Time-dependent Loading Research Articles

Nonlocal strain gradient-based meshless collocation model for nonlinear dynamics of time-dependent actuated beam-type energy harvesters at nanoscale

There is a diverse and well-constructed application of energy harvesting systems due to their innovate technology to provide the necessary power for low-energy electronics. In this regard, the prime objective of the current study is to analyze the size-dependent nonlinear dynamic performance of piezoelectric beam-type energy harvesters at nanoscale subjected to a time-dependent mechanical uniform load. A laminated structure containing an agglomerated nanocomposite core integrated with top and bottom piezoelectric surface layers is considered for the nanoscale bridge-type energy harvesters. To take the size dependency into account, the nonlocal strain gradient continuum elasticity is formulated based upon a quasi-3D beam theory incorporating the both features of size effects. Thereafter, the size-dependent nonlinear problem is then solved numerically relevant to simply supported and clamped end conditions via employing the meshless collocation technique. Accordingly, the numerical solving procedure is established without any background meshes as well as eliminating the integration and singularity by using proper multiquadric radial basis functions.

An investigation into the nonlinear rheological behavior of modified asphalt binders using large amplitude oscillatory shear rheology

ABSTRACT Asphalt binders have been studied extensively with respect to their linear viscoelastic properties. From these properties, performance metrics have been derived and used for specification purposes. However, these materials are used in asphalt concrete pavements where they may experience time-dependent loads in the nonlinear regime. In the past, the vast majority of asphalt binders exhibited strong correlations between their linear and nonlinear properties and so despite this mismatch in characterization and the actual use phase domains, a system based on linear properties could be reliably deployed. More recently though, novel binders and additives have been introduced with differing relationships between linear and nonlinear behaviors. As such there is a need to characterize the asphalt binder response under large strains and use specifications that more explicitly account for the binder nonlinearity. Here, an attempt has been made to characterize the nonlinear rheological properties of asphalt binder using large amplitude oscillatory shear. The response of a single terminal blend, crumb rubber modified binder under large strains is analyzed using Lissajous-Bowditch plots while the contribution of higher harmonics is evaluated using Fourier-transform rheology. Finally, the elastic and viscous contributions are obtained using stress decomposition to an orthogonal set of Chebyshev polynomials. It is found that the relative nonlinearity increases with increasing strain and frequency under the tested conditions. The asphalt binder evaluated in this study predominantly exhibits shear thinning and either strain stiffening or softening behavior depending upon the test conditions. The applicability of time-temperature superposition in the nonlinear regime for asphalt binders is also evaluated.

Experimental study on dynamic mechanical properties of projectile 155mm ERFB BT material

Artillery projectile 155mm high explosive (HE) extended range full bore boat tail (ERFB BT) and its components experience a high pressure loading of the propellant during gun launch. Mechanical properties of an engineering material are measured using quasi-static tensile test at room temperature. The materials of the projectile and its components are expected to survive time dependent propellant pressure loading inside the gun, which lasts for few microseconds. To investigate dynamic mechanical properties of the projectile and its components at medium strain rates and elevated temperature, the experimental analysis is undertaken. This research paper aims to examine the effect of medium strain rates and elevated temperatures on flow properties of the materials used in the projectile. The uniaxial tensile tests at the medium strain rates between 0.01 s-1 to 1s-1 and at elevated temperatures ranging between 150°C to 500°C are performed separately. The Considѐre criterion was applied to evaluate strain hardening exponent of the materials. Values of strain hardening exponents of shell body and boat tail materials are less than that of driving band material. Strain rate sensitivity of the materials is observed to be very low, thus indicating a good resistance to plastic deformation. The yield strength and true yield strength of the materials fall with increase in temperature.
 

