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In this paper, a rectangular bistable composite laminated plate is studied through dynamic modeling, numerical simulation and experiment. A theoretical model is elucidated, elaborating the dynamic snap-through and nonlinear dynamics of the rectangular bistable composite laminated plate. The potential energy curve, the restoring force curve and the stiffness curve are graphically presented, exhibiting differences from those of square bistable plates. The two potential wells and the negative stiffness region are asymmetric. The dynamic snap-through elucidated by curvature and displacement is graphically presented in phase diagrams and time history diagrams. Due to the asymmetry of the double potential wells, the dynamic snap-through may be unidirectional rather than repeated, and the nonlinear dynamic responses around the two potential wells are asymmetric, which depends on initial positions. In frequency sweep, the frequency-amplitude response curves are characterized by the softening nonlinear stiffness effect and the hysteresis, where there are multiple peaks displaying the first several modes of the rectangular bistable plate around one stable state. The nonlinear dynamic responses are characterized by the periodic and chaotic vibrations, the 1/2 subharmonic resonance, the unidirectional dynamic snap-through and the repeated dynamic snap-through. When the excitation frequency is equal to the first mode frequency for the lower stable state or the third mode frequency for the upper stable state, the dynamic snap-through is found to occur. Linear mode frequencies can show the mechanism of the snap-through to a certain extent. At mode frequencies, sufficient energy is gathered to actuate the snap-through. Unlike square bistable plates, rectangular bistable plates may only be characterized by the unidirectional snap-through under the specific energy input, which depends on initial positions. For rectangular bistable plates, two opportune excitation frequencies that have to be selected can lead to the repeated snap-through. This research is beneficial to the development of aerospace structures, bistable energy harvesters and vehicle vibration isolation devices. Compared to the old work, this work is more in line with the actual situation, where a high aspect ratio morphing wing can adjust its airfoil according to different tasks based on rectangular bistable plates which are more suitable for potential applications in the future. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework combining the state-based peridynamics (SBPD) with the extended finite element method (XFEM) for crack propagation in two-dimensional solids. Numerical examination is conducted fulfilling both the quasi-static and time-dependent loading conditions. The computational domain is partitioned into two regions: (a) SPBD region: the vicinity of crack tips and potential region where the crack is likely to propagate, and (b) XFEM region: the area behind the crack tip and the rest of the body. The salient features of the developed framework include: (a) avoiding requirement of a priori knowledge of enrichment functions like the conventional XFEM; (b) without fracture criteria for crack propagation; (c) no restriction on the value of Poisson's ratio like the bond-based peridynamics; and (d) higher computational efficiency than the pure peridynamics. The efficiency and accuracy of the proposed framework are systematically demonstrated through benchmark examples involving quasi-static crack growth and dynamic crack branching problems. [ABSTRACT FROM AUTHOR]

The bond-based peridynamics and its extended forms are widely used for crack predicting in many materials like concrete. In peridynamics, as for the bond failure, the tensile failure criterion or tensile-compression failure criterion are commonly applied, the combined tensile-shear or compression-shear failure are rarely considered. In this paper, a Cosserat peridynamic model with a novel bond failure criterion (CPD-BP) is proposed for concrete fracture simulation. The peridynamic bond failure criterion is derived from the Bresler–Pister criterion, with which the composite bond failure can be considered properly. Besides, the Cosserat parameters which relate to microstructures of concrete are introduced. Three benchmarks are designed: simple tensile, direct shear, and compression tests. Results show that the CPD-BP can simulate the combined tensile-shear and compressive-shear concrete failure. Crack patterns predicted by CPD-BP generally follow particle flow code in two dimensions results and physical experiments. The larger Cosserat shear modulus will enhance the shear effects. [ABSTRACT FROM AUTHOR]

A ring mesh is a large-scale manufacturable structure with versatile applications in architecture and for protective systems. However, the static and dynamic numerical simulation of a large-scale ring mesh is a resource-intensive task due to the many nonlinear contact points between the individual rings. To characterize the rigid body behavior of the ring mesh, in this paper, a representative volume element is loaded under different in-plane directions. The Green-Lagrangian strain tensor components are obtained as a result. An implicit one-step algorithm is used for this dynamic relaxation issue, modified by the use of stiff springs. Static convergence positions of a representative volume element are determined in several multiaxial tensile directions. The obtained deformation parameters can be used to simulate large deformations of large-scaled ring meshes. [ABSTRACT FROM AUTHOR]

