Existence for dislocation-free finite plasticity

2019 ◽  
Vol 25 ◽  
pp. 21 ◽  
Author(s):  
Ulisse Stefanelli
Keyword(s):  
Plastic Deformation ◽  
Elastic Deformation ◽  
Variational Formulation ◽  
Elastoplastic Deformation ◽  
Elastoplastic Problem ◽  
Reference Configuration ◽  
Plastic Deformations ◽  
Finite Plasticity ◽  
Fixed Reference ◽  
Intermediate Configuration

This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp, where the plastic deformation yp is defined on the fixed reference configuration and the elastic deformation ye is a mapping from the varying intermediate configuration yp(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic). We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.

scholarly journals Detection of Elastic Deformation in Metal Materials in Infrared Spectral Range

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5359
Author(s):  
Milan Sapieta ◽  
Vladimír Dekýš ◽  
Ondrej Štalmach ◽  
Alžbeta Sapietová ◽  
Martin Svoboda
Keyword(s):  
Plastic Deformation ◽  
Infrared Spectrum ◽  
Stress Tensor ◽  
Elastic Deformation ◽  
Testing Machine ◽  
Radiant Energy ◽  
Infrared Camera ◽  
Plastic Deformations ◽  
Temperature Changes ◽  
Lock In

The aim of this work is to verify the presence of deformation in the metal specimen from the material AISI 316L by means of lock-in thermography. The specimen was cyclically loaded by the three-point bending in the fatigue testing machine. A response of the specimen to such excitation can be detected in the infrared spectrum and to determine temperature changes during a loading cycle. By means of the lock-in method, an increased signal to noise ratio (radiation energy detected by an infrared camera) was achieved. Besides, the temperature changes were determined on the basis of amplitudes of radiant energy changes detected by the camera. The temperature change (all radiant energy) corresponds with the first invariant of the tensor of deformation and, after a calculation and regarding the material parameters, also the invariant of the stress tensor. The proportionality between the signal from the camera and the first deformation invariant is achieved if the specimen load is an adiabatic event. This process is achieved by choosing a sufficiently high load frequency. In case of a presence origin of plastic deformations, there takes place only part of radiant energy. When we accept the hypothesis of a presence of just elastic deformations and plastic deformation is also present in the monitored process, then the evaluated thermograms based on the assumption of the presence of elastic deformation present anomalies in a distribution of the determined tensor invariant of deformations. These anomalies are caused by a presence of plastic deformations. Based on the anomalies, plastic deformation can be detected and subsequently analyzed. For the tested specimen and the applied load, the calculation of stress tensor was performed. It confirmed a congruence of results obtained by the analysis of the physical process in the infrared spectrum of the mid-wave infrared camera.

scholarly journals Quasistatic evolution for dislocation-free finite plasticity

2020 ◽  
Vol 26 ◽  
pp. 123 ◽  
Author(s):  
Martin Kružík ◽  
David Melching ◽  
Ulisse Stefanelli
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Elastic Deformation ◽  
Second Order ◽  
Existence Theory ◽  
Evolution Problem ◽  
Total Deformation ◽  
Quasistatic Evolution ◽  
Finite Plasticity ◽  
Special Case

We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.

PALEO: Plastically Annealed Lamina Emergent Origami

2018 ◽  
Author(s):  
Yves Klett
Keyword(s):  
Plastic Deformation ◽  
Elastic Deformation ◽  
Deformation Potential ◽  
Flat Sheet

Origami is usually folded from a flat sheet of material. Folding mostly works by introduction of plastic deformation into that sheet, resulting in a permanently altered region, viz., the crease. Lamina emergent mechanisms also start by definition from the flat state, but make use of compliant elements to provide mobility by elastic deformation. We introduce a combination of origami tessellations with LEM elements that are annealed in a (partially) collapsed state and retain this shape afterwards, while still offering the elastic deformation potential in the annealed shape. A number of such Plastically Annealed Lamina Emergent Origami structures or PALEOs have been successfully designed and tested.

Experimental Verification of Constitutive Equations for Creep and Plasticity Based on Overlay Models

1983 ◽  
Vol 105 (3) ◽  
pp. 277-284 ◽  
Author(s):  
P. Meijers ◽  
F. Roode
Keyword(s):  
Plastic Deformation ◽  
Room Temperature ◽  
304 Stainless Steel ◽  
Model Parameters ◽  
General Description ◽  
Time Effects ◽  
Plastic Deformations ◽  
Biaxial Load ◽  
Theoretical Predictions ◽  
Good Agreement

A general description of creep and plastic deformation based on overlay models is presented. This includes the description of time effects during plastic deformation at room temperature. A detailed procedure to obtain the model parameters is also discussed. The description has been evaluated for a large number of uniaxial and biaxial load histories on thin walled tubes. The materials involved are a 2 1/4 Cr-1 Mo steel stabilized with Niobium (WN 1.6770) and a 304 stainless steel (WN 1.4948). The theoretical predictions of the plastic deformations are found to be sufficiently accurate. The evaluation of the phenomenological description for creep shows a fairly good agreement with the real creep deformation process. Special attention requires the description of softening due to microstructural changes.

