Small Deformation Conditions Research Articles

Deciphering non-elastic deformation in amorphous alloy: Simultaneous aging-induced ordering and rejuvenation-induced disordering

The mechanical and physical properties of amorphous alloys depend on their time, temperature, and stress history. Due to their out-of-thermodynamic-equilibrium nature, describing the nonelastic deformation while considering the evolution of the structural state poses a significant challenge. We address this challenge by incorporating a parameter for structural state changes into a conventional deformation theory. This allows us to account for aging-induced ordering and deformation-induced disordering in the description of the mechanical deformation. In the apparent elastic regime (small strain), aging dominates while disorder caused by deformation can be disregarded. In this context, we have also made modifications to the widely used stretched exponential function, incorporating in-situ aging during deformation. This modification successfully describes the stress relaxation behavior under small deformation conditions and provides insights into parameter evolution in this process. Under large deformation conditions, both aging and deformation induced rejuvenation effects on the structural state must be considered simultaneously. By analyzing the evolution of defect concentration during this process, we describe relevant experimental results within the framework of the free volume theory, effectively separating the contributions of aging and rejuvenation to the structural state during the deformation process.

Correlation between parameters in the microstructural vector theory and Hill's plastic potential

The dissipation inequality provides a useful method for specifying constitutive equations of plastic deformation. There are two main ways to use the dissipation inequality to determine the plastic deformation path: by utilizing a plastic potential with the normality rule, or by not utilizing the plastic potential to determine the plastic flow according to the elastic distortion of the material coordinate axis (microstructural vectors). While both methods satisfy the inequality condition and predict experimental results well, they have been developed separately without discussion on relationship. This study presents a physics-based mathematical discussion on the relative dependence between the two methods of determining plastic flow and their point of connection, using Hill's quadratic plastic potential. For this, the conversion of the distortional length and angle changes in microstructural vectors to deviatoric strain tensor under small elastic deformation conditions is mathematically demonstrated. Using these equations, the rate of inelastic deformation derived from microstructural vectors exhibited a similar form to that derived from Hill's quadratic potential. Moreover, the model parameters of the microstructural vectors can be calibrated using the Hill's function. The plastic flow derived from the microstructural vectors and Hill's function exhibited a remarkably similar trend under the assumption of small elastic deformation, although not identical. The newly defined relationships were implemented numerically and validated through simulations. The parameters of the microstructural vector theory derived from Hill's plastic potential can be utilized in materials science and engineering.

Numerical framework for anisotropic flexible piezoelectrics with large deformation

Flexible piezoelectric materials with high stretchability have been realized in industrialization production. Among them, piezoelectric fiber composites made of elastomers and piezoelectric polymers have gained widespread attentions in smart applications. In general, piezoelectric fiber composites can be considered as anisotropic materials. However, most existing piezoelectric constitutive models, especially those integrated into commercial software, only account for small deformation conditions, which are not suitable for anisotropic flexible piezoelectrics. In the present work, a novel model for anisotropic flexible piezoelectric material is established based on the anisotropic Neo-Hookean material model and electromechanical theory. The finite element framework is implemented in the commercial finite element software ABAQUS via a user element subroutine, with a monolithic algorithm procedure employed to solve the nonlinear governing equations. To validate the accuracy of finite element implementation, analytical solutions for equibiaxial stretching of transversely isotropic piezoelectric have been compared with simulated results. Furthermore, the influences of anisotropy level on electromechanical response are also discussed. Subsequently, numerical simulations of bending actuators and sensors further demonstrate the robustness of the developed elements. The obtained results show that the anisotropy direction and level have both favorable and unfavorable influences on structure performances, which could provide a reference for the design of anisotropic flexible piezoelectric structures.

Correlation between Mechanical and Morphological Properties of Polyphenol-Laden Xanthan Gum/Poly(vinyl alcohol) Composite Cryogels

This study aimed to evaluate the effect of the synthesis parameters and the incorporation of natural polyphenolic extract within hydrogel networks on the mechanical and morphological properties of physically cross-linked xanthan gum/poly(vinyl alcohol) (XG/PVA) composite hydrogels prepared by multiple cryo-structuration steps. In this context, the toughness, compressive strength, and viscoelasticity of polyphenol-loaded XG/PVA composite hydrogels in comparison with those of the neat polymer networks were investigated by uniaxial compression tests and steady and oscillatory measurements under small deformation conditions. The swelling behavior, the contact angle values, and the morphological features revealed by SEM and AFM analyses were well correlated with the uniaxial compression and rheological results. The compressive tests revealed an enhancement of the network rigidity by increasing the number of cryogenic cycles. On the other hand, tough and flexible polyphenol-loaded composite films were obtained for a weight ratio between XG and PVA of 1:1 and 10 v/v% polyphenol. The gel behavior was confirmed for all composite hydrogels, as the elastic modulus (G') was significantly greater than the viscous modulus (G″) for the entire frequency range.

