A. Paglietti

Rigid–plastic approximation to predict plastic motion under strong earthquakes

The paper shows that the rigid–plastic oscillator can be used to evaluate the maximum plastic displacement of any elastic–plastic oscillator under any earthquake. Motivated by this result a rigid–plastic response spectrum is introduced, which provides an easy method to calculate the maximum plastic displacement of a rigid–plastic oscillator for any given earthquake. Such a spectrum is easier to construct than the elastic–plastic response spectrum or the classical elastic one. By means of appropriate formulas presented in the paper, the rigid–plastic response spectrum can be used to determine a realistic upper bound to the maximum plastic displacement of any elastic–plastic oscillator under the given earthquake. Copyright

Thermodynamical bounds to the elastic behaviour of elastic materials

Abstract We propose to exploit the second principle of thermodynamics in a different way from that usually followed in continuum mechanics. We study the consequences of this approach as far as the path-dependent character of the constitutive equations is concerned. The analysis leads us to infer that for materials capable of thermoelastic behaviour there are, in general, states of deformation beyond which a deformation process cannot occur without violating the second principle of thermodynamics. The relation between these states of deformation and those relevant to the yield limit is considered.

Thermodynamic nature and control of the elastic limit in solids

Abstract The elastic limit of a solid is implicit in its thermo-elastic properties and can be determined from the constitutive equations of internal energy and entropy in the elastic range. The second law of thermodynamics is responsible for this, as it sets an upper bound to the internal energy that a material can store during isothermal elastic deformation processes. A link between irreversibility and elasticity can thus be established, which allows for a better control of the properties of strength, ductility and elastic limit of the material. For elastic-plastic materials of practical interest it implies that the yield limit cannot be assigned independently of the elastic constitutive equations, although the current approaches do so. An application to elastic-plastic materials with linear thermo-elastic properties reveals that, in the one-dimensional case, all information on the entropy of the material can be drawn from standard uniaxial tests. An easy procedure can then be devised to design the preparation process of the material so that the desired combination of strength, ductility and elastic limit can be achieved within the admissible values for these quantities.

Stress stability at the yield surface

Abstract An elastic-plastic material may be unstable at yield under work control, if the values of its free energy at yield are not properly restricted. This is true whether the material is stable in Druckers sense or not. In materials in which plastic volume change is unrestricted, stability under work control requires that the yield surface should be equipotential for free energy. On the other hand, if plastic flow is isochoric, the intersections of the yield surface with planes normal to the hydrostatic axis must be equipotential.

Stability on the Yield Surface

It is proved that, if plastic deformation is unrestrained, the yield surface has to be equipotential for free energy. On the other hand, if plastic deformation is isochoric, then the intersections of the yield surface with the planes at constant volume must be equipotential.

Interrelation between time-rates of temperature and deformation in continuum thermodynamics

Abstract It is shown that in a body, the time-rates of the deformation function and temperature distribution function cannot, in general, be assigned independently of each other. The implications of this result on the modern approach to continuum thermodynamics are briefly discussed.

Mechanical and thermodynamical basis for theories of generalized continuous media

Abstract We study the essential theoretical foundations to construct a model which represents the mechanical and thermodynamical behaviour of a real material. Particular reference is made to the case where the classical model of Cauchys continuum is not sufficient. Special attention is devoted to distinguishing between the constitutive features of the material on the one hand and what results from the postulated physical principles on the other. The subject develops on general lines and allows us to point out possible advances consistent with our assumptions. Finally we apply the proposed theory to prove an important restriction on the admissible constitutive equations.

The implications of thermal energy exchanges on material stability

Abstract By considering the heat transfer between material and external agency, a new inequality is obtained that should be added to Druckers well-known relations to guarantee material stability. The established result implies that the deviatoric cross-sections of the yield surface of materials with isochoric plastic flow should be equipotential for free energy.

Some remarks on the local form of the second principle of thermodynamics

Consider a cont inuous body made up of a set of part icles X. Le t ~, ~1, 0, s and h denote the mass density, the specific en t ropy, the absolute t empera tu re , the specific hea t ing supply and the hea t ing flux vector . These quant i t ies depend, in general, on the part ic le X and on t ime t. Assume t h a t s is posi t ive when it represents an amount of hea t absorbed by the body in the uni t t ime and tha t , moreover , h is ou tward directed wi th respect to the body surface whenever i t rcprescnts an a m o u n t of hea t which goes into the body in the uni t t ime. The following local form of the so-called ClausiusDuhem inequal i ty

Thermal fatigue resistance of elastic-plastic bodies under surface temperature changes

Abstract A rigorous elastic-plastic analysis allowing for a temperature-dependent yield condition is carried out in the present paper to determine the plastic strain of a semi-infinite solid subjected to uniform temperature changes at its surface. This leads to simple analytical and graphic procedures to evaluate the plastic deformation produced in a body of any shape by surface heating or cooling processes, provided that these processes are so fast-or that the thermal impedence of the body is so high-that all the temperature variations of the body are confined to within a thin layer near the body surface. The results are then applied to predict the occurence of rupture by thermal fatigue at the body surface once its temperature variations are known. In particular, for heating and cooling cycles that occur entirely above or entirely below the initial temperature of the body, it is found that there is a limit in the magnitude of the temperature variations, below which no thermal fatigue will occur at the body surface, no matter how many times the cycle is repeated.