Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.

Elastic-plastic deformation of sandwich rod on elastic basis

Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.

A new model to describe effect of plastic deformation on elastic modulus of aluminum alloy

In order to improve the prediction capability of spring-back in aluminum sheet metal forming, the influence of the plastic deformation on elastic modulus is considered when the material undergoes a large plastic deformation. The present work focused on establishing a new model to accurately describe the relation of elastic modulus and plastic deformation. The tensile tests were performed to investigate the influence of plastic deformation on elastic modulus at low strain rate. Two different aluminum sheets were used, AA2024-T3 and LY12-CZ, and the thickness of sheet metals was 1.3 mm and 2.0 mm, respectively. In order to overcome the drawback, which is directly measuring the slope of tension curve to obtain elastic modulus, an extrapolation method was adopted. The proposal macroscopic piecewise sinusoidal function can accurately model the elastic modulus variation.

Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity

The bulk metal forming processes were simulated by using a one-step finite element(FE)approach based on deformation theory of plasticity,which enables rapid prediction of final workpiece configurations and stress/strain distributions.This approach was implemented to minimize the approximated plastic potential energy derived from the total plastic work and the equivalent external work in static equilibrium,for incompressibly rigid-plastic materials,by FE calculation based on the extremum work principle.The one-step forward simulations of compression and rolling processes were presented as examples,and the results were compared with those obtained by classical incremental FE simulation to verify the feasibility and validity of the proposed method.

THE VARIATIONAL INEQUALITY FORMULATION FOR THE DEFORMATION THEORY IN PLASTICITY AND ITS NON-ITERATIVE SOLUTION

In this paper, the deformation theory in plasticity is formulated in the variational inequality, which can relax the constraint conditions of the constitutive equations. The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis. Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods. And the solutions can be made in one step without any diversion of the load.

ELASTIC－PLASTIC CONSTITUTIVE MODELS BASED ON THE MULTIPLICATION PROCESSES OF DEFORMED GRAINS

According to the characteristics of micro-deformation of polycrystalline metal,the author divides grains intothree kinds and proposes a new conceplion of deformed grains.multiplication,from which some explicit elastic-Plastic constitutive equations can be deduced and some experimental results can be explained quantitativelv,It shows that the macro-yield,rate-correlativity work hardening and other phenomena are all closely related to the kinetic process of grains deformation.

大塑性变形(severe plastic deformation,SPD)的研究现状

本文概述了近10年来大塑性变形(severe plastic deformation,SPD)研究成果,文章首先简述了各种SPD工艺的特点,其次对SPD强化机理研究现状做了分析,最后基于目前SPD技术的应用现状,对其发展和应用前景展开了必要的讨论和展望.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

THEORY OF ELASTICITY OF AN ANISOTROPIC BODY FOR THE BENDING OF BEAMS

A theory of elasticity for the bending of orthogonal anisotropic beams was developed in this paper by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two dimensions. The authors also presented a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory which takes into account the effect of transverse shear deformation is not suitable for the components of stress in our case.

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

ANOMALOUS BEHAVIOR REVISITED:DYNAMIC RESPONSE OF ELASTIC-PLASTIC STRUCTURES

Based on the minimum principle of acceleration in the elastic-plastic continua under finite def ormation, the dynamic response of an elastic-perfectly plastic pin-ended beam subjected to rectangular impulse loading is studied with the help of a numerical approach. The calculated results once again show the anomalous behavior of the beam during its response process, which was previously found in [1]. By carefully analyzing the instantaneous distribution of the bending moment, the membrane force, the curvature and displacement during the response process, it is concluded that the interactive effect between the geometry and materials nonlinearities of the structure is the key reason for leading to the anomalous behavior. This will be helpful for clarifying some misunderstandings in explaining the problem before.

Generalizing J_2 flow theory: Fundamental issues in strain gradient plasticity

It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.

Stability and reinforcement analyses of high arch dams by considering deformation effects

The strict definition and logical description of the concept of structure stability and failure are presented. The criterion of structure stability is developed based on plastic complementary energy and its variation. It is presented that the principle of minimum plastic complementary energy is the combination of structure equilibrium, coordination condition of deformation and constitutive relationship. Based on the above arguments, the deformation reinforcement theory is developed. The structure global stability can be described by the relationship between the global degree of safety of structure and the plastic complementary energy. Correspondingly, the new idea is used in the evaluations of global stability, anchorage force of dam-toe, fracture of dam-heel and treatment of faults of high arch dams in China. The results show that the deformation reinforcement theory provides a uniform and practical theoretical framework and a valuable solution for the analysis of global stability, dam-heel cracking, dam-toe anchorage and reinforcement of faults of high arch dams and their foundations.

