Koncepcje Opisu Zanikania Pamięci Materiału

The theory of simple materials which has undergone considerable development in recent years has become a foundation for the description of many properties of real materials. This theory is remarkable for its good physical foundations and great care for mathematical correctness. Owing to its generality it can be used for the description of the properties of some metals and also many polymers and soils. By applying various approximations to the constitutive equation describing the behaviour of a simple material many known theories of materials can be obtained. The constitutive equation can be simplified by imposing certain limitations on the memory of the material. These limitations are comprised, in general, within the frames of the assumption of fading memory of the material. The aim of the present paper is to give a detailed discussion of various conceptions of the phenomenon of fading memory. It is the author's wish to show the results obtained by many authors (with different assumptions in general), using a uniform approach based on the notion of a metrizable topologic space. This enables all the results obtained hitherto to be considered to constitute particular cases of a common theory and gives a means of a study of the relations between them. All the problems considered concern finite strains of a continuum occurring during isothermal processes.
Sec. 2 presents a brief discussion of the theory of a simple material. The forms of the constitutive equations studied in the subsequent parts of the paper are analysed in detail.
Sec. 3 is fundamental for the paper. It contains a discussion of the physical aspect of the phenomenon of fading memory. The mathematical foundations of its description are discussed. The domain of the constitutive functional is defined as a subset of a metric topologic space. The weak and strong principles of fading memory are defined, respectively, as the condition of continuity and differentiability of the constitutive functional in the metric space. The most important of the results that can be obtained from the above formulation of the principles of fading memory are discussed.
Sec. 4 brings a detailed discussion of the conception of description of fading memory proposed by B.D. Coleman and W. Noll. Much space is devoted to the fundamental theorem on the stress relaxation and to the approximations of the constitutive functional.
In Sec. 5 are discussed the two proposals of C.-C. Wang.
Sec. 6 is devoted to the conception of A.E. Green and R.S. Rivlin.
In the final conclusions (Sec. 7) the practical importance of the theory of materials with fading memory is pointed out.