scholarly journals Orientation Dependent Mechanical Responses and Plastic Deformation Mechanisms of ZnSe Nano Films under Nanoindentation

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 3014
Author(s):  
Chao Xu ◽  
Futi Liu ◽  
Chunmei Liu ◽  
Pei Wang ◽  
Huaping Liu
Keyword(s):  
Plastic Deformation ◽  
Elastic Recovery ◽  
Structural Evolution ◽  
Atomic Displacement ◽  
Deformation Mechanisms ◽  
Formation Mechanisms ◽  
Plastic Deformations ◽  
Mechanical Responses ◽  
Displacement Vectors ◽  
Dynamics Simulations

Although ZnSe has been widely studied due to its attractive electronic and optoelectronic properties, limited data on its plastic deformations are available. Through molecular dynamics simulations, we have investigated the indentations on the (001), (110), and (111) planes of ZnSe nano films. Our results indicate that the elastic modulus, incipient plasticity, elastic recovery ratio, and the structural evolutions during the indenting process of ZnSe nano films show obvious anisotropy. To analyze the correlation of structural evolution and mechanical responses, the atomic displacement vectors, atomic arrangements, and the dislocations of the indented samples are analyzed. Our simulations revealed that the plastic deformations of the indented ZnSe nano films are dominated by the nucleation and propagation of 1/2<110> type dislocations, and the symmetrically distributed prismatic loops emitted during the indenting process are closely related with the mechanical properties. By studying the evolutions of microstructures, the formation process of the dislocations, as well as the formation mechanisms of the emitted prismatic loops under the indented crystalline planes are discussed. The results presented in this work not only provide an answer for the questions about indentation responses of ZnSe nano films, but also offer insight into its plastic deformation mechanisms.

scholarly journals Achievements in Micromagnetic Techniques of Steel Plastic Stage Evaluation

2020 ◽  
Vol 20 (1) ◽  
pp. 16-55 ◽  
Author(s):  
M. F. de Campos
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Elastic Deformation ◽  
Magnetic Measurements ◽  
Soft Magnetic Materials ◽  
Hysteresis Curve ◽  
Hole Drilling ◽  
Hole Drilling Method ◽  
Drilling Method ◽  
The Difference

AbstractThe investigation of plastic deformation and residual stress by non-destructive methods is a subject of large relevance for the industry. In this article, the difference between plastic and elastic deformation is discussed, as well as their effects on magnetic measurements, as hysteresis curve and Magnetic Barkhausen Noise. The residual stress data can be obtained with magnetic measurements and also by the hole drilling method and x-ray diffraction measurements. The residual stress level obtained by these three different methods is different, because these three techniques evaluate the sample in different depths. Effects of crystallographic texture on residual stress are also discussed. The magnetoelastic term should be included in micromagnetic methods for residual stress evaluation. It is discussed how the micromagnetic energy Hamiltonian should be expressed in order to evaluate elastic deformation. Plastic deformation can be accounted in micromagnetic models as a term that increases the coercive field in soft magnetic materials as the steels are.

Experimental evaluation of fracture properties of bovine hip cortical bone using elastic–plastic fracture mechanics

2021 ◽  
pp. 1-10
Author(s):  
Waseem Ur Rahman ◽  
Rafiullah khan ◽  
Noor Rahman ◽  
Ziyad Awadh Alrowaili ◽  
Baseerat Bibi ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Plastic Deformation ◽  
Fracture Mechanics ◽  
Cortical Bone ◽  
Elastic Deformation ◽  
Compact Tension ◽  
J Integral ◽  
Elastic Plastic ◽  
American Society ◽  
Fracture Specimens

BACKGROUND: Understanding the fracture mechanics of bone is very important in both the medical and bioengineering field. Bone is a hierarchical natural composite material of nanoscale collagen fibers and inorganic material. OBJECTIVE: This study investigates and presents the fracture toughness of bovine cortical bone by using elastic plastic fracture mechanics. METHODS: The J-integral was used as a parameter to calculate the energies utilized in both elastic deformation (Jel) and plastic deformation (Jpl) of the hipbone fracture. Twenty four different types of specimens, i.e. longitudinal compact tension (CT) specimens, transverse CT specimens, and also rectangular unnotched specimens for tension in longitudinal and transverse orientation, were cut from the bovine hip bone of the middle diaphysis. All CT specimens were prepared according to the American Society for Testing and Materials (ASTM) E1820 standard and were tested at room temperature. RESULTS: The results showed that the average total J-integral in transverse CT fracture specimens is 26% greater than that of longitudinal CT fracture specimens. For longitudinal-fractured and transverse-fractured cortical specimens, the energy used in the elastic deformation was found to be 2.8–3 times less than the energy used in the plastic deformation. CONCLUSION: The findings indicate that the overall fracture toughness measured using the J-integral is significantly higher than the toughness calculated by the stress intensity factor. Therefore, J-integral should be employ to compute the fracture toughness of cortical bone.

