Elastic-Plastic State of Inhomogeneous Soil Array with a Spherical Cavity

2013 ◽  
Vol 842 ◽  
pp. 462-465 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Anatoliy S. Avershyev ◽  
Stanislaw Jemiolo
Keyword(s):  
Plastic Deformation ◽  
Outer Surface ◽  
Spherical Cavity ◽  
Plastic Material ◽  
Plastic State ◽  
Cavity Model ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The article deals with the elastic-plastic state of inhomogeneous array with a spherical cavity. Model is used thick-walled ball of an elastic-perfectly plastic material (Prandtl diagram). It is shown that in the inhomogeneous material, depending on the inhomogeneity functions describing the change of the modulus of elasticity and yield stress of soil plastic deformation may appear on both the inner and outer surface of the ball and inside it. Are found values of the limit loads, displacement diagrams are constructed in an array.

Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material

1968 ◽  
Vol 35 (2) ◽  
pp. 372-378 ◽  
Author(s):  
Chi-Hung Mok
Keyword(s):  
Spherical Cavity ◽  
High Speed ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Numerical Technique ◽  
Nonlinear Dependence ◽  
Static Approximation ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.

Case Study of Shakedown Evaluation of a Shell With Nozzle Based on Elastic-Plastic Analysis

2017 ◽  
Author(s):  
Jun Shen ◽  
Heng Peng ◽  
Liping Wan ◽  
Yanfang Tang ◽  
Yinghua Liu
Keyword(s):  
Temperature Change ◽  
Plastic Material ◽  
Material Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Temperature Loads ◽  
The Impact

In the past, shakedown evaluation was usually based on the elastic method that the sum of the primary and secondary stress should be limited to 3Sm or the simplified elastic-plastic analysis method. The elastic method is just an approximate analysis, and the rigorous evaluation of shakedown normally requires an elastic-plastic analysis. In this paper, using an elastic perfectly plastic material model, the shakedown analysis was performed by a series of elastic-plastic analyses. Taking a shell with a nozzle subjected to parameterized temperature loads as an example, the impact of temperature change on the shakedown load was discussed and the shakedown loads of this structure at different temperature change rates were also obtained. This study can provide helpful references for engineering design.

A Note on the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material With Finite Deformation

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Dorinamaria Carka ◽  
Robert M. McMeeking ◽  
Chad M. Landis
Keyword(s):  
Finite Deformation ◽  
Path Dependence ◽  
Plastic Material ◽  
Crack Tip ◽  
J Integral ◽  
Stationary Crack ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Plastic Material ◽  
Elastic Perfectly Plastic

In this technical brief, we compute the J-integral near a crack-tip in an elastic-perfectly-plastic material. Finite deformation is accounted for, and the apparent discrepancies between the prior results of the authors are resolved.

Causes and Consequences of Nonuniqueness in an Elastic/Perfectly-Plastic Truss

1986 ◽  
Vol 53 (2) ◽  
pp. 235-241 ◽  
Author(s):  
P. G. Hodge ◽  
K.-J. Bathe ◽  
E. N. Dvorkin
Keyword(s):  
Plastic Deformation ◽  
Plastic Material ◽  
Complete Solution ◽  
Physical Modelling ◽  
Equilibrium Equations ◽  
First Order ◽  
Perfectly Plastic ◽  
Points Of View ◽  
Elastic Perfectly Plastic

A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first-order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modelling, computational, and engineering points of view.

Elastic–Plastic Response of Clamped Square Plates Subjected to Repeated Quasi-Static Uniform Pressure

2018 ◽  
Vol 10 (06) ◽  
pp. 1850067 ◽  
Author(s):  
Shiyun Shi ◽  
Ling Zhu ◽  
Tongxi Yu
Keyword(s):  
Elastic Strain ◽  
Plastic Material ◽  
Elastic Strain Energy ◽  
Uniform Pressure ◽  
Elastic Plastic ◽  
Whole Process ◽  
Perfectly Plastic ◽  
Plastic Regime ◽  
Loading And Unloading ◽  
Elastic Perfectly Plastic

