Theory of deformation

Micromechanical theories of deformation must be based on physical evidence of shock-induced deformation mechanisms. One of the chapters in this book deals with the difficult problem of recovering specimens from shocked materials to perform material properties studies. At present, shock-recovery methods provide the only proven teclfniques for post-shock examination of deformation mechanisms. The recovery techniques are yielding important information about microscopic deformations that occur on the short time scales (typically 10 -10 s) of the compression process. 

The continuum theory of deformation of elastic solids is old and well developed [65T01, 74T01], and, in its linear version, is widely applied. Nonlinear theory is of much more recent origin. Most application of nonlinear theory has been to the behavior of highly deformable materials such as rubber or to the explanation of subtle effects observed by precise ultrasonic... 

The excluded volume in the theory of deformation of swollen network polymers. Vysokomolekul. Soedin. 1, 1659 (1959). 

Sadrakyan, L. C. Statistical Theory of Deformation. Erevan Apastan 1968 (Russ.)... 

To achieve the goals of dry granulation as discussed above, it is necessary to induce plastic deformation of the powders of interest to facilitate bonding into a compact for subsequent milling into granules. While the theory of deformation is well understood for many materials (1), it is less well described for powders and even less for powders of molecular organic particles. 

Approximate the dependence of Ty on T and by using a correlation suggested by Brown [91], who combined the kinetic theory of deformation [92] with the empirical observation that xy is approximately proportional to the shear modulus (G) just as oy(T) in uniaxial tension is roughly proportional to Young s modulus (E). 

Computer simulation of the deformation of microstructural models based on the kinetic theory of deformation, as in the work of Termonia et al [94-99], Bicerano et al [100] and Zaitsev et al [101], appears to be a more promising approach than the development of simple... 

Some novel statistical theories of solutions of polymers use the %i parameter, too. They predict the dependence of the %i parameter on temperature and pressure. According to the Prigogine theory of deformable quasi-lattice, a mixture of a polymer with solvents of different chain length is described by the equation ... 

During the derivation, we used the fact that the result is independent of how we obtained the final state of the system (i. e., body B) from the initial state. Strictly speaking, this is valid only for elastic bodies. If plastic deformations occur, the energy interpretation has to be handled with care. It is still valid if the so-called theory of deformation plasticity is used, which assumes that there is no unloading within the material. This condition is frequently met so that the J integral can used even in plasticity in many cases. 

By unifying the excess concept and the theory of deformation and introducing the individual capillary quantities, the set of tools for capillarity is logically completed. All of the variables and relationships can be defined. 

Suo Z, Zhao X, Green WH (2008) A nonlinear field theory of deformable dielctrics. J Mech Phys Solids 56(2) 467 86... 

Checking of the wall thicknesses of a container is either done on the theory of elasticity or on the theory of deformation, in which the compound stress - made up of tangential, radial and axial stresses - is referred to a reduced or comparative stress. At the present time the strength of the material is mostly calculated with the help of the theory of deformation, because reference stresses are obtained by this method, which are in good agreement with the tests and slightly higher than the reduced stresses obtained by the theory of elasticity. 

According to the theory of deformation, the material stress which is derived from the deformation energy, has its maximum value at that point where the comparison stress... 

Nowadays the theory of deformation is most commonly employed, the results of which correspond better with actual experiments. In this theory the stresses and Oi, calculated with the help of Bach s formulas, and additional stresses are reduced to the comparison stress... 

The stresses are determined in the critical points and from these values the stress (comparison stress as per the theory of deformation) and compared with the permissible value. 

From the summation stresses determined in points 0, 1, 2 and 3, the comparison stress in each of these points may be established. In order to avoid permanent sets, the comparison stress must not exceed the yield strength at elevated temperature. According to the theory of deformation, the comparison stress is... 

According to the theory of deformation, the optimum axial stress from which results at given values G and the smallest comparison stress, is ... 

The various simpler theories of deformation friction have been presented by Moore ... 

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