A method of successive approximations for nonlinear viscoelasticity based on the nonlinear correspondence principle and the method of approximations

Mechanics of Composite Materials -     

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–611, July–August, 1969.     

Estimation of the error of approximation of the analytic solution of problems for nonlinear viscoelastic materials

Estimates are given for the error of approximation of the solution of problems of nonlinear viscoelastic media, for which the nonlinear elastic solution depends analytically on the material characteristics, the body and surface forces, and on the boundary displacements. From the integral estimates particular estimates are derived for viscoelastic materials in cases when the nonlinear elastic solution is majorized by a geometric progression or the sum of products of geometric progressions.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 5, pp. 827–834, September–October, 1971.     

Small elastoplastic strains of dielectrics

The theory of small elastoplastic strains of dielectrics in the presence of an electric field is developed in the work. An expression is obtained for the electric part of the stress tensor. Total free energy minimum theorems with constant temperature and simple proportional loading and unloading theorems are proved. Experiments to calculate the mass functions are discussed.     

Critical levels of oriented defects in brittle fracture

Conclusions For an orthotropic system of defects we derived a brittle failure criterion whose coefficients are determined by the parameters of the structure. The discussed examples show that the proposed relationships can be used more efficiently to determine the behavior of the structure on the basis of the macroproperties of the material. The effects of variations in the dimensions of the defects, merging of the defects and the appearance of new defects are described quantitatively. After compiling a sufficient amount of information, the relations can be used to solve the main problem of determining the ultimate strength on the basis of the behavior of the structure of defects.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 623–630, July–August, 1989.