Showing papers on "von Mises yield criterion published in 2019"

Evolutionary topology optimization of continuum structures with stress constraints

Abstract: In this work, we propose to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization design subject to both constraints on volume fraction and maximum von Mises stress. To this end, the aggregated p-norm global stress measure is first adopted to approximate the maximum stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one or multiple Lagrange multipliers. The Lagrange multipliers are employed to yield compromised designs of the compliance and the p-norm stress. An empirical scheme is developed for the determination of the Lagrange multipliers such that the maximum von Mises stress could be effectively constrained through the controlling of the aggregated p-norm stress. To further enforce the satisfaction of stress constraints, the stress norm parameter p is assigned to a higher value after attaining the objective volume. The update of the binary design variables lies in the computationally efficient sensitivity numbers derived using the adjoint method. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.

Bridging finite element and machine learning modeling: stress prediction of arterial walls in atherosclerosis.

Abstract: Finite element and machine learning modeling are two predictive paradigms that have rarely been bridged. In this study, we develop a parametric model to generate arterial geometries and accumulate a database of over 12,000 finite element simulations of mechanical behaviour and stress distribution in these arterial models representative of atherosclerotic plaques. We formulate the training data to predict the maximum von Mises stress which could indicate risk of plaque rupture. Trained deep learning models are able to accurately predict the max von Mises stress within 9.86% error on a held-out test set. The deep neural networks outperform alternative prediction models and performance scales with amount of training data. Lastly, we examine the importance of attributing features on stress value and location prediction to gain intuitions on the underlying process. Moreover, deep neural networks can capture the functional mapping described by the finite element method which has far-reaching implications for real-time and multi-scale prediction tasks in biomechanics.

The yield normal stress

Abstract: Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to, or even larger than, the shear stress. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting nonviscometric flow behavior. Very little attention has thus far been paid to the normal stresses of yield stress fluids, which are difficult to measure. We report the first systematic study of the first and second normal stress differences in both continuous and slow oscillatory shear of three model nonthixotropic yield stress fluids, with N1 > 0 and N2 < 0. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress. However, the contribution of the normal stresses to the von Mises yield criterion for these materials is small.

Molecular dynamics simulation of subsurface damage mechanism during nanoscratching of single crystal silicon

Abstract: Three-dimension molecular dynamics (MD) simulation is employed to investigate the nanoscratching process of monocrystalline silicon with diamond tools. The effects of tool geometry on subsurface damage and scratching surface integrity are investigated by analyzing phase transformation, chip, defect atoms, hydrostatic stress, von Mises stress and workpiece deformation. In addition, a theoretical analytical model to study the subsurface damage mechanism by analyzing the zone size of phase transformation and normal force with diamond tools at different half-apex angles on silicon surfaces is established. The results show that a bigger half apex angle causes a higher hydrostatic stress, a larger chip volume, a higher temperature and a higher potential energy, and increases subsurface damage. The results also reveal that the evolution of crystalline phases is consistent with the distribution of hydrostatic stress and temperature. In addition, tip scratching with a bigger half-apex angle would result in a large...

Ductile fracture of an aluminum sheet under proportional loading

Abstract: The ductile fracture of an AA6111 aluminum sheet after a thermal cycle typical of auto-body paint-baking is investigated with the hybrid experimental-numerical method. The plastic flow of the material is examined by uniaxial tension, plane-strain tension, disk-compression and notched-tension experiments, that are used to calibrate the Yld2004-18p anisotropic yield criterion and the combined Swift-Voce hardening model. Then, the fracture behavior under equibiaxial and plane-strain tension, as well as uniaxial tension and shear, is characterized using a specially-developed cruciform specimen, along with center-hole and shear specimens, respectively. The cruciform fracture specimen proposed here contains two shallow hemispherical depressions (dimples) in the test-section, to initiate fracture. For the fracture characterization, special emphasis is put on specimen design, so that the stress states developed at the neighborhood of the fracture initiation point remain proportional throughout the loading history. In all experiments, the surface strain fields are measured by a stereo-type digital image correlation system. This information is used to validate finite element simulations of the fracture experiments. It is found that the Yld2004-18p model provides a better agreement with experiments than von Mises does, which underscores the sensitivity of the hybrid method to the plasticity models adopted. Once validated, these simulations are used to obtain the fracture loci in terms of two stress-state metrics, i.e., the stress triaxiality and Lode angle parameter.

