Analysis and Research of the High-Cycle Fatigue Fracture Mode Based on Stress Ratio and Residual Stress of Ti-6Al-4V

The content of titanium is about 0.63% in the earth’s crust, and it ranks 10th among all elements. The content of titanium is next to the metal elements of aluminum, iron and magnesium, iron, and magnesium; titanium alloys have low density, high specific strength (the ratio of tensile strength to density), wide working range (−253°C–600°C), and excellent corrosion resistance melting point; the chemical activity of titanium alloy is very high, and it easily reacts with hydrogen, oxygen, and nitrogen, so it is difficult to be smelted and processed, and the processing cost is high. Titanium alloys also have poor thermal conductivity (only 1/5 of iron and 1/15 of aluminum), small deformation coefficient, large friction coefficient, and other characteristics. They are widely used in aircraft fuselage, gas turbine, petrochemical, automotive industry, medical, and other fields for important parts.

Real-Time Numerical Simulation for Accurate Soft Tissues Modeling during Haptic Interaction

The simulation of fabrics physics and its interaction with the human body has been largely studied in recent years to provide realistic-looking garments and wears specifically in the entertainment business. When the purpose of the simulation is to obtain scientific measures and detailed mechanical properties of the interaction, the underlying physical models should be enhanced to obtain better simulation accuracy increasing the modeling complexity and relaxing the simulation timing constraints to properly solve the set of equations under analysis. However, in the specific field of haptic interaction, the desiderata are to have both physical consistency and high frame rate to display stable and coherent stimuli as feedback to the user requiring a tradeoff between accuracy and real-time interaction. This work introduces a haptic system for the evaluation of the fabric hand of specific garments either existing or yet to be produced in a virtual reality simulation. The modeling is based on the co-rotational Finite Element approach that allows for large displacements but the small deformation of the elements. The proposed system can be beneficial for the fabrics industry both in the design phase or in the presentation phase, where a virtual fabric portfolio can be shown to customers around the world. Results exhibit the feasibility of high-frequency real-time simulation for haptic interaction with virtual garments employing realistic mechanical properties of the fabric materials.

Chaos and pole-skipping in rotating black holes

We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency ω∗ = i2πT there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of “pole-skipping” — namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT.

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity. Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time steps perform well long-term when stabilizing Hamiltonian errors, regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincaré sections and fast Lyapunov indicators is applied to investigate the effects of the parameters, including the four free deformation parameters, on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances, as the magnitude of the magnetic parameter or any one of the negative deformation parameters increases. However, they are weakened when the angular momentum or any one of the positive deformation parameters increases.

Stability of a nonlinear thermoelastic plate

The problem of loss of stability of a circular plate under lateral compression in an inhomogeneous temperature field is considered. The theory of superposition of a small deformation on a finite one is used. A similar approach to the study of the equilibrium bifurcation of nonlinear thermoelastic bodies was used in the following works.

The Characteristics of Seismic Rotations in VTI Medium

Under the assumptions of linear elasticity and small deformation in traditional elastodynamics, the anisotropy of the medium has a significant effect on rotations observed during earthquakes. Based on the basic theory of the first-order velocity-stress elastic wave equation, this paper simulates the seismic wave propagation of the translational and rotational motions in two-dimensional isotropic and VTI (transverse isotropic media with a vertical axis of symmetry) media under different source mechanisms with the staggered-grid finite-difference method with respect to nine different seismological models. Through comparing the similarities and differences between the translational and rotational components of the wave fields, this paper focuses on the influence of anisotropic parameters on the amplitude and phase characteristics of the rotations. We verify that the energy of S waves in the rotational components is significantly stronger than that of P waves, and the response of rotations to the anisotropic parameters is more sensitive. There is more abundant information in the high-frequency band of the rotational components. With the increase of Thomsen anisotropic parameters ε and δ, the energy of the rotations increases gradually, which means that the rotational component observation may be helpful to the study of anisotropic parameters.

A Substructure Synthesis Method with Nonlinear ROM Including Geometric Nonlinearities

Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.

Relative Lagrangian Formulation of Finite Thermoelasticity

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

Strain Localization Modes within Single Crystals Using Finite Deformation Strain Gradient Crystal Plasticity

The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

Confined Monolayer Ice Between CaF2 (111) and Graphene: Structure and Stability

Water monolayer can form in layered confined systems. Here, CaF2 (111) and graphene are chosen as modeling systems to explore the structure and stability of confined monolayer water. First, water molecules tend to intercalate into a confined space between graphene and CaF2, rather than on a bare surface of graphene. Water molecules can move fast in the confined space due to a low diffusion barrier. These water molecules are likely to aggregate together, forming monolayer ice. Four ice phases including ice II, ice III, ice IV, and ice Ih are compared in this confined system. Intriguingly, all the ice phases undergo very small deformation, indicating the 2D monolayer ice can be stable in the CaF2–graphene–confined system. Beyond, projected band structures are also plotted to understand the electronic behavior of these confined ice phases. Nearly all the bands originated from confined ices are flat and locate about 2–3 eV below the Fermi level. Binding energy calculations suggest that the stability sequence in this confined system as follows: Ih-up ≈ Ih-down ≈ II < IV < III. Our results bring new insights into the formation of water monolayer production in such a confined condition.