A finite strain theory for elastic-plastic deformation

An elastic-plastic theory that is applicable when the elastic part of the strain is finite is proposed. A flow rule for an incompressible solid is obtained from Drucker's postulate [1]. Isothermal simple shear of a material which is neo-Hookean both before yielding and during elastic unloading after yielding is considered as an application of the theory. The problem is solved for two yield conditions and associated flow rules.     

A finite deformation theory of strain gradient plasticity

Plastic deformation exhibits strong size dependence at the micron scale, as observed in micro-torsion, bending, and indentation experiments. Classical plasticity theories, which possess no internal material lengths, cannot explain this size dependence. Based on dislocation mechanics, strain gradient plasticity theories have been developed for micron-scale applications. These theories, however, have been limited to infinitesimal deformation, even though the micro-scale experiments involve rather large strains and rotations. In this paper, we propose a finite deformation theory of strain gradient plasticity. The kinematics relations (including strain gradients), equilibrium equations, and constitutive laws are expressed in the reference configuration. The finite deformation strain gradient theory is used to model micro-indentation with results agreeing very well with the experimental data. We show that the finite deformation effect is not very significant for modeling micro-indentation experiments.     

On the representation of finite rotation in nonlinear field theory of continuum mechanics

One of the important basic theoretical problems in the development of continuum mechanics is the separation of finite strain and finite rotation at a point in the displacement field. Now it is certain that S-R decomposition theorem provides a rational theoretical solution for this problem. The purpose of this paper is to clarify some misleading basic concepts of finite rotation of deformed body in current literature, and to promote further progress.The detailed abstract of this paper was published in 1985 Shanghai International Conference of Nonlinear Mechanics. In the present paper some new results are included.     

Localization in NiTi tubes under bending

Nearly equiatomic NiTi can exhibit pseudoelastic behavior due to reversible solid-to-solid stress induced phase transformation at room level temperatures. In tension, the transformation leads to localized deformation of several percent that tends to spread at nearly constant stress. The deformation is recovered upon unloading while again localized deformation is exhibited. Under compression, while still pseudoelastic, the transformation strains are smaller, the stress is higher, the response is monotonic, and the deformation is essentially homogeneous. This study examines how this texture-driven, complex material asymmetry affects a simple structure: the bending of a tube. To this end, NiTi tubes are bent in a custom four-point bending facility under rotation control and isothermal conditions. The phase transformations lead to a closed moment-rotation hysteresis comprised of loading and unloading moment plateaus. During loading, localized nucleation of martensite results in a high curvature for the transformed sections of the tube and low curvature for the untransformed. Martensite, which corresponds to the higher curvature regime, spreads gradually while the moment remains nearly constant. The nucleation of martensite is in the form of bands inclined to the axis of the tube that organize themselves into diamond shaped deformation patterns on the tensioned side of the structure. The patterns are similar to those observed in bending of steel tubes with Lüders bands, however, for NiTi they develop only on the tensioned side due to the material asymmetry. A lower moment plateau is traced upon unloading with similar localized bending and the erasure of the diamond deformation patterns. This complex behavior was found to repeat for a number of temperatures in the pseudoelastic regime of NiTi with the moment-rotation hysteresis moving to higher or lower moment levels depending on the temperature.     

A nonlocal strain gradient plasticity theory for finite deformations

Strain gradient plasticity for finite deformations is addressed within the framework of nonlocal continuum thermodynamics, featured by the concepts of (nonlocality) energy residual and globally simple material. The plastic strain gradient is assumed to be physically meaningful in the domain of particle isoclinic configurations (with the director vector triad constant both in space and time), whereas the objective notion of corotational gradient makes it possible to compute the plastic strain gradient in any domain of particle intermediate configurations. A phenomenological elastic–plastic constitutive model is presented, with mixed kinematic/isotropic hardening laws in the form of PDEs and related higher order boundary conditions (including those associated with the moving elastic/plastic boundary). Two fourth-order projection tensor operators, functions of the elastic and plastic strain states, are shown to relate the skew-symmetric parts of the Mandel stress and back stress to the related symmetric parts. Consistent with the thermodynamic restrictions therein derived, the flow laws for rate-independent associative plasticity are formulated in a six-dimensional tensor space in terms of symmetric parts of Mandel stresses and related work-conjugate generalized plastic strain rates. A simple shear problem application is presented for illustrative purposes.     

轴对称弹性应变梯度理论公式推导及有限元实现

用张量运算推导了弹性应变梯度轴对称问题的基本公式.建立了应变梯度轴对称不协调元的弱连续条件,进一步建立了满足弱连续条件的应变梯度轴对称18-DOF三角形单元(BCIZ+ART9),其中BCIZ满足线性应变C0连续,用于计算应变ε;ART9满足常曲率C1弱连续,用于计算应变梯度η0数值结果表明该单元通过C0-1分片检验并能体现材料的尺度效应.     

The behavior of elastic tubes in a cohesion-free continuum

A model is made of a plain cross section of a tube (tunnel lining) in a cohesion-free continuum (rolling material, sand) which is represented by steel rollers of different diameters. The compactibility of sand in this model is represented by rubber inserts around the tunnel lining. The stress of the tube is measured by photoelasticity. These experiments are the start of a large program of investigation to calculate the stress deformation and buckling of elastic tubes under different loading conditions in rolling material.     