Meshless generalized finite difference method for two- and three-dimensional transient elastodynamic analysis

In this paper, a meshless collocation method is introduced for two-dimensional (2D) and three-dimensional (3D) transient elastodynamic problems by applying the generalized finite difference method (GFDM) in conjunction with the Houbolt scheme. Coupled equilibrium equations with a time-dependent loading are transformed into the static equations at time nodes by adopting the Houbolt method. After then, the solution of the static equations is achieved with the GFDM with second-order and fourth-order expansions. Several numerical examples involving complicated geometries and different initial and boundary conditions are simulated to validate the performance of the present approach.

Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading

Additive manufacturing has been recognized as an industrial technological revolution for manufacturing, which allows fabrication of materials with complex three-dimensional (3D) structures directly from computer-aided design models. Using two or more constituent materials with different physical and mechanical properties, it becomes possible to construct interpenetrating phase composites (IPCs) with 3D interconnected structures to provide superior mechanical properties as compared to the conventional reinforced composites with discrete particles or fibers. The mechanical properties of IPCs, especially response to dynamic loading, highly depend on their 3D structures. In general, for each specified structural design, it could take hours or days to perform either finite element analysis (FEA) or experiments to test the mechanical response of IPCs to a given dynamic load. To accelerate the physics-based prediction of mechanical properties of IPCs for various structural designs, we employ a deep neural operator (DNO) to learn the transient response of IPCs under dynamic loading as surrogate of physics-based FEA models. We consider a 3D IPC beam formed by two metals with a ratio of Young’s modulus of 2.7, wherein random blocks of constituent materials are used to demonstrate the generality and robustness of the DNO model. To obtain FEA results of IPC properties, 5000 random time-dependent strain loads generated by a Gaussian process kennel are applied to the 3D IPC beam, and the reaction forces and stress fields inside the IPC beam under various loading are collected. Subsequently, the DNO model is trained using an incremental learning method with sequence-to-sequence training implemented in JAX, leading to a 100X speedup compared to widely used vanilla deep operator network models. After an offline training, the DNO model can act as surrogate of physics-based FEA to predict the transient mechanical response in terms of reaction force and stress distribution of the IPCs to various strain loads in one second at an accuracy of 98%. Also, the learned operator is able to provide extended prediction of the IPC beam subject to longer random strain loads at a reasonably well accuracy. Such superfast and accurate prediction of mechanical properties of IPCs could significantly accelerate the IPC structural design and related composite designs for desired mechanical properties.

Optimal Control of a Rate-Independent System Constrained to Parametrized Balanced Viscosity Solutions

We analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one. The optimal control problem uses the external load as control variable and is constrained to normalized parametrized balanced viscosity solutions (BV solutions) of the rate-independent system. Solutions of this type appear as vanishing viscosity limits of viscously regularized versions of the original rate-independent system. Since BV solutions in general are not unique, as a main ingredient for the existence of optimal solutions we prove the compactness of solution sets for BV solutions.

Consolidation by Vertical Drains Considering the Rheological Characteristics of Soil under Depth and Time-Dependent Loading

Vertical drains have been widely used in soil improvement projects to accelerate consolidation and improve the strength of soft soil. Previous consolidation models are mainly based on instantaneous loading, which cannot reflect the actual time-variable loading condition. This paper presents a set of analytical solutions for consolidation with vertical drains under depth and time-dependent loading, involving one-step loading, multi-step loading, and cyclic loading. A four-element model, which is a combination of the Merchant model and Maxwell model, is introduced to consider the rheological characteristics of the soil. By simulating the results of a consolidation test, it is found that the four-element model is more accurate than the Merchant model in predicting the changes in pore pressure and settlement during the clay consolidation process. Based on the solutions obtained, several factors affecting consolidation behavior are investigated. It has been shown that the rheological behavior becomes more and more obvious at the later stage of consolidation with the decrease both in the modulus of the spring in the Kelvin body and the viscosity coefficient of the independent dashpot. With the increase in the viscosity coefficient of the dashpot in the Kelvin body, the rate of consolidation becomes faster at an initial stage but slower at a later stage. For cyclic loading, the consolidation degree in each cycle reaches a maximum at the end of unloading and reaches a minimum at the beginning of the loading.

