Explosion as a phase transition due to the change of the gradient symmetry of the distortion tensor.

It is shown that the destruction of a continuous elastic medium is a phase transition associated with a change in the gradient symmetry of the equations of state for the distortion tensor. The equations of state for the distortion tensor, as a compensating field of the minimal fundamental interaction, are derived from the action minimum. In a continuous elastic medium, the distortion tensor is proportional to the conjugate stress tensor. The continuous medium is destroyed at critical stresses or pressures. At the same time, the vortex tension of the distortion tensor penetrates into it and the elasticity disappears. As a result of this phase transition, linear defects and cracks are formed in solids state, and high-temperature plasma occurs in the gas and an explosion occurs. It is shown that the explosion and lightning are the same phase transition, which is caused by the occurrence of a critical vortex tension of the distortion tensor.

The minimal interaction induced by the translation subgroup has a gap and possible relates to the strong fundamental interaction.

The paper investigates the low-symmetric state of the compensating field of the distortion tensor and proves that there is a gap in this state. It is shown that the distortion tensor is the compensating field of the minimal interaction induced by the translation subgroup. On the example of electron pairing in a Cooper pair it was proved that the distortion tensor is responsible for the electron-phonon interaction. In this paper, for the first time, an exact wave solution for sound pressure in a continuous medium is obtained from the equations of state for the distortion tensor. It is shown that the sound is described as "massive" wave of the distortion tensor, the spectrum of which has the minimal frequency, which corresponds to a gap. The presence of a gap in the low-symmetric state gives grounds to believe that the distortion tensor, as a compensating interaction field, describes a strong fundamental interaction. As it is known, the description of the gap in the strong fundamental interaction is declared a Millennium problem by the Clay Mathematical Institute (CMI).

Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient

The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

Кинетика развития паттернов макролокализации пластического течения металлов

The features of the macroscopic inhomogeneity of plastic deformation in the form of autowaves with a pulsating amplitude are analyzed, and data on the localization of sources of acoustic emission at different stages of plastic flow in the stretching of fcc mono- and polycrystals are presented. The relationship between the local components of the plastic distortion tensor in the strain localization zone is traced. The role of acoustic phenomena accompanying the localization of plastic strain in the development of the process of plastic deformation is considered.

Характер деформаций на границе раздела упругих сред при условии скольжения

Fresnel coefficients obtained when solving the problem of wave propagation through the interface of two elastic media and expressions for components of the elastic-distortion tensor allow one to study the character of dynamic deformations at the interface. Deformation modes different from zero at the interface of the elastic media under the slip-contact condition have been determined. Dependences of deformation amplitudes at the interface on the wave incidence angle and parameters of the adjacent media for incident longitudinal and transverse waves have been constructed and analyzed.

Estimation of the Full Nye Tensor by EBSD-Based Dislocation Microscopy

An extension to a previously published, novel stereological method is reported which infers experimentally inaccessible components of the Nye GND tensor. Limitations imposed by electron-opacity of metals prevent direct measurement of four components of the Nye tensor, but it is possible to use additional experimentally-obtainable information in connection with underlying field equilibrium equations to estimate these additional components. This approach uses derivatives to the infinitesimal elastic distortion tensor to reduce error imposed by pattern center inaccuracy.