Simulation and Visualization of Ductile Fracture with the Material Point Method

Abstract: We present novel techniques for simulating and visualizing ductile fracture with the Material Point Method (MPM). We utilize traditional particle-based MPM [Stomakhin et al. 2013; Sulsky et al. 1994] as well as the Lagrangian energy formulation of [Jiang et al. 2015] that utilizes a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. Material is elastic until its deformation exceeds a Rankine or von Mises yield condition, at which point we use a softening model that shrinks the yield surface until a damage threshold is reached. Once damaged, the material Lame coefficients are modified to represent failed material. We design visualization techniques for rendering the boundary of the material and its intersections with evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to represent crack surfaces that utilizes an extrapolation technique based on the MPM simulation. For traditional particle-based MPM we use an initial Delaunay tetrahedralization to connect randomly initialized MPM particles. Our visualization technique is a post-process and can be run after the MPM simulation for efficiency. We demonstrate our method with a number of challenging simulations of ductile failure with considerable and persistent self-contact.

Stresses in constant tapered beams with thin-walled rectangular and circular cross sections

Abstract: Tapered beams are widely employed in efficient flexure dominated structures. In this paper, analytical expressions are derived for the six Cauchy stress components in untwisted, straight, thin-walled beams with rectangular and circular cross sections characterised by constant taper and subjected to three cross-section forces. These expressions pertain to homogeneous, isotropic, linear elastic materials and small strains. In fact, taper not only alters stress magnitudes and distributions but also evokes stress components, which are zero in prismatic beams. A parametric study shows that increasing taper decreases the von Mises stress based fatigue life, suggesting that step-wise prismatic approximations entail non-conservative designs.

A stress-based topology optimization method for heterogeneous structures

Abstract: In this work, we introduce a method to incorporate stress considerations in the topology optimization of heterogeneous structures. More specifically, we focus on using functionally graded materials (FGMs) to produce compliant mechanism designs that are not susceptible to failure. Local material properties are achieved through interpolating between material properties of two or more base materials. Taking advantage of this method, we develop relationships between local Young’s modulus and local yield stress, and apply stress criterion within the optimization problem. A solid isotropic material with penalization (SIMP)–based method is applied where topology and local element material properties are optimized simultaneously. Sensitivities are calculated using an adjoint method and derived in detail. Stress formulations implement the von Mises stress criterion, are relaxed in void regions, and are aggregated into a global form using a p-norm function to represent the maximum stress in the structure. For stress-constrained problems, we maintain local stress control by imposing m p-norm constraints on m regions rather than a global constraint. Our method is first verified by solving the stress minimization of an L-bracket problem, and then multiple stress-constrained compliant mechanism problems are presented. Results suggest that good designs can be produced with the proposed method and that heterogeneous designs can outperform their homogeneous counterparts with respect to both mechanical advantage and reduced stress concentrations.

Prediction of Interfacial Debonding in Fiber‐Reinforced Composite Laminates

Abstract: An analytical method is established to estimate the load level when interfacial debonding occurs between fibers and matrix of a composite under an arbitrary load. Only the transverse tensile strength and the components' properties of the unidirectional (UD) composite are required for this estimation. For internal stress analysis based on micromechanics, the homogenized stresses in matrix must be converted into true values because of the nonuniform stress distribution due to embedded fiber. The stress concentration factors (SCFs) of matrix before and after the interfacial debonding are both essential, between which the difference indicates the effect of debonding on the stress fluctuations in matrix. A final true stress is obtained by accumulating the products of stress increments of matrix arising before and after debonding and corresponding SCFs. Letting the predicted transverse tensile strength of a UD composite with an initial perfect and later cracked interface be equal to the measured corresponding value, a critical von Mises stress of matrix at which the interfacial cracks appear is obtained. For a UD composite subjected to an arbitrary load, when the principal stress is positive and the von Mises stress of matrix reaches the critical value, the applied load level when interfacial debonding occurs is determined accordingly. POLYM. COMPOS., 2018. (c) 2018 Society of Plastics Engineers

Significance of Orthotropic Material Models to Predict Stress Around Bone-Implant Interface Using Numerical Simulation