Cover Image, Volume 47, Issue 5

The cover image is based on the Research Article A novel coupled thermo-mechanical solution for layered isotropic media under various time-dependent loadings by Yong Zhi Zhao and Zhi Yong Ai https://doi.org/10.1002/nag.3494.

The Temperature Field Effect on Dynamic Stability Response of Three-layered Annular Plates for Different Ratios of Imperfection

Abstract The paper presents the temperature field effect on the dynamic stability problem of plates with imperfection. The main objective is to conduct numerical investigations which show the relations between the imperfection ratio and plate dynamic response in a thermal environment. The plate is composed of three layers: thin facings and a thicker core. The plate can be loaded mechanically and thermally or only thermally. The facings are mechanically compressed with the forces acting in a plane. The temperature field model is defined by the temperature difference, which occurs between the plate edges. Two plate models are examined as follows: built using the approximation methods – orthogonalization and finite differences – and composed of finite elements. The analytical and numerical solution procedure is the main one, which is the proposal to perform the problem analysis. The plate reaction is described by the obtained values of the critical temperature differences for plates loaded only thermally and by the critical mechanical loads and the corresponding temperature differences for plates loaded mechanically and subjected to the uncoupled temperature field. The effect of the plate imperfection ratio under time-dependent loads is shown by numerous observations and results, which are shown graphically. The importance of the imperfection ratio on the plate's dynamic stability response in complex loading conditions is studied.

Closed-form consolidation solutions for known loading functions

In engineering practice, loading varies with time. However, the classical one-dimensional theory of consolidation assumes the stress increase is instantaneously applied. Many approaches to the problem of time-dependent loading have been proposed over the years, from approximate methods to full developments of differential equations. The paper presents a simple method for finding a closed-form consolidation solution for time-dependent loading without the need for differential equations. Two sets of general equations were derived for both excess pore pressure and average degree of consolidation. Equations were solved for linear, parabolic, sinusoidal, and exponential load functions. Stepped and cyclic loads were also addressed and a numerical solution was developed to verify the obtained result. The method proved to be easy to apply and provides solutions with great simplicity. A case study of non-instantaneous loading on soft clay was also analyzed, and settlement prediction showed good results when compared to readings of the settlement plates.

Theoretical analysis for thermal consolidation of marine sediments with depth variability subjected to time-dependent loading and heating

Because the spatial distribution of energy is restricted, many energies geotechnics would build on marine sediments and the resulting thermal consolidation would pose an inevitable threat to the safety and stability of the project. In this study, a new governing equation for thermal consolidation of saturated marine sediments is proposed, by considering the depth variability of the marine sediment layer and the time-dependent external loading and temperature. The corresponding one-dimensional (1D) analytical solution for thermal consolidation of saturated marine sediments is derived. The average degree of consolidation (Ua) and the normalized excess pore water pressure (u/u0) in the saturated marine sediment layer at different depths and time durations are calculated and compared with the typical loading case. The results show that the loading rate of the external force only affects the amplitude of the excess pore water pressure u and does not affect the proportion of u with depth; the depth variability of bulk modulus has a greater effect on the distribution of Ua relative to the depth variability of permeability; the depth variability of permeability has a greater effect on the distribution of u/u0 with depth relative to the depth variability of bulk modulus when Ua = 50%; the assumption of instant thermal loading will lead to an over-assessment of Ua and u/u0. This study provides useful insights for energy geotechnical engineering design and practice.

The novel PINN/gPINN-based deep learning schemes for non-Fickian coupled diffusion-elastic wave propagation analysis

This paper presents a cutting-edge approach inspired by the physics-informed neural network (PINN) to solve the coupled non-Fickian diffusion-elasticity system. This is the first time that the PINN framework has been applied to non-Fick diffusion-elasticity in order to investigate the transient behavior of the concentration and displacement fields. This problem pertains to a strip subjected to a time-dependent shock loading. In light of recent developments in gradient-enhanced PINN (gPINN), there is now considerable concern regarding its applicability to systems of coupled partial differential equations (PDEs). As of yet, this methodology has only been applied to a single ordinary differential equation (ODE) or a single PDE. gPINN's performance is also examined for coupled PDEs in the current problem. Moreover, some analyses are performed to analyze the impact of parameter selection on the outputs. Successful implementations of the PINN approach without the need for mesh generation or the limitations of earlier numerical approaches confirm its capabilities in solving complex systems of coupled PDEs.

