A lightweight strain-glass alloy showing nearly temperature-independent low modulus and high strength

Fast development of space technologies poses a strong demand for elastic materials that are lightweight, strong, but compliant to achieve high density of elastic energy storage, and such properties need to be temperature-insensitive in space environments1-4. However, existing materials do not meet this demand. Here we report a lightweight magnesium-scandium (Mg-21.3 at. % Sc) alloy meeting this demand. It is as light and compliant as organic-based materials like bones and glass fiber reinforced plastics, but stronger than them5-7; thus, it exhibits a record-high elastic energy density ~0.5 kJ/kg among various metallic and organic-based composite materials at a moderate stress level of 200 MPa8,9. Importantly, the performance can persist for 1 million stress cycles and over a wide temperature range from ambient to cryogenic temperatures. Its exceptional properties stem from a strain-glass transition. In-situ microstructure observations during cooling show strain-glass nanodomains continuously form from the matrix phase, which enables low modulus, high strength, fatigue-resistance, and temperature-insensitivity. The lightweight strain-glass Mg-Sc alloy may find applications in space technologies and other fields such as orthopedics1,9-11.

Sliding Impact Mechanism of Square Roadway Based on Complex Function Theory

To clarify the process of stress change and plastic zone evolution of square roadways under high-stress conditions, the rotational square expansion plastic zone evolution model of square roadway was established by theoretical analysis, numerical simulation, and engineering verification. The shear slip impact stress criterion of square roadway based on complex variable function theory was studied, and the law of surrounding rock stress distribution, plastic zone expansion, elastic energy density, local energy release rate (LERR), and total energy release of square roadway were analyzed. The results show that the compressive stress is concentrated in the four corners of the roadway after the roadway excavated and transfers with the change of plastic zone. Main shear failures start from the four corners and develop in a rotating square shape, forming square failure zones I and II. The square failure zone I is connected with the roadway contour and rotated 45°. The square failure zone II is connected with the square failure zone I and rotated 45°. When the original rock stress is low, the surrounding rock tends to be stable after the square shear slip line field formed. When the original rock stress is high, the shear failure of the surrounding rock continues to occur after the square failure zone II formed, showing a spiral slip line. Corners of the square roadway and square failure zones I and II are the main energy accumulation and release areas. The maximum elastic energy density and LERR increase exponentially with the ratio of vertical stress to uniaxial compressive strength (Ic). When square corners of the roof are changed to round corners, the plastic zone of the roof expands to form an arch structure. The maximum elastic energy density decreases by 22%, which reduces the energy level and possibility of rock burst. This study enriches the failure mechanism of roadway sliding impact. It can provide a basic theoretical reference for the design of the new roadway section and support form based on the prevention of rock burst.

Experimental Investigation on the Energy Storage Characteristics of Red Sandstone in Triaxial Compression Tests with Constant Confining Pressure

The elastic energy stored in deep rock in three-dimensional stress environment is the energy source of rockburst. To investigate the energy storage characteristics of deep rock under different confining pressures, a series of triaxial single-cyclic loading-unloading compression tests were conducted on red sandstone specimens under eight confining pressures. The input energy density, elastic energy density, and dissipative energy density of the specimen in axial, circumferential, and total directions can be obtained by the area diagram integration method. The results show that the input energy density in the axial direction accounts for the largest logarithmic proportion of the total input energy density, and the relationship between all energy density parameters and unloading level can be described by quadratic function. In the axial direction, there is a linear function relationship among elastic energy density, dissipative energy density, and input energy density. In the circumferential direction, there is a quadratic function relationship among elastic energy density, dissipative energy density, and input energy density. For the total energy density parameters of the rock specimen, the relationship among elastic energy density, dissipative energy density, and input energy density conforms to the quadratic function. According to the above correlation function, the elastic energy stored in deep rock under different confining pressures can be accurately obtained, which provides a foundation for studying the mechanism of rockburst under three-dimensional unloading from the energy perspective.

Hooke’s law and elastic constants

Hooke’s law and elastic constants are introduced. The symmetry of the elastic constant tensor follows from the symmetry of stress and strain tensors and the elastic energy density. The maximum number of independent elastic constants is 21 before crystal symmetry is considered, and this leads to the introduction of matrix notation. Neumann’s principle reduces the number of independent elastic constants in different crystal systems. It is proved that in isotropic elasticity there are only two independent elastic constants. The directional dependences of the three independent elastic constants in cubic crystalsare derived. The distinction between isothermal and adiabatic elastic constants is defined thermodynamically and shown to arise from anharmonicity of atomic interactions. Problems set 3involves the derivation of elastic constants atomistically, the numbers of independent elastic constants in non-cubic crystal symmetries, Cauchy relations, Cauchy pressure, invariants of the elastic constant tensorand compatibility stresses.