On deformation and fracture of PBX simulant employing modified three-body potential peridynamics model with deformation-based failure criteria

The modified three-body potential peridynamics (PD) model is used to study the macroscopic mechanical responses of polymer bonded explosive (PBX) mock materials. Combined with PD functions, under small deformation conditions, bond shear form of the PD model is derived from the micro-potential incorporating modified three-body interaction potential, giving some attention to the applicable condition for its two expression forms, i.e., general form and bond shear form. Subsequently, an improved mode Ⅱ failure criterion considering collective shear deformation of family members is proposed to enhance the deformation-based failure criteria adopted in the present study. A series of PBX simulants associated with elastic deformation and brittle fracture behaviors are carried out by the proposed numerical method. And the numerical results are verified by experimental and other numerical ones published previously, which show that the proposed numerical method is suitable for modeling PBX mock materials.

Out-of-plane load-bearing and mechanical energy absorption properties of flexible density-graded TPU honeycombs

Honeycomb structures are widely used in applications that require excellent strain energy mitigation at low structural weights. The load-bearing and energy absorption capacity of honeycomb structures strongly depend on their cell wall thickness to edge ratios. This work studies the mechanical response and strain energy absorption characteristics of hexagonal honeycomb structures with various cell wall thicknesses in response to out-of-plane loading conditions. Honeycomb structures with various nominal densities are first additively manufactured from flexible thermoplastic polyurethane (TPU). A comprehensive experimental study characterized the mechanical strength, energy absorption performance, and the strain recoverability of the structures. Density-graded structures are then fabricated by stacking multiple density layers of the honeycombs. Mechanical characterization of the density-graded structures points to their superior load-bearing response at large deformation conditions. From a strain energy absorption perspective, density graded structures are shown to outperform their uniform density counterparts at small deformation conditions. The results obtained in this work highlight the significance of density gradation as a practical means for the development of honeycomb structures with highly tailorable, application-specific mechanical properties.

The conditions for plane sections remaining plane

The Euler–Bernoulli hypothesis that plane sections before bending remain plane after bending is a cornerstone of the sciences, especially in mechanics and engineering, and an enabler of the Second Industrial Revolution. Although it is widely applied in science and engineering, especially in structural engineering, its general validity has never been established theoretically, except in some special cases such as linear elastic and small deformation conditions. Its applicability to a particular problem requires extensive experimental evaluation or practical observation. Through a thought experiment commonly used in the derivation of physics theory, this paper rigorously deduces the theorem that gives the conditions for the Euler–Bernoulli hypothesis. The new theorem is general and applies to flexural members composed of any number of different materials, regardless of the properties of the materials, magnitude of deformation, and elastic or plastic strain conditions. This new theorem paves the way for future secure applications of this hypothesis without the need for experimental verification before use.

Modeling vorticity stretching of viscoelastic droplets during shearing flow

In the present work, we focus on the large deformation of a viscoelastic droplet suspended in a Newtonian matrix. We use the constrained volume model as a basic theoretical framework for the description of droplet shape evolution, and we account for the viscoelasticity of the droplet phase using the single-mode Giesekus model. The velocity gradient term describing flow inside the droplet is modified by the viscoelastic stresses, and the resulting model—we herein call the non-Newtonian constrained volume model—is calibrated by matching its predictions to those of the model of Yu et al. [J. Rheol. 48, 417–438 (2004)] at small deformation and slow flow conditions. The non-Newtonian constrained volume model is then examined under conditions of large deformation and/or fast flow, and its predictions are compared against experimental results. The new model shows the growth of the droplet's width in the vorticity direction at conditions of large capillary number, moderate-to-large viscosity ratio, and small elastocapillary number.