Abstract: Several finite element models of bone-implant prosthetic derived with geometrical topology and material properties. Most of them adopted linear isotropic material properties to predict stresses around bone-implant interface. The objective of the present study is to compare stress distribution around bone-implant interface between two material models. In order to understand the biomechanical stress behavior at bone-implant interface, four different implant models were selected for the study. Mandibular bone section material models for isotropic and orthotropic material is defined with the contact between bone and implant surface to predict the von Mises stresses in the cancellous and cortical bone under the influence of vertical load of 100 N (coronal-apical), lateral load of 40 N (mesial-distal), and oblique load of 100 N at 45° to the axis of implant on crown surface. A nonlinear Abaqus CAE code is used to predict stresses distribution comparison between two material models. The current study compares the result of stress in cancellous and cortical bone with isotropic and orthotropic material models. The stress distribution along the interface was presented for vertical, lateral, and oblique loading of selected implant models. Finite element (FE) numerical simulation result shows that the orthotropic material model is more acceptable than the isotropic material model to predict stress along bone-implant interface.

Modeling of Buckling Restrained Braces (BRBs) using Full-Scale Experimental Data

Abstract: Hysteretic performance of buckling restrained braces (BRBs) having various core materials, namely, steel and aluminum alloy and with various end connections are numerically investigated. As a computational tool, nonlinear finite element analyses (FEAs) are performed to better model the hysteretic behavior. For the simulation, various aspects such as 1) stress — strain relationship including the strain hardening effect 2) von Mises yield criterion 3) contact surface parameters between the core metal and surrounding high strength grout and 4) friction are defined. Experimental results from near-full scale cyclic tests on two steel core BRBs having steel casing as a restraining environment (named as BRB-SC4 and BRB-SC5) and an aluminum alloy core & aluminum alloy casing tube (named as BRB-AC3) are used in the analyses. All cyclically tested specimens have been designed according to AISC Seismic Provisions. Numerical results obtained from 3D models developed in ANSYS-Workbench give satisfactory response parameters when compared with the experimental ones (e.g., hysteretic curves, dissipated energies). Further, a convergence analysis regarding element numbers in the developed model is conducted for each BRB specimen. Finally, key issues that influence the hysteretic modeling of BRBs are identified.

Effect of thread depth and implant shape on stress distribution in anterior and posterior regions of mandible bone: A finite element analysis.

Abstract: Background: The ability of modern implant dentistry to achieve goals such as normal contour, function, comfort, esthetics, and health to totally or partially edentulous patients guaranteed it to be more effective and reliable method for the rehabilitation process of many challenging clinical situations. In regard to this, the current study evaluates the effect of changing implant shape design parameters on interface stress distribution within the mandible bone. Materials and Methods: A numerical procedure based on finite element (FE) method was adopted to investigate the influence of using different body design and thread depth of the inserted implant on the final stress situation. For the purpose of evaluation, a three‑dimensional realistic FE models of mandible bone and inserted implant were constructed and analyzed using a pack of engineering software (Solidworks, and ANSYS). Six different commercial implant models (cylindrical and tapered) with three different V‑shaped thread depths (0.25 mm, 0.35 mm, and 0.45 mm) were designed to be used in this study. The suggested implants used in this study were threaded in two different locations of mandible bone; the anterior region (Type I model) and posterior region (Type II model). A vertical static load of 250 N was directly applied to the center of the suprastructure of the implant for each model. Results: For both models, evaluations were achieved to figure out the stress distribution patterns and maximum equivalent von Mises. The results obtained after implementation of FE dental‑implant models show that the highest stresses were located at the crestal cortical bone around the implant neck. In addition, the simulation study revealed that taper body implant had a higher peak value of von Mises stress than that of cylinder body implants in all types of bones. Moreover, a thread depth of 0.25 mm showed highest peak of maximum von Mises stresses for Type I and Type II models. Conclusion: The simulation results indicate that all models have the same von Mises stress distribution pattern and higher peak von Mises stresses of the cortical bone were seen in tapered implant body in contrast to the cylindrical body. Key Word: Dental Implant‑Abutment Design, finite element analysis, mandible, stress

Numerical Simulation on the Effect of Friction Stir Welding Parameters on the Peak Temperature, Von Mises Stress, and Residual Stresses of 6061-T6 Aluminum Alloy