Transport Phenomena in Fluid Films with Curvature Elasticity

Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins, and curvature elastic deformation of lipid bilayers. The proteins in the membrane are modeled such that they influence membrane bending by inducing a spontaneous curvature. We formulate the free energy of the membrane with a Helfrich-like curvature elastic energy density function modified to account for the chemical potential energy of proteins. We derive the conservation laws and equations of motion for this system. Finally, we present results from dimensional analysis and numerical simulations and demonstrate the effect of coupled transport processes in governing the dynamics of membrane bending and protein diffusion.

Numerical Analysis of Roadway Rock-Burst Hazard Under Superposed Dynamic and Static Loads

Microseismic events commonly occur during the excavation of long wall panels and often cause rock-burst accidents when the roadway is influenced by dynamic loads. In this paper, the Fast Lagrangian Analysis of Continua in 3-Dimensions (FLAC3D) software is used to study the deformation and rock-burst potential of roadways under different dynamic and static loads. The results show that the larger the dynamic load is, the greater the increase in the deformation of the roadway under the same static loading conditions. A roadway under a high static load is more susceptible to deformation and instability when affected by dynamic loads. Under different static loading conditions, the dynamic responses of the roadway abutment stress distribution are different. When the roadway is shallow buried and the dynamic load is small, the stress and elastic energy density of the coal body in the area of the peak abutment stress after the dynamic load are greater than the static calculations. The dynamic load provides energy storage for the coal body in the area of the peak abutment stress. When the roadway is deep, a small dynamic load can still cause the stress in the coal body and the elastic energy density to decrease in the area of the peak abutment stress, and a rock-burst is more likely to occur in a deep mine roadway with a combination of a high static load and a weak dynamic load. When the dynamic load is large, the peak abutment stress decreases greatly after the dynamic loading, and under the same dynamic loading conditions, the greater the depth the roadway is, the greater the elastic energy released by the dynamic load. Control measures are discussed for different dynamic and static load sources of rock-burst accidents. The results provide a reference for the control of rock-burst disasters under dynamic loads.

Superior electrostrictive strain achieved under low electric fields in relaxor ferroelectric polymers

A relaxor ferroelectric polymer exhibits record electromechanical performance, including the largest electrostrain of −13.4%, the highest elastic energy density of 3.1 J cm−3 and the best energy conversion efficiency of 0.5, among the known ferroelectric polymers. Notably, the excellent electromechanical responses are realized under much lower fields than those of ferroelectric polymers.

Energy Evolution Characteristics and Distribution Laws of Rock Materials under Triaxial Cyclic Loading and Unloading Compression

To explore the influence of confining pressure on the energy evolution characteristics of loaded rocks, triaxial cyclic loading-unloading experiments on sandstones were carried out under 6 kinds of confining pressures using the axial loading and circumferential deforming control modes. Total energy density, elastic energy density, and dissipated energy density absorbed by rock specimens under different confining pressures were obtained. The confining pressure effect of the evolution process and distribution law in energy accumulation and dissipation was analyzed. Energy conversion mechanism from rock deformation to failure was revealed, and energy conversion equations in different stress-strain stages were established. The method of representing the rock energy accumulation, dissipation, and release behaviors by energy storage limit density, maximum dissipated energy density, and residual elastic energy density was established. The rock showed that, with the increase of confining pressure, the characteristic energy density of rock increased in the power exponent form, and the energy storage limit density increased faster than the maximum dissipated energy density. The greater the confining pressure was, the greater the proportion of elastic energy before peak was. It is indicated that the confining pressure increased the energy inputting intensity, improved the energy accumulating efficiency, and inhibited the energy releasing degree.

Combined polarization field gradient and strain field gradient effects in elastic flexoelectric materials

We consider a constitutive model for the behavior of elastic flexoelectric materials including strain gradient fields and polarization gradient fields. This model is based on a stored elastic energy density function which depends on four independent variables: the polarization field and the polarization field gradient as well as the strain field and the strain field gradient. A generalized Toupin variational approach is utilized to find the governing equations (constitutive relations, equilibrium equations and boundary conditions) of the material. The present model is then applied to the problem of a thick walled cylindrical tube of elastic isotropic flexoelectric material, subjected to axisymmetric loading. The resulting radial displacement field noticeably differs from the elastic and strain gradient elastic cases.