Parallel Efficiency Analysis of Large Increment Method Based on OpenMP

Large Increment Method (LIM) is a novel force-based method based on the generalized inverse matrix theory for solving material nonlinear problems in small deformation and small displacement conditions. For the spatial parallel computation, LIM can compute the constitutive equations of each element in parallel. By analyzing the parallel-calculating characteristics of LIM, the OpenMP is used for the parallel computation in spatial domain. Through the parallelism analysis of the spatial and time domain for LIM, it shows that LIM has an excellent parallel efficiency in space parallel computation.

Numerical simulation of droplet deformation in low frequency half-sinusoidal electric field

For investigating the influence of various parameters on the droplet deformation under the AC electric field condition, a simulation model for the droplet deformation in immiscible two fluids was established based on the phase field method. The distribution of flow field and electric field force are analyzed by simulation; the effects of electric field frequency, electric field intensity, droplet diameter, surface tension and continuous phase viscosity on the droplet deformation are simulated under the half-sinusoidal wave electric field condition. The simulation is performed in the low frequency half-sinusoidal waveform electric field. The simulation results show that the frequency of droplet oscillation is the same as that of the electric field. With the increase of electric field intensity and droplet diameter, the droplet deformation increases. However, the increase presents exponentially and linearly, respectively. Besides, the droplet deformation decreases exponentially with the surface tension increasing, and linearly with the continuous phase viscosity increasing. Under the condition of small deformation, there exists a linear relationship between the droplet maximum deformation and the Weber Number. More important, the influence of various factors on the deformation from strong to weak is electric field intensity, droplet diameter, surface tension, electric field frequency, continuous phase viscosity. And there is interaction between these factors. The simulation results provide theory evidence for the further research on electrostatic coalescence mechanism and the development of effective and compact electrostatic coalescence equipment.

Analysis of crystallographic orientation and morphology of microstructure during hot working for an alpha/beta titanium alloy

This work focuses on analysis of microstructure morphology and crystallographic orientation for Ti-17 alloy during hot working. The results show that alpha phase and beta phase influence each other and there is a coordinate deformation between them. The non-uniform deformation is observed under small deformation conditions. The observing area can be divided into small deformation zone (area L) and large deformation zone (area H). Both alpha and beta phases remain the initial morphology, and they have better capability of coordinate deformation in area L, while coordinate capability is weak in area H in which alpha phase is globularized. Correspondingly, the Burgers orientation relations are well preserved in area L, but the orientation relations are more or less destroyed in area H. Dynamic recovery is the main mechanism of beta phase evolution when height reduction is lower. By contrast, the continuous dynamic recrystallization (CDRX) of beta phase gradually dominates the deformation pattern as the deformation increases. An uniformly globularized alpha structure is obtained under large deformation condition. The unsynchronized rotation of alpha phase around <11−20> pole occurs during deformation, which leads to the uniform crystal structure inside the same alpha lamellae. This process is an important step of globularization of the lamellar structure.

Size-dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory

This paper studies the bending, buckling and free vibration analyses of functionally graded (FG) sandwich microbeams using the third-order beam theory. The modified strain gradient theory (MSGT) with three material length scale parameters (MLSPs) is used to capture the size effect. The Mori-Tanaka homogenization scheme is employed to model the material distributions through the thickness. Finite element model is formulated to solve the problems. Verification studies for epoxy and FG microbeams are carried out to validate of the present model. Comparisons of the results of three different models such as MSGT, the modified couple stress theory (MCST) and classical continuum theory (CCT) are presented. Effects of small size, gradient index, shear deformation and boundary conditions on the structural behaviours of microbeams are investigated. Some new results of FG sandwich microbeams for both models (MCST and MSGT) are presented for the first time and can be used as benchmark in future studies.

Stability Study on Steel Structural Columns with Initial Blast Damage under High Temperatures

Blast may bring light-weight steel columns with initial damages, resulting in lowering its critical fire-resistance temperature whose reduced amplitude is relevant to the form and degree of the damages. Finite element analysis software ANSYS was used in the paper to analyze the issue of the fire-resistance temperature of the column with the blast damages, and the coupling method for heat and structure was applied during the simulation. The emphasis was laid on parametric factors of axial compression ratio, the form and the degree of the initial damages, as well as the confined condition at the ends of the columns. The numerical results showed that the fire-resistance temperature will lower as increasing of the axial compression ratio, the form and the degree of the initial damages and it will be also affected by the restraint conditions at the ends of the columns. The critical stress formula with initial bending damage under elevated temperature was set up under flexural small deformation condition, then the stability coefficient was determined and the method for evaluating the limit temperature of the column was put forward. The theoretical result was also compared with that of the finite element method (FEM). The results both showed that the stability capacity for the damaged columns was dramatically reduced as increasing the temperature and the initial damage level.