In this paper, an elastic–plastic analytical method is proposed to predict the cyclic deformation of the fully clamped square plates made of elastic–perfectly plastic material under repeated quasi-static uniform pressure. The whole process can be divided into the loading and unloading phases. The loading phase is formulated as three separate regimes: the elastic regime, the mixed elastic–plastic regime and the fully plastic regime. Unloading from a status in each phase is modeled as an elastic process. The total and elastic strain energies are characterized by the loading and unloading paths together with the displacement profiles, respectively. It is theoretically revealed that the elastic strain energy and the structural stiffness of the plate increase with the increasing transverse deflection. In addition, the effect of material elasticity is highlighted in the scenario of repeated loadings. The theoretical results are validated against the numerical simulations conducted by the commercial software ABAQUS. It is shown that the proposed elastic–plastic theoretical model has reasonable accuracy and can be employed to predict pressure–deflection relationship for this class of problems.

scholarly journals GBT-Based Elastic-Plastic Analysis of Cold-Formed Steel Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Plastic Material ◽  
Beam Theory ◽  
Mapping Algorithm ◽  
First Order ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Steel Members ◽  
Shell Finite Element ◽  
Elastic Perfectly Plastic

This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform thorough first-order elastic-plastic analyses of thin-walled members subjected to arbitrary deformations and made of an isotropic non-linear material. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of a simply supported Z-section beam made of an elastic-perfectly plastic material (e.g., carbon steel) and acted by a load uniformly distributed along the flanges. The set of GBT-based results comprises the load-deflection curves (equilibrium paths), displacement profiles, stress distributions (diagrams and 3D contours), and deformed shapes (modal amplitude functions and 3D configurations). These results are compared with the ones obtained from shell finite element analyses (SFEA) using ABAQUS. It is seen that the GBT results display a very good agreement with the SFEA values.

Mechanical and Thermodynamic Considerations of an Assemblage of Homogeneous Elastic-Plastic States

1968 ◽  
Vol 35 (3) ◽  
pp. 596-603 ◽  
Author(s):  
David Rubin
Keyword(s):  
Plastic Deformation ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Material Behavior ◽  
Free State ◽  
Elastic Plastic ◽  
Elastic Range ◽  
Perfectly Plastic ◽  
Stress Free State ◽  
Elastic Perfectly Plastic

The mechanics and the thermodynamics of plastic deformation are considered in terms of a general assemblage or continuum of elastic, perfectly plastic elements or states. Such models not only match the external mechanical behavior of real materials structures and continua, but they also afford a simple thermodynamic definability. A consideration of the internal behavior shows that the stress-free state has the maximum elastic range. Hardening in the sense of an increasing macroscopic elastic range is accompanied by a release of stored strain energy; the stress-free state always is restorable. This behavior is appropriate for real structures and continua. However, it is precisely these continuum characteristics which make the assemblages inappropriate models of material behavior. Barriers to continuing plastic deformation are required which do exist on the microscale, but lie outside of the scope of the most complex of these thermodynamically well-defined assemblages.

Elastic-Plastic J and COD Estimates for Circumferential Through-Wall Cracks Between Elbows and Straight Pipes Under Bending

2007 ◽  
Author(s):  
Tae-Kwang Song ◽  
Yun-Jae Kim
Keyword(s):  
Crack Opening ◽  
Small Strain ◽  
Opening Displacement ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Elastic Perfectly Plastic ◽  
Reference Stress Approach

A method for elastic-plastic fracture mechanics analyses is presented for the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending, based on the reference stress approach. Based on small strain finite element limit analyses using elastic-perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks in between elbows and straight pipes under bending are given. Then applicability of the reference stress based method to approximately estimate J and crack opening displacement (COD) is proposed.

Approximate Elastic-Plastic Analysis of Intersecting Equal Diameter Cylindrical Shells

1981 ◽  
Vol 103 (1) ◽  
pp. 111-115
Author(s):  
D. P. Updike
Keyword(s):  
Plastic Material ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Pressure Vessels ◽  
Ductile Materials ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Design of connections of pipes and pressure vessels on the basis of a calculated maximum elastic stress often proves to be too conservative in the case of ductile materials. Elastic-plastic analysis by the finite element method proves to be too costly. This paper presents an alternative method which reduces the calculations to those of a rotationally symmetric shell subjected to axisymmetric loading. Using this approach approximate elastic-plastic deformations on the meridian passing through the crotch of a tee branch connection of cylindrical shells of equal diameter and thickness are determined. The method is limited to cases of the normal intersection of very thin shells of identical diameter, thickness, and material and to internal pressure loading. Numerical results for the intersection of two shells of R/t equal to 100 are given for an elastic-perfectly plastic material satisfying the von Mises yield condition.

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