alone does not lead to shear localization.

On dynamic behavior and failure of high lock bolted joints: Testing, analysis and predicting

A bidirectional synchronous dynamic loading technique based on electromagnetic split Hopkinson tensile bar (ESHTB) system was employed to investigate the dynamic behavior and failure of high lock bolted joints. Force-displacement curves over wide ranges of loading speed (5 × 10−6 m/s to 15 m/s) and loading state (tension, shear and three kinds of tension-shear coupling) were obtained by combining with results obtained from quasi-static tests. An obvious elevation of failure load levels when changing the loading state from shear to tension or improving the loading speed was observed. Meanwhile, such strengthening effect of loading state on failure loads presented positive correlation with the loading speed. Detailed analysis for effect of loading state on mechanical behavior of bolted joints was conducted by applying von Mises yield criterion together with failure load analysis. Moreover, on this base, the influence of loading speed on failure loads was reasonably defined by applying a relation equal to the different strain rate effect between shear and tension for bolt material. Finally, a failure criterion considering coupling effect of loading speed and loading state on failure load of bolted joint was proposed. Prediction results showed a good agreement with the experimental results, indicating the determination of failure loads for bolted joints under different loading states over a wide range of loading speeds can be achieved.

Quasistatic anisotropic induced behaviour of a tatb-based plastic-bonded explosive

The constitutive law of a plastic-bonded explosive (PBX) based on TATB crystals is studied in the quasistatic loading range. The experimental data highlight a viscoelastic behaviour with damage, and an anisotropy induced by plastic flow. The existing models for PBXs being not appropriate, a constitutive law accounting for the observed mechanisms is proposed. The linear viscoelasticity is integrated in a microplane model describing an effective anisotropic damage. A multilayer viscoplasticity is used to yield a non-linear kinematic hardening. A von Mises yield criterion is defined on each surface and a dilatancy function describes the volumetric plastic yield. This law is implemented in the Abaqus/Standard finite element code in the form of a UMAT subroutine. The model is calibrated on ten tests. The simulations performed to compare the model to each experimental test correctly reproduce the behaviour of the studied explosive composition.

Mode III analysis of a piezoelectric rectangular plane weakened by multiple cracks and cavities

This study presents an analytical model for a piezoelectric rectangular plane weakened by multiple cracks and cavities, under in-plane electric displacement and anti-plane shear stress. The defects are considered either electrically permeable or impermeable. First, the piezoelectric rectangular plane is weakened by a Volterra-type screw dislocation. The electric and stress displacement fields of the domain under consideration are determined using finite Fourier transform. Then, the problem is reduced into a set of Cauchy integral equations in the piezoelectric rectangular plane using the distributed dislocation approach. The solution to these integral equations determines electric displacement and stress intensity factors and hoop stress around cavities in the piezoelectric rectangular plane. Also, the boundary of the plastic zone is found using the stress field in the vicinity of crack tips and the Von Mises yield criterion. Finally, multiple numerical results are provided to illustrate the capability of the dislocation method in handling different cases of crack and cavity configurations and arrangements.

Residual stress evolution for tooth double-flank by gear form grinding

In gear form grinding, the complexity of tool-workpiece geometries affects the grinding force and heat distribution along the tooth profile, thus resulting in difficulties in the calculation of residual stress. Specifically, the stress and heat generated on the newly machined tooth flank were influenced by the former grinding passes. Unfortunately, this issue was ignored in the previous research. To fill this gap, this paper presents a thermal-mechanical coupling calculation model considering the differences in gear double-flank, and a new heat source optimization algorithm is proposed. Firstly, according to the kinematic analysis of gear form grinding, the Lagrange interpolation method is used to solve unevenly distributed moving heat sources on the curved surface. Secondly, based on the theory of plastic increment combined with the von Mises yield criterion considering work hardening, the relationship between the temperature and the grinding stress on the first grinding tooth flank and the second grinding tooth flank is obtained through load cyclic loading. Finally, the residual stress field in the final state of all tooth flanks is obtained through the release procedure. The gear grinding experiments were conducted to verify the model, and the comparison results showed good consistency. The influence of unevenness in gear form grinding is not only reflected in the stress distribution along the tooth profile, but also on the different flanks. Based on the correlation law between the processing parameters and the residual stress on the tooth flanks, the optimal machining parameter range is obtained. The study provides an important reference for the understanding of gear form grinding mechanisms and the optimization of the grinding process.

A Compound Damage Constitutive Model Considering Deformation of Nonpersistent Fractured Rock Masses

This paper describes a study on the interaction between joint fissures in a nonpersistent jointed rock mass by introducing a self-consistent methodology, amending the traditional method of self-consistency by increasing the number of joints one by one, and deducing a new compound mesoscale and macroscale constitutive damage model based on the Betti energy reciprocity theorem. By analyzing the Mohr–Coulomb failure criterion and generalized von Mises yield criterion and their impact on the calculation result of macroscopic damage, the generalized von Mises criterion is proven to be more appropriate, and it is, thus, chosen for this compound damage constitutive model. Comparing the theoretical calculation and laboratory results of the compound damage model with the existing theoretical calculation results indicates the following: 1. The compound damage model in this paper provides a better fit of the stress–strain curves from the laboratory tests. 2. The theoretical calculative results for the compound damage model in this paper are consistent with the experimental results; that is, the peak load decreases as the connectivity rate increases. 3. For different joint angles and connectivity rates, the overall absolute deviations and relative deviations of the peak stress from the theoretical calculations and the laboratory tests are less than those from the theoretical calculations provided in the original literature. The theoretical calculations of the compound damage model in this paper are more aligned with the experimental results, verifying its correctness and rationality.