Determining Loading Field based on Required Deformation for Isotropic Hardening Material

Eringen's and Trusedell's polar decomposition are formulated by explicit formulation of displacement field, based on Chen's additive decomposition of deformation gradient. Then the strain introduced by the multiplicative decomposition and the strain introduced by the additive decomposition are formulated explicitly with displacement gradient. This formulation clears the intrinsic contents of strains defined by taking the Eringen's and Trusedell's polar decomposition. After that, Chen's strain definition was introduced to show that the plastic deformation can be understood as the irreversible local average rotation. For initial isotropic simple elastic material, the research shows that path-dependent feature of classical plasticity theory is naturally expressed in Chen's strain definition. For rate-independent plasticity, the related deformation stress was discussed. The research shows that for isotropic hardening material the relation equation between the required geometric configuration and the corresponding loading field is explicitly formulated. Hence, for metal forming, this paper explicitly formulates the related fields by displacement field and invariant elastic constants.

Dislocation Inelastic Effects in Zinc Single Crystals

Dislocation internal friction,elastic modulus defect and their ratio r have been studied in an- nealed and plastically deformed Zn single crystals in the temperature range of 80 to 300 K in a wide range of oscillation amplitudes.The results ob- tained are discussed within the present notion about the nature of dissipative elastic oscillation losses in solids.

On the Advantages of the Theories of Plasticity with Singular Loading Surface

This paper analyzes the peculiarities of plastic flow of metals for the case of non-proportional loading when the loading path consists of two portions—uniaxial tension and subsequent infinitesimal pure shear (torsion). The issue is discussed from the point of view of the hardening rules governing the kinetics of loading surface. Three cases are considered, flow plasticity theory with isotropic and kinematic hardening rule, as well as the synthetic theory of plastic deformation. As a result, the synthetic theory leads to the results that correlate with experiments, whereas the former two theories associated with smooth loading surfaces give a principal discrepancy with experimental data.

STUDY ON STRIP AND ROLL DEFORMATION COUPLING OF COLD STRIP ROLLING ON 4-H MILL

The cold strip rolling process on a 4 h mill is studied by coupling the 3 dimensional plasticity deformation of the strip with the elastic deformation of the rolls. On the conditions of that the width to thickness ratio of the strip is 660 and the exit strip shapes are respectively edge wave, centre wave and good, the computed results of the transverse distributions of the roll gap, the rolling pressure, the inter roll pressure, and the front and back tension agree with the experimental results well. The studing methods and the studied results are of great importance to forming shape theory and guiding the development of shape control technology.

COMPUTER SIMULATED ANALYSES ON DEFORMATION AND FRACTURE OF NON-CRACKED AND CRACKED SPECIMENS

A unified damage and fracture model,the combinatory work density model,which is suitable for ei- ther non-cracked body or cracked body has been suggested.In the present paper,the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel have been simulated by using the new mod- el together with the large èlastic-plastic deformation finite element method.The results give a good picture of the whole deformation and fracture processes of the specimens in experiments;especially,the results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading point P-Δ,and between crack ex- tension and displacement at the loading point Δα-Δ,the resistance curve J_R-Δa and the fracture toughness J_(IC).All the results are in remarkable agreement with those obtained by experiments.Therefore the model suggested here can be used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propa- gation in cracked body.

The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials

With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.

Measurement of the Energy Absorbed during Nanoscale Deformation of Human Peritubular and Intertubular Dentin

Mineralized tissues are usually constructed of nanosized materials with ordered hierarchical structures. The main reason for their high load-bearing ability is the multi-scale hierarchy. It is important to have a method for measuring the energy absorbed during the nanoscale deformation of mineralized tissues. The objective of this study was to use a combination of nanoindentation and elastic-plastic mechanics techniques to measure the damage resistance of peritubular and intertubular dentin, based on the energy consumed in the plastic deformation regime and the volume created by the indents. The control materials were soda-lime glass, gold, and poly-methyl methacrylate (PMMA). Plastic deformation energy was calculated from the plastic part of load-displacement curves. The mean values of peritubular dentin and intertubular dentin were 3.8 × 109, and 5.2 × 109 J/m3, respectively, compared to glass, PMMA, and gold which were 3.3 × 107, 1.3 × 109, and 3.1 × 109 J/m3, respectively. This method can be applied to study the resistance of mineralized tissues or organic/inorganic hybrid materials to deformation at the nanoscale.