In this paper, a novel locking-free finite beam element is proposed utilizing the absolute nodal coordinate formulation. By incorporating a gradient vector along the transverse direction at the boundary points, the linear interpolation of the gradient vector field within this element is achieved. Consequently, the problem of constant transverse strain distribution, which is observed in the Omar–Shabana beam element, is effectively addressed. Building upon this concept, this study further extends the proposed element from two dimensions to three dimensions. Additionally, it analyzes and compares the locking alleviation mechanism of the newly developed element and Patel–Shabana beam element. The analysis aims to provide insights into the factors contributing to the locking alleviation of different absolute nodal coordinate formulation (ANCF) elements. Furthermore, to demonstrate the effectiveness of the new element, six numerical simulation examples are designed, comprising three and three dynamic examples. These examples encompass small deformation statics, large deformation statics, small-scale motion, large-scale motion, and rotational motion problems. Finally, the results indicate that the proposed ANCF beam element can effectively alleviate the locking problem. The element exhibits robust adaptability, rationality, and effectiveness when subjected to complex mechanical characteristics by comparing the numerical results of this element with the classical Omar–Shabana, high-order Shen, and Patel–Shabana elements. [ABSTRACT FROM AUTHOR]

The effects of cracks on the dynamic behavior of engineering structures affect the structure safety. In this paper, a generalized multi-symplectic approach is developed to investigate the effects of crack on a dynamic behavior of a simply supported beam in detail. First, the effect of the crack on the bending stiffness of the simply supported beam is expressed by an equivalent bending stiffness and the dynamic model with variable coefficients is established to describe the transverse vibration of the cracked beam. Then, the approximate symmetric form of the dynamic model is constructed and its dynamic symmetry breaking factors are discussed. The Preissmann scheme of the approximate symmetric form is constructed based on the generalized multi-symplectic theory. In numerical simulations, the structure-preserving properties of the Preissmann scheme are illustrated and the validity of the dynamic model is verified. Then, the effects of the crack on the vibration of the beam are investigated by using the generalized multi-symplectic method in detail. The numerical results presented prove that the proposed generalized multi-symplectic method is an effective approach to investigate the dynamic behavior of cracked structures. [ABSTRACT FROM AUTHOR]

The mechanism of drag reduction via polymer additives is long debated in the literature. This journal published a paper (Volokh in Acta Mech 229(10):4295–4301, 2018), in which the drag reduction was explained based on the Navier–Stokes model enhanced with the viscous strength. This explanation was limited by a qualitative consideration of the onset of material instability in the laminar pipe flow. In the present work, we use the theoretical setting of Volokh (2018) in 3D numerical simulations of the realistic pipe flow where material instabilities develop into turbulence. We observe in the simulations that the addition of the polymer solute suppresses the chaotic turbulent motion, indeed, in accordance with the experimental observations of the phenomenon. [ABSTRACT FROM AUTHOR]

Accurate control of mixing between two fluids is a fundamental aspect in many applications and generally implies the use of small devices operating at low velocities. This is often achieved using micromixers which, due to the combination of small dimensions and low velocities, work in the laminar regime and generally process very limited flow rates. The flow rates can be increased using more mixers at the same time. In this respect it is appealing to use several micromixers connected in a unique device. In this paper we propose and characterize a simple strategy to connect several T-mixers together by aligning them in a row and feeding them by shared inlet channels. Since engulfment is the preferred flow regime for mixing, we investigate the proposed devices specifically focusing on the onset and on the properties of the engulfment regime. This investigation is carried out by a combined use of numerical simulation and linear stability analysis. The results reported here show that the proposed strategy can lead to compact devices in which the single mixers manifest engulfment, although some important differences in comparison with isolated T-mixers may exist depending on the spacing between the inlet/outlet channels in the device. [ABSTRACT FROM AUTHOR]