Finite element analysis of newly developed hip prosthesis

AbstractThe present study focuses on the design and finite element analysis of a novel hip prosthesis comprising truss structures intended to equally distribute the stress along the prosthesis. The prosthesis is designed to suit three different inclination angles of 20°, 40° and 60°. The three designs were subjected to loading conditions that emulate walking, jogging, and cycling activities via finite element simulations. Using the von Mises yield criterion and Goodman relation for fatigue, it is found that the safety factor and the life cycle of the proposed prosthesis design was within the acceptable range. Furthermore, the truss structures incorporated in the prosthesis appear to reduce the stress levels in the femur.

Mechanism of void healing in cold rolled aeroengine M50 bearing steel under electroshocking treatment: A combined experimental and simulation study

M50 bearing steel, as the important material used in aeroengine bearing, exhibits low cold working capacity with high susceptibility to produce voids. This would lead to the deterioration of mechanical property, which critically limits the industrial application of cold ring rolling (CRR) in M50 bearing rings. In this work, the mechanism of void healing in cold rolled aeroengine M50 bearing steel subjected to electroshocking treatment (EST) was investigated by combining experimental and simulation studies. The experimental results obtained using the three-dimensional X-ray microscopy (3D-XRM) technique show that the porosity of the CRR samples decreases from 0.26% to 0.09% after EST. The healing effect of larger voids is not obvious, while small voids are likely to be healed under EST. The simulation results indicate that due to the inhomogeneous distribution of the physical field, the local thermal compressive stress of as high as 2565.9 MPa is generated around the ellipsoidal void and thus drives void healing process. The healing process of ellipsoidal voids under EST can be divided into elastic and plastic deformation stages considering von Mises yield criterion. In the initial stage, only a small elastic deformation of 53.53 nm occurs in the minor axis direction of the void. In the plastic deformation stage, the material flows along the normal direction of the void with a reduction in the aspect ratio, thereby compressing the void surfaces and promoting their healing. Additionally, the degree of void healing depends on the shape characteristics (curvature and aspect ratio) of the void rather than the current direction. This research elucidates a new elastoplastic mechanism of void healing under EST, which also provides a promising prospect for the application of CRR in M50 bearing steel. • In situ characterization of voids before and after EST was realized using 3D-XRM. • A new elastoplastic mechanism of void healing under EST was elucidated. • The driving force of void healing was revealed by analysing the physical field distribution. • The ellipsoidal void is healed with the reduction in the aspect ratio. • The degree of void healing depends on the shape of the void rather than the current direction.

Failure analysis of composite repaired pipes subjected to internal pressure

While around 60% of pipelines transmitting oil and gas worldwide experience corrosion and metal loss, the composite repair technique has become a popular option developed in recent decades. Employing a theoretical methodology, this study deals with corroded metallic pipes repaired by composite repair systems such that the focus is the impact of elastoplastic deformations on the failure pressure. In this methodology, the elastoplastic strains are taken into account by employing the bilinear isotropic hardening plastic flow theory with the von Mises yield criterion. Three modes are recognized based on the region where failure occurs, and the results are presented. The findings revealed that when the failure happens in the defect region, the proposed formula estimates the failure pressure more accurately than when it occurs either far from the defect or in the composite sleeve. Moreover, studying the bonding strength between the pipe, infill material, and composite patch shows that the interface bonding strength between the pipe and the polymer filler plays a more significant role than the interface bonding strength between the polymer filler and the composite repair. The results of this study can assist maintenance engineers in better evaluating the reliability of composite repaired pipelines.

Limit Load Solution for Thin-Walled Cylinder with Circumferential Crack under Combined Internal Pressure, Axial Force, Bending Moment and Torsion Moment

T his research aims to establish the limit load solution for thin-walled cylinder with circumferential crack under combined internal pressure, axial force, bending moment and torsion moment. The solution is derived based on the net-section collapse principle and the von Mises yield criterion. The material considered in this work is assumed to be elastic-perfectly plastic. The solutions obtained from this work are compared with the results from the finite element models. The comparison shows that the equations established from NSC analysis provide acceptable results for the case of cracked cylinder under combined axial force and bending moment. For the case of cylinder subjected to internal pressure or torsional moment, however, these equations can be used to predict the limit load only if np ≤ 0.40 and nT ≤ 0.6 . This is because when the effects of internal pressure or torsional moment are included, the distribution of stresses on the crack plane at the yielding does not correspond to the NSC principal.

Analytical model of the in-plane torsion test

In research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination.

Adaptive XIGA shakedown analysis for problems with holes

Shakedown analysis plays a substantial role in safety assessment, especially in nuclear plant industry, chemical industry and civil engineering. This paper presents numerical investigations of shakedown problems with holes using the adaptive extended isogeometric analysis (XIGA). An adaptive strategy performed in the discretized framework of a kinematic approach and second-order cone programming (SOCP) is presented. The main idea is to integrate XIGA based on locally refined non-uniform rational B-splines (LR NURBS) into the SOCP to form an efficient approach for shakedown analysis. A SOCP form based on the von Mises yield criterion is established. By means of an effective SOCP solver, the arising optimization problem is then solved. In addition, the level set function is adopted to detect the position of holes. The L2-norm of plastic strain rates is used to guide local mesh refinement. The merits of the developed approach are its easy implementation and high computational efficiency. We consider several benchmark examples to illustrate the accuracy, reliability and efficiency of the developed method.