Ductile deformation and microstructures

2021 ◽  
pp. 58-85
Author(s):  
Jean-Luc Bouchez ◽  
Adolphe Nicolas
Keyword(s):  
Plastic Deformation ◽  
Grain Size ◽  
Elastic Deformation ◽  
Applied Stress ◽  
Deformation Mechanism ◽  
Chemical Elements ◽  
Shear Zones ◽  
Ductile Deformation ◽  
Deformation Mechanisms ◽  
Solid Materials

In contrast to the elastic deformation, which is reversible, usually neglected by field geologists but important for geophysicists working in seismology, ductile deformation is irreversible. This chapter is restricted to solid materials. Materials containing a melt fraction will be examined in Chapter 7. In the geological literature, ‘ductile’ is often used as a synonym for ‘plastic’. The latter is rather used, and will be used to specify deformation mechanisms that dominantly involve the action of dislocations. In contrast to brittle deformation, which by essence is discontinuous and highly localized (see Chapter 3), ductile deformation is generally continuous and affects large volumes of rock. However, ductile deformation may be concentrated into restricted rock volumes (or domains). Such localization is common in shear zones and/or when superplastic deformation mechanism is involved. Plastic deformation mechanisms naturally depend on temperature, magnitude of the applied stress, mineral nature and grain-size of the rocks. In upper parts of the crust, fluids are able to carry chemical elements over large distances and influence the deformation mechanisms. Micrographs of several microstructural types as well as deformation maps for olivine and calcite are given at the end of this chapter.

scholarly journals Dynamic Behavior and Energy Evolution Characteristic of Deep Roadway Sandstone Containing Weakly Filled Joint at Various Angles

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qinyong Ma ◽  
Qingqing Su ◽  
Pu Yuan
Keyword(s):  
Plastic Deformation ◽  
Energy Release ◽  
Elastic Deformation ◽  
Joint Angle ◽  
Deformation Modulus ◽  
Peak Strain ◽  
Energy Evolution ◽  
Absorbed Energy ◽  
Filled Joint ◽  
Dynamic Compressive Strength

Dynamic impact tests were carried out by implying split-Hopkinson pressure bar (SHPB) apparatus under three-dimensional stress state to investigate the influences of weakly filled joint at seven kinds of angles on dynamic behavior and energy evolution characteristic of deep roadway sandstone (985 m below the surface). The results indicated that rebound strain phenomenon was obvious and the growth rate of stress was in two kinds of phased variations. Dynamic peak strain was inversely proportional to joint angle under three different strain rates. Dynamic compressive strength, elastic deformation modulus, and plastic deformation modulus were in similar variable tendencies with incremental joint angles, showing firstly decrease to minimum value at joint angle of 45° and then increase to maximum value at joint angle of 90°. Moreover, the sensitivity of plastic deformation modulus to joint angle was obviously inferior to that of elastic deformation modulus when joint angle increased from 0° to 45°. Furthermore, both elastic deformation modulus and plastic deformation modulus were independent of strain rate, which was contrary to dynamic compressive strength and dynamic peak strain. Additionally, absorption energy release rate was introduced and defined to describe energy release and conversion characteristics of joint specimens. The changed trend of energy reflection coefficient was completely opposite to that of energy transmission coefficient and absorbed energy release rate. Absorbed energy density was linearly decreased with incremental joint angle and was increased with the increase of strain rate.

Numerical Analysis for Influence of Plastic and Elastic Deformation of Rough Surfaces on PEHL for Line Contacts

Tribology ◽  
2005 ◽  
Author(s):  
R. J. Niu ◽  
P. Huang
Keyword(s):  
Plastic Deformation ◽  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Paper Analysis ◽  
Line Contact ◽  
Plastic Deformations ◽  
Rolling Contacts ◽  
Line Contacts ◽  
Elastic And Plastic Deformations ◽  
Strain Relationship

In the present paper, analysis of elasto-plasto-hydrodynamic lubrication (PEHL) in the line contact is carried out to investigate the effect of heavily loaded roll-over on the change in profile of indents. The pressure and film thickness profiles are obtained to solve the Reynolds and film thickness equations simultaneously. And, both the elastic and plastic deformations of the contact, featured with an indent, have been considered. A multi-grid numerical algorithm used in EHL of line contacts is modified and then used for the oil lubricated rolling contacts. In the program, stress and plastic deformation of the indent profile are calculated with the hardening plastic stress-strain relationship according to the theories of plasticity when pressure excesses the yield stress. The results, with and without considering plastic deformation, are compared to show the different influences on the pressure and film thickness. Analysis shows that since the plastic deformation will change the surface roughness, it will significantly change the pressure but film thickness.

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