Shakedown analysis of structures made of materials with temperature-dependent yield stress

In this work, the shakedown of structures made of materials with temperature-dependent yield stress is considered. Under some restrictions on the thermal loading condition the yield stress is linearized and shakedown theorems are established. Based on these linearized shakedown theorems, the shakedown limit is formulated as a problem of convex optimization. An algorithm is built to compute shakedown limits. Numerical tests show good agreement with analytic solutions and experimental data.     

On shakedown theory for elastic-plastic materials and extensions

The idea that an elastic-plastic structure under given loading history may shake down to some purely elastic state (and hence to a safe state) after a finite amount of initial plastic deformation, can apply to many sophisticated material models with possible allowable changes of additional material characteristics, as has been done in the literature. Despite some claims to the contrary, it is shown; however, that the shakedown theorems in a Melan-Koiter path-independent sense have been extended successfully only for certain elastic-plastic hardening materials of practical significance. Shakedown of kinematic hardening material is determined by the ultimate and initial yield stresses, not the generally plastic deformation history-dependent hardening curve between. The initial yield stress is no longer the convenient one (corresponding to the plastic deformation at the level of 0.2%) as in usual elastic-plastic analysis but to be related to the shakedown safety requirement of the structure and should be as small as the fatigue limit for arbitrary high-cycle loading. Though the ultimate yield strength is well defined in the standard monotonic loading experiment, it also should be reduced to the so-called “high-cycle ratchetting” stress for the path-independent shakedown analysis. A reduced simple form of the shakedown kinematic theorem without time integrals is conjectured for general practical uses. Application of the theorem is illustrated by examples for a hollow cylinder, sphere, and a clamped disk, under variable (including quasiperiodic dynamic) pressure.     

不同后继屈服函数在弹塑性有限元中的应用评估

构造了一种在π平面上为椭圆的后续屈服函数,将该屈服函数、“Tresca”及“Misses型”后继屈服函数分别应用于干涉孔及冷胀孔问题的弹塑性有限元分析,并对这三种屈服函数在弹塑性有限元中的应用进行了评估。本文三种屈服函数在弹塑性问题中的应用评估对更有效地解决工程中的弹塑性问题有着实际的应用价值。     

On the overall moduli of non-linear elastic composite materials

From the work of R. Hill on constitutive macro-variables it is known that for an inhomogeneous elastic solid under finite strain an overall elastic constitutive law may be defined. In particular, the volume average of the strain energy of the solid is a function only of the volume-averaged deformation gradient. In view of the importance of this result it is re-derived in this paper as a prelude to a discussion of composite materials. A composite material consisting of a dilute suspension of initially spherical inclusions embedded in a matrix of different material is considered. For second-order isotropic elasticity theory an expression for the overall bulk modulus of the composite material is obtained in terms of the moduli of the constituents. When the inclusions are vacuous a known result for the bulk modulus of porous materials is recovered. In certain situations the strengthening/ weakening effects of the inclusions are less pronounced in the second-order theory than in the linear theory.     

Dependence of the yield stresses of certain materials on loading rate

The dependence of the dynamic yield stresses of certain metals and alloys on loading rate has been investigated at temperatures of +20 and –196°C. In the experiments the loading rate remained constant up to the appearance of plastic strains, i.e., , where . The yield stresses of the materials and the time to the appearance of plastic strains were determined from the oscillograms representing the strain and load as functions of time.     