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

In this paper we present a continuum theory for large strain anisotropic elastoplasticity based on a decomposition of the modified plastic velocity gradient into energetic and dissipative parts. The theory includes the Armstrong and Frederick hardening rule as well as multilayer models as special cases even for large strain anisotropic elastoplasticity. Texture evolution may also be modelled by the formulation, which allows for a meaningful interpretation of the terms of the dissipation equation.     

Experimental determination of bending strain power spectra from vibration measurements

Experimental results are presented of the power spectral density of the random bending strain on the surface of a beam obtained using a scanning laser vibrometer. The strain spectra were obtained by processing vibration data measured at discrete locations along the beam's length. The beam was driven by a stationary broad-band random force. The experimental setup is described along with the data analysis procedure. The results presented here indicate that the method is practical and can lead to reliable estimates.     

A non-singular continuum theory of dislocations

We develop a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure. The expressions are self-consistent in that the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach-Koehler formula. The singularity intrinsic to the classical continuum theory is removed here by spreading the Burgers vector isotropically about every point on the dislocation line using a spreading function characterized by a single parameter a, the spreading radius. A particular form of the spreading function chosen here leads to simple analytic formulations for stress produced by straight dislocation segments, segment self and interaction energies, and forces on the segments. For any value a>0, the total energy and the stress remain finite everywhere, including on the dislocation lines themselves. Furthermore, the well-known singular expressions are recovered for a=0. The value of the spreading radius a can be selected for numerical convenience, to reduce the stiffness of the dislocation equations of motion. Alternatively, a can be chosen to match the atomistic and continuum energies of dislocation configurations.     

Buckling life estimation of circular tubes under cyclic bending

In this paper, an experimental investigation of the degradation and buckling of circular tubes subjected to cyclic bending is discussed. The machinery specimens (with different diameter-to-thickness ratios but the same inside diameter) and method of testing (cyclic bending) in this study were the same as the ones used by Lee et al. (Lee, K.L., Pan, W.F., Kuo, J.N., 2001. The influence of the diameter-to-thickness ratio on the stability of circular tubes under cyclic bending. International Journal of Solids and Structures 38, 2401–2413.) for 316L stainless steel circular tubes. The experimental investigation was extended to different outside and inside diameters of the same circular tubes subjected to cyclic bending. Based on the experimental findings, the empirical formulation proposed by Lee et al. (2001) was modified so that it can now be used to simulate the relationship between the prescribed curvature and the number of cycles necessary to produce buckling. In addition, it was found that the experimental curve of the ovalization and the number of cycles necessary to produce buckling could be divided into three stages – an initial, secondary and tertiary stage. An empirical relationship, similar to the Bailey–Norton creep formulation, was proposed for simulating the aforementioned curve for the initial and secondary stages in this study. The derived empirical relationship was in good agreement with the experimental data.     

A continuum theory of structural change

Summary A comprehensive treatment of structural change (excluding the effects of induced anisotropy) is given which admits changes, and the associated variation of mechanical properties, from a variety of different influences. The treatment can accommodate the simultaneous effect of various influences and gives wider meaning and scope to the commonly used term thixotropy. A specific example of thixo-viscoelasticity is described in some detail. Most non dilute polymeric and solid-liquid systems can be expected to show some degree of thixotropy.     

Laser generated and recorded transient bending waves in composite tubes

Propagating bending waves are studied in three different composite tubes by holographic interferometry. A conical mirror is placed axially inside the tubes. Axial illumination and observation directions make it possible to view the circumference of the tube, with a high sensitivity to radial deformation. It is shown how the deformation field can be numerically evaluated using a phase stepping and unwrapping technique. Transient bending waves in the tubes are both generated and recorded by the same pulsed laser, which makes the experiments easy to perform. Finite element simulations of the impacted tubes are compared to corresponding experiments. Both the geometry and the material properties of the tubes affect the wave propagation. For unidirectional composite tubes, the 0-deg and 90-deg directions have different dynamic behavior. The proposed method could be used in nondestructive testing of tubes.     

Heat transfer from horizontal tubes in pool boiling: influence of three-dimensional heat conduction in the wall of the evaporator tube—a finite element analysis

In pool boiling, the electrically heated tube releases the energy non-uniformly to the liquid, due to different surface roughness and flowing liquid. The heat transfer coefficient therefore varies with axial and azimuthal position on the tube. Hence a finite element analysis has been carried out on a horizontal 1in. copper tube for evaporation in pool boiling for three-dimensional conduction heat transfer. A test tube has been made with different surface structures, tested and analysed for heat conduction effects. It has been observed that significant amount of heat flows in azimuthal and axial directions in addition to the heat flow in radial direction.     

Holographic interferometry measurements of transient bending waves in tubes and rings

Propagating bending waves are studied in a tube of steel and in a ring of aluminum. The waves are generated by the impact of a ballistic pendulum. Holographic interferometry, with a double-pulsed ruby laser as light source, is used to record the waves. A conical mirror is placed axially inside the tube. Axial illumination and axial observation directions, make it possible to view all sides of the tube simultaneously with a high sensitivity to radial deformation. The interferograms, which have an unusual perspective, are captured with a CCD-camera and then spatially transformed into an unwrapped strip of the tube wall. This makes the interpretation of the measurements simpler. The geometry of the tube causes the wave pattern to propagate with different speed and amplitude along and across the tube, even when the material itself is isotropic. A finite-element simulation of the impact is compared to the corresponding experiment. An impact on a ring with a defect is performed in order to study the effect on the wave pattern. The proposed method could be used in nondestructive testing of pipes.