Rheological behaviour in the interaction of lecithin and guar gum for oil-in-water emulsions

The effects of guar gum and lecithin concentrations (1, 0.75, and 0.5%wt) on the stability of oil in water emulsion were investigated. All emulsions can be stabilized at the studied concentrations of stabilizers. The samples tested by steady shear flow and dynamic viscoelasticity tests were carried out to characterize the rheological behaviour of emulsions as influenced by concentration. Emulsions presented a non-Newtonian behaviour type with shear thinning and flow curves that could be described by the Carreau model. The dynamic viscoelastic properties characterized by an oscil­latory frequency sweep under small deformation conditions showed fluid-like viscoelastic behaviour. The interaction of the stabilizers in the mixture with each other at the interface appears to play a decisive role for the stabilization of emulsions.

Lateral vibration analysis of pre-bent pendulum bottom hole assembly used in air drilling

In the air drilling process, the pre-bent pendulum bottom hole assembly (PBP-BHA) has excellent performance in controlling the well deviation and improving the wellbore quality, but the mechanism that is closely related to the dynamics of the PBP-BHA has not been ascertained. In this paper, an effective technique combining the weighted residuals method with the finite element method is presented to study the PBP-BHA lateral vibration. First, a three-dimensional nonlinear static model of pre-bent BHA is established under small deformation condition and solved by the weighted residuals method and optimization method, so as to define the tangent point according to the deformation characteristics of the PBP-BHA. This tangent point determines the end of the effective PBP-BHA length that starts from the drill bit. Subsequently, the finite element model of PBP-BHA is established to solve the lateral natural frequencies and mode shapes of the PBP-BHA. After considering the borehole wall constraint, the modal superposition technique is used to obtain the steady dynamic responses of the PBP-BHA. Meanwhile, the dynamic performance of the PBP-BHA used in the actual air drilling process is calculated to obtain its critical speeds and working status chart. The critical speeds of the PBP-BHA are 80 r/min and 190 r/min, which are far away from the surface rotary speed in the actual drilling site. Through comparing with the dynamic characteristics of regular BHA with the same structural parameters, it is discovered that the bend angle in the PBP-BHA plays a crucial role in improving the dynamic performance of the PBP-BHA. Moreover, the technique presented in this study can be used to make a reasonable design of BHA configuration and optimize drilling parameters.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution. The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction. Thus, it is more realistic than the Winkler model, which only represents compressive soil resistance. However, the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation; hence, the beam under inclined loads cannot be considered in the model. In this study, a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model, which tends to disregard the tangential interaction between the beam and the foundation. The horizontal spring reaction is assumed to be proportional to the relative tangential displacement. The governing equation can be deduced by theory of elasticity and Newton's laws, combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition. Double Fourier transformation is used to simplify the geometric equation into an algebraic equation, thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam. Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution. The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS. Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam. Results are realistic and can be used as reference for future engineering designs.

Radial Basis Functional Model of Multi-Point Dieless Forming Process for Springback Reduction and Compensation

Springback in multi-point dieless forming (MDF) is a common problem because of the small deformation and blank holder free boundary condition. Numerical simulations are widely used in sheet metal forming to predict the springback. However, the computational time in using the numerical tools is time costly to find the optimal process parameters value. This study proposes radial basis function (RBF) to replace the numerical simulation model by using statistical analyses that are based on a design of experiment (DOE). Punch holding time, blank thickness, and curvature radius are chosen as effective process parameters for determining the springback. The Latin hypercube DOE method facilitates statistical analyses and the extraction of a prediction model in the experimental process parameter domain. Finite element (FE) simulation model is conducted in the ABAQUS commercial software to generate the springback responses of the training and testing samples. The genetic algorithm is applied to find the optimal value for reducing and compensating the induced springback for the different blank thicknesses using the developed RBF prediction model. Finally, the RBF numerical result is verified by comparing with the FE simulation result of the optimal process parameters and both results show that the springback is almost negligible from the target shape.