On the thermodynamics of thermoelastic materials with additional scalar degrees of freedom

This work deals with the thermodynamic formulation of a model for a class of materials containing microstructure which evolves or changes relative to\/ the (global) bulk material. The approach taken here is based on a generalization of the total energy, total energy flux, and total energy supply to take into account the corresponding additional degrees of freedom involved. Restricting attention for simplicity to thermoelastic materials with scalar-valued such degrees of freedom, the thermodynamically-consistent forms of the remaining balance and corresponding constitutive relations for this material class are obtained in the context of the Müller-Liu entropy principle. In particular, the thermodynamically-consistent form of the evolution relation for the additional scalar-valued degrees of freedom obtained in this fashion contains in part\/ the well-known generalized Euler-Lagrange or Ginzburg-Landau relations established in many previous work, with the remaining terms accounting for effects associated with microinertia, or with non-equilibrium processes. Received September 14, 1998     

Measurement of elastic-plastic stresses by scattered-light photomechanics

Several birefringent materials were studied for their suitability for use in three-dimensional photoplasticity. This study resulted in the selection of cellulose propionate as model material. Its close match in index of refraction with ordinary mineral oil makes cellulose propionate suitable for scattered-light photomechanics. Viscoelastic behavior of the material is used to simulate elastic-plastic behavior of metals. The stress, strain and optical behavior of the material has been studied under slow loading in finite steps. A successful solution of an elastic-plastic torsion problem was obtained, demonstrating the applicability of the techniques of scattered-light photoplasticity to three-dimensional problems. This experimental method does not require the unloading and slicing of the model, avoiding any errors that might be introduced by residual stresses due to unloading. A major advantage of the method is the use of live loading, which allows the investigation of several load levels with the same model. Stress- and strain-concentration factors for the grooved shaft in torsion showed excellent agreement with Neuber's analytical results. Distributions of shear stress and shear strain across the minimum section of the model were compared to elastic theory. Integration of the shear-stress distributions showed good agreement with the measured values of applied torque.     

A model of an elastic-plastic medium with delayed yield

Stress-strain relationships for metals at high strain rates have long been studied, but no really reliable and generally accepted theory has emerged. It is sometimes assumed that the dynamic stress-strain diagram is largely insensitive to the rate over a certain range. Another approach is to insert derivatives of the stress and strata with respect to time. One difficulty in establishing the actual reIationships is that experiment provides only indirect evidence (direct tests are usually impossible). Any real dynamic experiment tends to produce complicated effects, which can be interpreted only if the basic equations are taken as known. The best that experiment can then do is to confirm or reject some prior assumptions.Many experimental studies deal with mechanical characteristics such as breaking strength and yield point as functions of strain rate; however, strain rate characterizes a range of conditions rather than defines a parameter. We therefore have to use simple models that allow formulation and solution of definite mechanical problems in relation to the dynamics of elastic-plastic media.     

On the effective stiffness of plates made of hyperelastic materials with initial stresses

Within the framework of the direct approach to the plate theory we consider the infinitesimal deformations of a plate made of hyperelastic materials taking into account the non-homogeneously distributed initial stresses. Here we consider the plate as a material surface with 5 degrees of freedom (3 translations and 2 rotations). Starting from the equations of the non-linear elastic body and describing the small deformations superposed on the finite deformation we present the two-dimensional constitutive equations for a plate. The influence of initial stresses in the bulk material on the plate behavior is considered.     

State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources

A two-dimensional equation of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with the elastic modulus dependent on temperature and with an internal heat source is established using a Laplace transform in time and a Fourier transform in the space variable. The problem for the transforms is solved in the space of states. The problem of heating of the upper and the lower surface of a plate of great thickness by an exponential time law is considered. Expressions for displacements, temperature, and stresses are obtained in the transform domain. The inverse transform is obtained using a numerical method. Results of solving the problem are presented in graphical form. Comparisons are made with the results predicted by the coupled theory and with the case of temperature independence of the elastic modulus.     

Integral constitutive equations of elastic-plastic materials

In this paper the integral constitutive equations of elastic-plastic materials are studied. The endochronic theory can be deduced from this theory. It is shown that the endochronic should be selected compatible with the yield function of the calssical plasticity and this can be considered as a principle of selecting endochronic. Applying this principle the appropriate endochronics of the plastically compressible materials and the orthotropic materials are derived. The second approximate theory of the integral constitutive equation is also discussed in this paper.This paper was reported by the National Natural Science Foundation of China.