Remaining at Yield During Unloading and Other Unconventional Elastic-Plastic Response

1987 ◽  
Vol 54 (1) ◽  
pp. 22-26 ◽  
Author(s):  
D. C. Drucker ◽  
Devo Seereeram
Keyword(s):  
Plastic Deformation ◽  
Path Following ◽  
Elastic Response ◽  
Plastic Response ◽  
Elastic Plastic ◽  
Current State ◽  
Prior Plastic Deformation ◽  
Elementary Form ◽  
Special Time ◽  
Critical Aspects

A rather special time-independent or elastic-plastic response is proposed in which, although there is elastic response to unloading, the material remains at yield for all or a significant portion of the unloading path following plastic deformation. In the most elementary form, the material exhibits no memory of prior plastic deformation; the current state of the material is given solely by the current state of stress. A simple but unconventional field of plastic moduli then can be chosen to produce a limit surface that cuts through a nested set of yield surfaces and to model critical aspects of the behavior of sand.

Large Deformation Analysis of an Elastic-Plastic Cantilevered Beam

1989 ◽  
Vol 111 (3) ◽  
pp. 312-315 ◽  
Author(s):  
D. W. Nicholson
Keyword(s):  
Large Deformation ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Elastic Response ◽  
Graphical Form ◽  
Deformation Analysis ◽  
Plastic Response ◽  
Large Deformation Analysis ◽  
Elastic Plastic ◽  
Cantilevered Beam

This study concerns the analysis of the deflection of an elastic-plastic cantilevered beam. Three regions of solution are treated: (i) purely elastic response at low loads; (ii) elastic-plastic response without a hinge, for intermediate loads; and (iii) elastic-plastic response with a hinge for loads corresponding to the fully plastic bending moment at the built-in end. Most existing solutions for this type of problem involve various approximations avoided here, for example, ignoring the elastic part of the strain or using upper bounds based on limit analysis. By avoiding such approximations, the solution given here may be useful as a benchmark for validating finite element codes in the large deformation elastic-plastic regime. Several aspects of the solution are analyzed: (i) the load-deflection relation; (ii) the growth of the elastic-plastic zone; (iii) limiting cases; (iv) the residual configuration; (v) the small bending configuration. A numerical procedure based on Runge-Kutta methods is used, leading to the load-deflection relation in graphical form.

A New Incremental Formulation of Elastic–Plastic Deformation of Two-Phase Particulate Composite Materials

2014 ◽  
Vol 81 (6) ◽  
Author(s):  
Hong Teng
Keyword(s):  
Plastic Deformation ◽  
Composite Materials ◽  
Spherical Particles ◽  
Particulate Composites ◽  
Plastic Response ◽  
Two Phase ◽  
Elastic Plastic ◽  
Inclusion Model ◽  
The Matrix ◽  
Incremental Formulation

In this study the double-inclusion model, originally developed to determine the effective linear elastic properties of composite materials, is reformulated in incremental form and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The study is limited to composites consisting of purely elastic particles and elastic–plastic matrix of von Mises yield criterion with isotropic strain hardening. The resulting nonlinear problem of elastic–plastic deformation of a double inclusion embedded in an infinite reference medium (that has the elastic–plastic properties of the matrix) subjected to an incrementally applied far-field strain is linearized at each load increment through the use of the matrix tangent moduli. The proposed incremental double-inclusion model is evaluated by comparison of the model predictions to the exact results of the direct approach using representative volume elements containing many particles, and to the available experimental results. It is shown that the incremental double-inclusion formulation gives accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions. In particular, the incremental double-inclusion model is capable of capturing the Bauschinger effect often exhibited by heterogeneous materials. A unique feature of the proposed incremental formulation is that the composite matrix is treated as a two-phase material consisting of both an elastic and a plastic region.