Closed-form solution considering the tangential effect under harmonic line load for an infinite Euler–Bernoulli beam on elastic foundation

• Analytical solution for dynamic response of infinite beam on foundation is developed. • The elastic foundation considered the horizontal tangential effect. • Double Fourier transformation is used for deduction and the residue theorem is employed to obtain the solution. • The analytical solution for the beam under inclined dynamic load is presented. The dynamic response of an infinite Euler–Bernoulli beam resting on an elastic foundation, which considers the tangential interaction between the beam and foundation under harmonic line loads, is developed in this study in the form of a closed-form solution. Previous studies have focused on elastic Winkler foundations, wherein the tangential interaction between the bottom of the beam and the foundation is not considered. In this study, a series of separate horizontal springs is diverted to the contact surface between the foundation and beam to simulate the horizontal tangential effect. The horizontal spring reaction is assumed proportional to the relative tangential displacement. As the geometric equation and linear-elastic constitutive equation of beam under the condition of small deformation have been presented based on the basic principle of elasticity mechanics, the analysis model is built and the governing differential equations about normal and tangential deflections of beam are deduced. Double Fourier transformation and the residue theorem are used to derive the closed-form solution to this problem. The proposed solution is then validated by comparing the degraded solution with the known results and comparing the numerical solution with the analytical solution. We also discuss the case in which the load direction is not vertical to the beam. Results can be used as a reference for engineering design.

Revisit to three-dimensional percolation theory: Accurate analysis for highly stretchable conductive composite materials.

A percolation theory based on variation of conductive filler fraction has been widely used to explain the behavior of conductive composite materials under both small and large deformation conditions. However, it typically fails in properly analyzing the materials under the large deformation since the assumption may not be valid in such a case. Therefore, we proposed a new three-dimensional percolation theory by considering three key factors: nonlinear elasticity, precisely measured strain-dependent Poisson’s ratio, and strain-dependent percolation threshold. Digital image correlation (DIC) method was used to determine actual Poisson’s ratios at various strain levels, which were used to accurately estimate variation of conductive filler volume fraction under deformation. We also adopted strain-dependent percolation threshold caused by the filler re-location with deformation. When three key factors were considered, electrical performance change was accurately analyzed for composite materials with both isotropic and anisotropic mechanical properties.

Mechanical metamaterial with negative Poisson&amp;rsquo;s ratio based on circular honeycomb core

Mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. As a new type of metamaterials with unique mechanical properties and promising prospects, mechanical metamaterials have attracted great attention and become a new hot spot in the field of metamaterials. Mechanical metamaterials with negative Poisson’s ratio can exhibit novel mechanical properties such as excellent resistance capability of bending deformation and indentation. This type of materials have good prospects in many applications such as variant flexible wing skin. In this article, we adopt the design method of mechanical metamaterials to improve the structure of traditional honeycomb core and propose a new type of circular honeycomb core unit to obtain negative Poisson’s ratio. The advantage of circular honeycomb core is that this new structure is more stable than traditional concave hexagon honeycomb core. We established the corresponding mechanical model of this structure and adopted energy method to study the dependencies of structure parameters for its effective elastic modulus. The bending strain energy was taken into consideration while the tension and shear strain energy were ignored because they are very small compared with the bending strain energy. Then the expressions of effective elastic modulus in the directions of X and Y axis can be established in the condition of small deformation. In order to verify the validity of theoretical results, finite-element simulation method was employed to our study and we adopted periodic structure as the finite-element simulation model and aluminium alloy as the base material. The results of theory and the simulation have good agreements, and we found that its effective elastic modulus E x is mainly depending on its height h and thickness t while E y is mainly depending on its radius r and thickness t . And the thickness t may bring about deviation between theory and the simulation when it increases. The Poisson’s ratio of this material was also investigated through finite-element simulation method and different values of structure parameters were selected. Among these structure parameters, when h =35 mm, r ³ 21 mm and h =40 mm, r ³ 24 mm or h =45 mm, r ³ 26 mm, negative Poisson’s ratio can be obtained. The results indicate that the composite structure based on circular honeycomb core units can achieve negative Poisson’s ratio, which can be controlled by structure parameters. The excellent mechanical performance of light-weight and its negative Poisson’s ratio make circular honeycomb core a promising candidate as engineering material. And our study may pave a useful path to mechanical metamaterials with negative Poisson’s ratio.