Elastoplastic Material Laws with Linear Yield Conditions

Author(s):  
E. Anderheggen ◽  
H. Elmer
2005 ◽  
Vol 33 (1) ◽  
pp. 38-62 ◽  
Author(s):  
S. Oida ◽  
E. Seta ◽  
H. Heguri ◽  
K. Kato

Abstract Vehicles, such as an agricultural tractor, construction vehicle, mobile machinery, and 4-wheel drive vehicle, are often operated on unpaved ground. In many cases, the ground is deformable; therefore, the deformation should be taken into consideration in order to assess the off-the-road performance of a tire. Recent progress in computational mechanics enabled us to simulate the large scale coupling problem, in which the deformation of tire structure and of surrounding medium can be interactively considered. Using this technology, hydroplaning phenomena and tire traction on snow have been predicted. In this paper, the simulation methodology of tire/soil coupling problems is developed for pneumatic tires of arbitrary tread patterns. The Finite Element Method (FEM) and the Finite Volume Method (FVM) are used for structural and for soil-flow analysis, respectively. The soil is modeled as an elastoplastic material with a specified yield criterion and a nonlinear elasticity. The material constants are referred to measurement data, so that the cone penetration resistance and the shear resistance are represented. Finally, the traction force of the tire in a cultivated field is predicted, and a good correlation with experiments is obtained.


Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2784
Author(s):  
Georgios Maliaris ◽  
Christos Gakias ◽  
Michail Malikoutsakis ◽  
Georgios Savaidis

Shot peening is one of the most favored surface treatment processes mostly applied on large-scale engineering components to enhance their fatigue performance. Due to the stochastic nature and the mutual interactions of process parameters and the partially contradictory effects caused on the component’s surface (increase in residual stress, work-hardening, and increase in roughness), there is demand for capable and user-friendly simulation models to support the responsible engineers in developing optimal shot-peening processes. The present paper contains a user-friendly Finite Element Method-based 2D model covering all major process parameters. Its novelty and scientific breakthrough lie in its capability to consider various size distributions and elastoplastic material properties of the shots. Therewith, the model is capable to provide insight into the influence of every individual process parameter and their interactions. Despite certain restrictions arising from its 2D nature, the model can be accurately applied for qualitative or comparative studies and processes’ assessments to select the most promising one(s) for the further experimental investigations. The model is applied to a high-strength steel grade used for automotive leaf springs considering real shot size distributions. The results reveal that the increase in shot velocity and the impact angle increase the extent of the residual stresses but also the surface roughness. The usage of elastoplastic material properties for the shots has been proved crucial to obtain physically reasonable results regarding the component’s behavior.


Author(s):  
Nengxiu Deng ◽  
Yannis P. Korkolis

The shear modulus of orthotropic thin sheets from three advanced high-strength steels (AHSS) is measured using the anticlastic-plate-bending (APB) experiment. In APB, a thin square plate is loaded by point forces at its four corners, paired in opposite directions. It thus assumes the shape of a hyperbolic paraboloid, at least initially. The principal stress directions coincide with the plate diagonals, and the principal stresses are equal and opposite. Hence, at 45 deg to these, a state of pure shear exists. A finite element (FE) study of APB is reported first, using both elastic and elastoplastic material models. This study confirms the theoretical predictions of the stress field that develops in APB. The numerical model is then treated as a virtual experiment. The input shear modulus is recovered through this procedure, thus validating this approach. A major conclusion from this numerical study is that the shear modulus for these three AHSS should be determined before the shear strain exceeds 2 × 10−4 (or 200 με). Subsequently, APB experiments are performed on the three AHSS (DP 980, DP 1180 and MS 1700). The responses recorded in these experiments confirm that over 3 × 10−4 strain (or 300 με) the response differs from the theoretically expected one, due to excessive deflections, yielding, changing contact conditions with the loading rollers and, in general, the breaking of symmetry. But under that limit, the responses recorded are linear, and can be used to determine the shear modulus.


1956 ◽  
Vol 23 (3) ◽  
pp. 395-402
Author(s):  
Jerome Weiner

Abstract The thermal stresses in a free plate of elastoplastic material subjected to a varying heat input over one face are determined. A heuristic solution is first found by suitable modifications of the known elastic solution. It is then verified that the solution satisfies all the conditions of the appropriate uniqueness theorem and represents therefore the unique solution to the problem. Residual stresses are determined and found to depend markedly on the peak magnitude of the heat input.


2020 ◽  
Vol 82 (1) ◽  
pp. 5-15
Author(s):  
S.M. Gertsik ◽  
Yu.V. Novozhilov

The paper presents the results of numerically modeling the dynamics of a concrete beam reinforced by longitudinal rods and transversal frames of rods under the effect of a falling massive impactor. The dynamic behavior of the material of concrete is described using the Holmquist - Johnson - Cook model. The reinforcement of the beam is modeled by beam elements, using the bilinear model of elastoplastic material with isotropic hardening. Binding between the reinforcement and concrete is described by introducing additional kinematic equations that couple degrees of freedom of the related nods of the beam and volumetric finite elements. The mathematical model makes it possible to introduce additional failure criteria to predict propagation of tensile cracking. Pressure lower than the minimal one (failure only in the tension zone) and volumetric strain higher than the threshold value are taken as a criterion of tensile failure. Failure is modeled by removing elements from the computational pattern, when the above failure criteria are satisfied. The effect of accounting for failure on the response of the beam is analyzed. Numerical modeling is done using the finite-element method with explicit time integration in the LOGOS and LS-DYNA systems. Concrete is modeled using linear four-node finite elements with one integration point. The impactor is modeled as an absolutely solid body with a detailed description of the impacting end. The obtained results are compared with experimental data. It is demonstrated that the Holmquist - Johnson - Cook material model developed for analyzing high-velocity impacts can also be applied to problems of low-velocity impact.


2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Samir H. Saker

We will prove some new dynamic inequalities of Opial's type on time scales. The results not only extend some results in the literature but also improve some of them. Some continuous and discrete inequalities are derived from the main results as special cases. The results will be applied on second-order half-linear dynamic equations on time scales to prove several results related to the spacing between consecutive zeros of solutions and the spacing between zeros of a solution and/or its derivative. The results also yield conditions for disfocality of these equations.


1973 ◽  
Vol 5 (11) ◽  
pp. 1341-1344
Author(s):  
Yu. M. Pochtman ◽  
Z. I. Pyatigorskii

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