Simplified Methodology for Analysis of Reflected Detonation and DDT: Part 2 — Elastic-Plastic Analysis

2014 ◽  
Author(s):  
Thomas C. Ligon ◽  
David J. Gross ◽  
John C. Minichiello
Keyword(s):  
Plastic Deformation ◽  
Time History ◽  
Initial Pressure ◽  
Elastic Response ◽  
Detonation Pressure ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Modeling Methodology ◽  
Plastic Analysis ◽  
Unburned Fuel

This paper applies a simplified conservative approach for analyzing elastic-plastic response of piping due to reflected gaseous detonations and deflagration-to-detonation transitions (DDT). A consequence associated with gaseous explosions is the potential for DDT to occur near the end of a closed pipe or gas pocket. As an accelerating deflagration flame approaches a closed end, the unburned fuel ahead of the flame front is compressed to an elevated initial pressure. This process is often referred to as pressure piling or pre-compression, and the combination of detonation reflection with the elevated initial pressure can produce extremely high peak pressures and large values of impulse. In this paper, the event where DDT occurs immediately ahead of the reflecting surface is referred to as a reflected-DDT (R-DDT). Due to the extreme pressures that R-DDTs can achieve, the piping can frequently experience elastic-plastic deformation. In this second part, the pressure time-history modeling methodology developed for elastic response in part one is extended to elastic-plastic analysis. The inelastic response of the piping material is modeled using a lower-bound strain hardening curve at a single representative strain rate. The pressure model is compared to a published reflected detonation pressure model for the stoichiometric mixture of ethylene and oxygen, and finite-element analysis results using the simplified methodology are compared to two recent sets of published plastic deformation data from ethylene oxygen explosion tests in austenitic stainless steel tubing and piping.

scholarly journals Large elastic-plastic deformation of square membranes subjected to localised pulse pressure loads

2019 ◽  
pp. 126-133
Author(s):  
N. Mehreganian ◽  
A. S. Fallah ◽  
L. A. Louca
Keyword(s):  
Pulse Pressure ◽  
Constitutive Relations ◽  
Energy Functional ◽  
Steel Plates ◽  
Elastic Response ◽  
Plastic Response ◽  
Closed Form Solutions ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Ductile isotropic materials are widely used in protective systems against transient pulse pressure loads, such as those of localised blasts. This is due to the combined elastic-plastic response which contributes to dissipation of total impulse from extensive loading as the energy stored elastically limits deformation while the energy expended plastically limits the level of transferred forces in the structure. In the case of thin, modern armour graded steel plates, the tailored metallurgy helps the structure store energy within the bounds of elastic region, which may be dissipated at a later stage as damping kills it off in subsequent cycles. On the other hand, the plastic work is almost entirely converted to heat and dissipates. The present work focuses on the elastic and plastic energies in the membrane and aims at deducing, from the minimization of Föppl-Von-Kármán (FVK) energy functional combined with enforcing the constitutive relations of limit analysis, the dynamic elastic-plastic response of localised blast loaded square membranes undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various temporal shapes (e.g. rectangular, linear, exponential). Considering the elastic response, a single-degree-of-freedom model was developed from the prescribed displacement field and associated stress tensor having clamped and simply supported boundary conditions. The explicit closed form solutions were sought by using the Ritz-Galerkin’s variational method as well as the Poincaré-Lindstedt perturbation method. The theoretical solutions of rigid-perfectly plastic square membranes subjected to the same blast scenarios were then discussed. From the combined effects we deduce the load displacement curves representing the trajectory of the nonlinear elastic-perfectly plastic structure.

Friction Force and Stresses Analysis for Contact of Assembled Details

2006 ◽  
Vol 113 ◽  
pp. 334-338
Author(s):  
Z. Dreija ◽  
O. Liniņš ◽  
Fr. Sudnieks ◽  
N. Mozga
Keyword(s):  
Mechanical Properties ◽  
Surface Roughness ◽  
Plastic Deformation ◽  
Friction Force ◽  
Sliding Friction ◽  
Friction Model ◽  
Contact Interface ◽  
Finite Element Program ◽  
Elastic Plastic ◽  
Element Program

The present work deals with the computation of surface stresses and deformation in the presence of friction. The evaluation of the elastic-plastic contact is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. Several factors of sliding friction model are discussed: surface roughness, mechanical properties and contact load and areas that have strong effect on the friction force. The critical interference that marks the transition from elastic to elastic- plastic and plastic deformation is found out and its connection with plasticity index. A finite element program for determination contact analysis of the assembled details and due to details of deformation that arose a normal and tangencial stress is used.

Energy storage and dissipation of elastic-plastic deformation under shock compression: Simulation and Analysis

2021 ◽  
Vol 158 ◽  
pp. 103876
Author(s):  
Qi-lin Xiong ◽  
Zhenhuan Li ◽  
Takahiro Shimada ◽  
Takayuki Kitamura
Keyword(s):  
Plastic Deformation ◽  
Energy Storage ◽  
Shock Compression ◽  
Elastic Plastic
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