Strategy for Crack Width Measurement of Multiple Crack Patterns in Civil Engineering Material Testing Using a Monocular Image Sequence Analysis

An image sequence analysis procedure is developed to quantitatively analyze complex multiple crack patterns in tension tests of fiber-reinforced composite specimens. Planar textured surfaces of such specimens can be observed with a monocular image sequence using a camera of suitable spatial and temporal resolution. Due to the narrow crack paths, a dense high-precision displacement vector field is computed applying least-squares image matching techniques. Some uniformly distributed matching points are triangulated into a mesh. To measure deformations, principal strains and crack widths are computed for each face. Stretched triangles presumably containing one or multiple cracks are subdivided into three new triangles to densify the mesh in critical regions. The subdivision is repeated for some iterations. The crack width computation of the triangles requires at least three vertices and its displacements. Due to the dense displacement vector field, there are more points available. In this paper, an algorithm for the crack width computation in a least-squares fit is presented.

Modified f(R,T) cosmology with observational constraints in Lyra’s geometry

In this paper, we have investigated modified [Formula: see text] cosmological models with observational constraints in Lyra’s geometry. We have studied the models in two cases: in the first one it is taken as constant displacement vector field and in second case it is taken as time-dependent. We have established a relationship among energy parameters [Formula: see text], respectively, called as matter, anisotropy and dark energy (DE) density parameters in Bianchi type-I space-time in Lyra’s geometry. We have compared our models with observational data sets with union 2.1 compilation SNe Ia data and [Formula: see text] data sets and have found best fit values of various energy parameters for [Formula: see text]. We have found that the model with constant displacement vector field is the best fit to the study of the whole evolution of the model and the gauge function [Formula: see text] of Lyra geometry behaves like a DE candidate. Also, the various physical and kinematical parameters have been studied in this study.

An extended theory of gravity in a modified Riemann’s geometry

In this work, we study the evolution of an isotropic universe in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field [Formula: see text] as a complex vectorial function depending on a dynamical scalar field [Formula: see text]. By using the latest observational data, we observe that for [Formula: see text] the universe starts accelerating at the critical scale factor [Formula: see text] which corresponds to a redshift of [Formula: see text]. We also find that the dark energy fluid considered in this model is a generalized fluid with equation of state [Formula: see text].

An obstacle problem for elliptic membrane shells

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity

This paper deals with the fully coupled linear theory of thermoelasticity for triple porosity materials. The system of general governing equations of motion is expressed in terms of the displacement vector field, the pressures in the three pore systems (macro-, meso- and micropores) and the temperature. The fundamental solutions are constructed explicitly by means of elementary functions for the five special cases of the equations of motion: (1) equations of steady vibrations; (2) equations in the Laplace transform space; (3) equations of steady vibrations in the quasi-static theory; (4) equations of equilibrium; and (5) equations of steady vibrations for rigid body with triple porosity. Finally, the basic properties of these solutions are established.

Static traversable wormholes in Lyra manifold

At first, considering the Einstein framework, we introduce some new static traversable wormholes and study the effects of a dark energy-like source on them. Thereinafter, a brief review on Einstein field equations in Lyra manifold is presented, and we address some static traversable wormholes in the Lyra manifold which satisfy the energy conditions. It is also shown that solutions introduced in the Einstein framework may also meet the energy conditions in the Lyra manifold. Finally, we focus on vacuum Lyra manifold and find some traversable asymptotically flat wormholes. In summary, our study shows that it is theoretically possible to find a Lyra displacement vector field in a manner in which traversable wormholes satisfy the energy conditions in a Lyra manifold.

Аналитическое выражение для распределения упругой деформации, создаваемой включением в форме многогранника с произвольной собственной деформацией

Analytical expressions for the displacement vector, stain tensor, and Eshelby tensor have been obtained in the case where an inclusion in an elastically isotropic infinite medium has a polyhedral shape. The eigenstrain (e.g., the lattice mismatch) is assumed to be constant inside the inclusion but not obligatorily hydrostatic. The obtained expressions describe the strain both inside the inclusion and in its environment. It has been shown that a complex three-dimensional configuration of the elastic strain field (as well as of the displacement vector field) is reduced to a combination of simple functions having an illustrative physical and geometrical interpretation.

Inhomogeneous cosmology with quasi-vacuum effective equation of state on Lyra manifold

<p>A class of inhomogeneous Lemaître-Tolman cosmological models is obtained in the context of Lyra’s geometry. Cosmological models in Lyra’s geometry are studied under the condition of the minimal coupling of matter with the displacement vector field and the varying Λ term. Exact solutions to the model equations are obtained subject to the quasi-vacuum effective equation of state. As a result, the displacement field as well as the cosmological term can be expressed in terms of the energy density of matter. The rate of expansion and the deceleration parameter of the model are also studied</p>