Narrow Results

This paper advances the state-of-the-art by extending the study of the analogy between the fabric of spacetime and elasticity. As no prior work exists about a potential spacetime thermal expansion coefficient $\alpha$, we explore the analogy of general relativity with the theory of elasticity by considering the cosmological constant $\mathrm{\Lambda }$ as an additional space curvature of the structure of space due to a thermal gradient coming from the cosmic web and the cold vacuum and we propose ${(\frac{{\alpha }_S\mathrm{\Delta }T}{e})}^2={(\frac{1}{R_0})}^2=\mathrm{\Lambda }$ with $R_0$ being the curvature radius of the space fabric. It follows from this analogy and from the supposed space model consisting of thin sheets of Planck thickness $l_p$ curved by this thermal gradient $\mathrm{\Delta }$T a possible thermal expansion coefficient of the equivalent elastic medium modeling the space ${\alpha }_S=\frac{l_p\sqrt{\mathrm{\Lambda }}}{\mathrm{\Delta }T}$ of the order of ${\alpha }_{\mathrm{\text{space-QFT}}}=1.16\times 10^{-6}$K${}^{-1}$. As spacetime and not only space must be considered in general relativity, this paper also proposes an innovative approach which consists in introducing into the interval ds² of special relativity a temperature effect $T:d_s^2={(1\pm {\alpha }_{t}T)}^2{c}^2{dt}^2-{(1\pm {\alpha }_{s}T)}^2[{dx}^2+{dy}^2+{dz}^2]$ (entropy variations correlated with time laps, based on temperature variations affecting always physically the clocks) based on different thermal expansion coefficients for space and time with for the flow of time $t:\frac{ct}{cn\tau }=\frac{k_{B}t}{nh}\times \mathrm{\Delta }T={\alpha }_t\mathrm{\Delta }T$. With $T\approx$ 10⁶K, $n=1$, the associate time interval is ${4.8\times 10}^{-17}$s and ${\alpha }_t=1.0\times 10^{-6}{K}^{-1}$. The consequence of this hypothesis is that dark energy potentially becomes a thermal spacetime curvature ${(\frac{{\alpha }_{f}T}{l_p})}^2$ with $f$ equal to $s$ or $t$ depending of the temperature, the thermal entropy variation of the universe, the Planck thickness and time, that increases since the Big bang, depending on thermal expansion coefficients for spacetime ${\alpha }_s$ and ${\alpha }_t$ as a function, respectively, of $\mathrm{\Lambda }$, $\frac{k_B}{h}\times t$, in opposition to spacetime curvature gravity due to mass/energy density as described in general relativity.

After recalling the principles that allow spacetime to be considered by analogy as an elastic medium, we show how the modified gravity according to the MOND theory concerning the anomaly of the velocities of stars at the periphery of galaxies can be seen as a creep of space acting on the radius of galaxies that give a creep coefficient of ${\phi }_{\mathrm{\text{space}}}=\frac{a_0}{a}\frac{{\rho }_{\mathrm{\text{local}}}}{{\rho }_{\mathrm{\text{mean}}}}-1$. The values vary between 0.2 and 9 depending on the type of galaxy and density distribution. Considering the gravitational lensing effect of the ball cluster we obtain a creep coefficient ${\phi }_{\mathrm{\text{space}}}=\frac{1-p_v}{p_v}$ with $p_v$ the percentage of visible matter and $p_{\mathrm{\text{DM}}}$ the percentage of dark matter from the global mass ($p_v+p_{\mathrm{\text{DM}}}=1$). The values vary between 0.66 and 4 for this cluster. This paper therefore raises the question, via these creep coefficients, of the possible granular nature of the vacuum and therefore of space fabric on the one hand and proposes another dark matter-free approach based on the creep of the texture of space to explain gravitational anomalies on the other hand.

Helices are ubiquitous building blocks in natural systems, and have since become major sources of inspiration for engineering design of helical devices with a range of applications in sensors, transducers, transistors and micro-robotics devices. In this work, we illustrate the mechanical self-assembly principle in spontaneous helical structures, and perform finite element simulations to model such large deformation of thin structures in three dimensions. Our work can facilitate designs of tunable helical structures at both macroscopic and microscopic scales with desirable geometric parameters for engineering applications such as in nanoelectromechanical systems (NEMS), drug delivery, sensors, acturators, optoelectronics and microbotics.

In this paper, geometrical interpretation of the Timoshenko–Ehrenfest theorem is given. It is based on a vector-valued version of continuum mechanics, which considers the deformed body as a surface in extended coordinate space. Scalar parameters of the metrics of this hypersurface determine the strain. In the bending beam case, this surface is formed by a twisted cylinder rolled into a cone. Accordingly, three kinds of metric parameters, the stretch ratio, the twist and cone angles responsible for stretching, shear, and bending determine the shape of the elastic curve. The balance equations for generalized forces taking into account shear deformation and rotational bending effects are derived. A new formula for the shear coefficient comes out of the derivation. It is shown that its magnitude 5/6 for quasistatic Timoshenko beam remains fair for the exact form of the cross-section at the free end.

This study proposed exact solutions for the purpose of investigating and understanding the time-varying bending behavior of a multilayer orthotropic beam bonded by viscoelastic interlayers. In the analytical model, each orthotropic layer involved four independent elastic constants and was modeled on the basis of the two-dimensional (2D) elasticity theory. The interlayer exhibited viscoelastic properties and was described by the standard linear solid model. By means of Fourier series expansion, the general solutions of stresses and displacements were derived with unknown coefficients, which were analytically determined by interfacial and loading conditions, in which the convolution was converted by the Laplace transform. The results of numerical examples showed that the present solutions converged rapidly and were consistent with the finite element solutions. Comparison of the present 2D solutions with the one-dimensional (1D) solutions based on the Euler–Bernoulli beam theory indicated that the 1D solutions were inaccurate for thick beams. The effects of viscoelastic material and orthotropic constants on the long-term stresses and displacements in the beam were thoroughly examined. These results provided a reference for the optimization of a multilayer orthotropic beam design.