Abstract: The friction stir welding (FSW) has become an important welding technique to join materials that are difficult to weld by traditional fusion welding technology. The model used in this study is a simplified version of the thermo-mechanical model developed by Zhu and Chao for FSW with aluminum alloy A6061-T6. Zhu and Chao presented nonlinear thermal and thermo-mechanical simulations using the finite element analysis code ANSYS APDL 16.2. They initially formulated a heat transfer problem using a moving heat source and later used the transient temperature outputs from the thermal analysis to determine residual stresses in the welded plates via a 3-D elastoplastic thermo-mechanical simulation. Two welding cases with two different parameters the feed rate and the rotation speed are analyzed. In the first part, we fixed the speed of advance and varied the speed of rotation (140 mm/min, 600, 1000, 1400 rpm) and in the second part fixed the speed of rotation and varied the speed of advance (600 rpm, 80, 100, 140 mm/min). The objective of this paper is to study the variation of transient temperature and distribution of Von Mises stress and evaluate the residual stress in a friction stir welded plate of AA 6061-T6. We have used the thermo-mechanical model developed by Zhu and Chao and implemented our program under the code ANSYS APDL. We see that the peak temperature obtained from simulation is approximately near the measured one. However, the peak temperature at the welded joints increased by increasing the rotation speed with the same tool profile and constant value of welding speed. The residual stresses are affected by the FSW processes, otherwise, by the welding temperature and mixing which have a relationship with the welding parameters. An increase in the welding speed apparently lead to an increase in the residual stress. The residual stresses found by this FE model have never exceeded the value of 54% of the elastic limit. We concluded that the model gives a good result in terms of stress. The results of the simulation are in good agreement with that of experimental results.

Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication

Abstract: Case-hardening is widely used to enhance gear loading capacity. Simulation of the material gradient properties and contact characteristics are the key issues in contact fatigue analysis of case-hardened gears. In this work, a plasto-elastohydrodynamic lubrication (PEHL) model incorporating the hardness gradient and surface roughness is developed to investigate the contact performance of case-hardened gears. The generalized Reynolds equation is solved to determine film thickness and contact pressure. The plastic deformation and residual stress are obtained via the half-space eigenstrain problem solving. The Dang Van multiaxial fatigue criterion and the Euler transformation are employed to evaluate the contact fatigue parameter based on the predetermined stress field. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for accelerating the computation. The influences of effective case depth, surface hardness and surface roughness on the contact performance are investigated. Numerical results indicate that as the surface hardness increases, the probability of fatigue crack nucleation decreases, and the depth of the crack initiation site increases. For a lower surface roughness case, the maximum von Mises stress and equivalent plastic strain appear at a deeper layer. As the surface roughness increases, the maximum values of pressure and stress increase sharply and move closer to the surface.

An equivalent von Mises stress and corresponding equivalent plastic strain for elastic–plastic ordinary peridynamics

Abstract: Simple formulas for calculating equivalent von Mises stress and von Mises effective plastic strain in an elastic–plastic ordinary peridynamic analysis are proposed. The equivalent von Mises stress is calculated by equating the deviatoric part of strain energy obtained from classical continuum mechanics and peridynamics. The effective plastic strain is proposed so that it reduced to uniaxial plastic strain in uniaxial tension test. Two example problems of the plate with a hole and a central crack under tension are considered to verify the validity of the proposed formulas. The plots of von Mises stress, equivalent plastic strain, plastic zone area and horizontal and vertical displacements are extracted and compared with the results obtain from the finite element analysis. The results show the good accuracy of the peridynamics in predicting the above mentioned parameters as well as the validity of the suggested formulas in predicting von Mises stress and equivalent plastic strain.

Strength-based topology optimisation of plastic isotropic von Mises materials

Abstract: Conventionally, topology optimisation is formulated as a non-linear optimisation problem, where the material is distributed in a manner which maximises the stiffness of the structure. Due to the nature of non-linear, non-convex optimisation problems, a multitude of local optima will exist and the solution will depend on the starting point. Moreover, while stress is an essential consideration in topology optimisation, accounting for the stress locally requires a large number of constraints to be considered in the optimisation problem; therefore, global methods are often deployed to alleviate this with less control of the stress field as a consequence. In the present work, a strength-based formulation with stress-based elements is introduced for plastic isotropic von Mises materials. The formulation results in a convex optimisation problem which ensures that any local optimum is the global optimum, and the problems can be solved efficiently using interior point methods. Four plane stress elements are introduced and several examples illustrate the strength of the convex stress-based formulation including mesh independence, rapid convergence and near-linear time complexity.