The natural processes involved in the scouring of submerged sediments are crucially relevant in geomorphology along with environmental, fluvial, and oceanographic engineering. Despite their relevance, the phenomena involved are far from being completely understood, in particular for what concerns cohesive or stony substrates with brittle bulk mechanical properties. In this frame, we address the investigation of the mechanisms that govern the scouring and pattern formation on an initially flattened bed of homogenous and brittle material in a turbulent channel flow, employing direct numerical simulation. The problem is numerically tackled in the frame of peridynamic theory, which has intrinsic capabilities of reliably reproducing crack formation, coupled with the Navier–Stokes equations by the immersed boundary method. The numerical approach is reported in detail here and in the references, where extensive and fully coupled benchmarks are provided. The present paper focuses on the role of turbulence in promoting the brittle fragmentation of a solid, brittle streambed. A detailed characterization of the bedforms that originate on the brittle substrate is provided, alongside an analysis of the correlation between bed shape and the turbulent structures of the flow. We find that turbulent fluctuations locally increase the intensity of the wall-stresses producing localized damages. The accumulation of damage drives the scouring of the solid bed via a turbulence-driven fatigue mechanism. The formation, propagation, and coalescence of scouring structures are observed. In turn, these affect both the small- and large-scale structures of the turbulent flow, producing an enhancement of turbulence intensity and wall-stresses. At the small length scales, this phenomenology is put in relation to the formation of vortical cells that persist over the peaks of the channel bed. Similarly, large-scale irregularities are found to promote the formation of stationary turbulent stripes and large-scale vortices that enhance the widening and deepening of scour holes. As a result, we observe a quadratic increment of the volumetric erosion rate of the streambed, as well as a widening of the probability density of high-intensity wall stress on the channel bed. [ABSTRACT FROM AUTHOR]

In this work, the periodic homogenization method is applied to a system of two equations of diffusion coupled through heterogeneous chemical reactions at the solid–fluid interface. This upscaling is discussed according to the order of magnitude of the Damköhler number. For large values of Damköhler number, a new homogenized diffusion reaction model coupling chemical reaction and diffusion is obtained. The homogenized diffusion and co-diffusion tensors are function of the heterogeneous reaction rate coefficients. The relevance of this homogenized model is analysed with respect to the order of magnitude of the Damköhler number. Some numerical simulations using this homogenized model are carried out and compared to numerical simulations at pore scale. [ABSTRACT FROM AUTHOR]

In this article, we present a numerical study of liquid droplet evaporation in three-component multiphase flows formulated on the basis of the lattice Boltzmann model. The main application of this research is the evaporation process in liquid propellant rocket engines, and therefore, the well-known fuels and oxidizers such as hydrogen and oxygen have been assigned to droplets material. A three-fluid (incompressible and immiscible) system is considered, and the interfaces of three fluids are captured by the Cahn–Hilliard flow model. A recent ternary-fluid model is developed to consider all the three fluids in phase-change phenomena for the first time. The present LB model is validated against some analytical and numerical solutions to evaluate the developed model accuracy in binary- and ternary-fluid systems. Effects of some related non-dimensional numbers on the droplets evaporation rate are studied, and velocity field and temperature contour are presented and analyzed. As a noticeable result, the higher evaporation rate is obtained at lower Reynolds number of droplets. Finally, as a more practical application, the evaporation of a hydrogen droplet and a few surrounded oxygen droplets in different conditions is studied. The results show that the increase in oxygen droplet numbers has a different effect on hydrogen and oxygen evaporation rates. [ABSTRACT FROM AUTHOR]

The principle of material objectivity used in classical continuum mechanics states that the description of material behaviors has to be frame-invariant. Moreover, geometric considerations show that objectivity can be extended by use of a covariant principle. Covariance can be naturally expressed using a four-dimensional spacetime. We thus propose to consider a thermodynamic approach within this framework to obtain covariant constitutive models in the case of finite deformation. A four-dimensional form of the Clausius–Duhem inequality is thus derived for continuum thermomechanics applications. In this article, we are able to propose a new thermo-hyperelastic constitutive model from such a generalized thermodynamics approach with the implementation of the spacetime Lie derivative. The resulting model is then illustrated for different mechanical or thermal loadings with numerical simulations. [ABSTRACT FROM AUTHOR]

The problem of attitude stabilization of a rigid body exposed to a nonstationary perturbing torque is investigated. The control torque consists of a restoring component and a dissipative one. Linear and nonlinear variants of restoring and perturbing torques are analyzed. Conditions of the asymptotic stability of the programmed orientation of the body are found with the use of the Lyapunov direct method and the averaging technique. The results of computer modeling, illustrating the conclusions obtained analytically, are presented. [ABSTRACT FROM AUTHOR]