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads.

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical systems where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.

Effect of in-plane compression on the non-harmonic resonance of moderately thick time-dependent plates

This study investigates the nonlinear p-delta analysis and introduces a viscoelastic plate non-harmonic resonance in which the critical displacement will be several times more than the displacement at time zero. An innovative closed-form solution of Mindlin viscoelastic plate, under a dynamic out-of-plane exponential load decreasing over time and a constant in-plane compressive load is presented. The displacement vector of the Mindlin viscoelastic plate is explicitly formulated in space and time domains. Also, the critical time in which the non-harmonic resonance occurs is calculated. The stress–strain relationship of the viscoelastic material is defined according to the Boltzmann integral law. The displacement field is expressed by the product of a determinate geometrical function and a time function with two indeterminate coefficients. The time function coefficients are calculated with the help of the Laplace transform, satisfying the equilibrium equation at two asymptotic times. Abaqus software is used to confirm the results. The numerical results consider the effect of time-dependent material parameters, loads, boundary conditions, thickness-to-side ratios, and aspect ratios on the maximum displacements of moderately thick time-dependent plates.

One-dimensional large strain nonlinear thaw consolidation model for saturated frozen soil

Based on the piece-linear finite difference approach, a one-dimensional large strain thaw consolidation model, TCS1, for saturated frozen soil was established. The model couples the heat transfer considering phase change of pore ice with consolidation deformation, and accounts for large strain, soil self-weight, unfrozen water, variable hydraulic conductivity and compressibility, flexible boundary conditions and time-dependent loading during the process of thaw consolidation. The FORTRAN is used to implement computation of the model. TCS1 was verified by the existing numerical solutions and laboratory tests. The results were in good agreement with the large strain numerical solutions and tests results. Computational examples were conducted for further study of the influence of strain value, loading types and periodic temperature boundaries on the thaw consolidation of frozen soil.

Analysis of Combined Vertical and Radial Consolidation of Soil under Time-Dependent Loading

Fine-grained compressible soils are usually associated with strength challenges in the course of carrying structures, roadways, embankments, and other civil engineering facilities. In addition, due to their low permeabilities, compressible soils take an awfully long duration to achieve optimal consolidation, with its attendant negative effects on the facilities supported by the soils. Engineering practitioners and researchers have established the efficacy of vertical drains for accelerating the consolidation process of such soils through the shortening of horizontal flow distances, thereby stabilizing them and improving their load-bearing capacities. Application of the pre-loading surcharge provides additional drive for rapid consolidation. The case of soils carrying time-dependent loading is quite topical because it reflects reality most appropriately. However, a rigorous analysis of soils undergoing vertical and radial consolidation with a constant or time-varying surcharge is conspicuously lacking in the literature because most authors of publications in this subject area have largely based their solution procedure on the assumed decoupling of the vertical and radial flows by treating their associated pore pressures as separate. This assumption, notwithstanding the simplification it introduces into the mathematics of the problem, is not supported by physics. Therefore, the theory presented herein aims at addressing that gap in the literature. Throughout this analysis, the coupled (vertical and radial) flow, driven by a common pore water pressure, is handled as a single process. Successive applications of the integral transformations of Laplace and finite Hankel have been used to obtain an explicit expression for the image of the pore water pressure as a function of the transformation parameters. This is followed by successive inversions of the integral transforms, leading to a closed-form solution in the sense of a generalized Fourier series. The classical definition of the average degree of consolidation is easily applied in this case, unlike other methods in the literature that rely on the principle of superposition, whose applicability in this circumstance remains questionable. The validity of the present analysis has been established through logical checks and comparison with previous results in the literature. This theory has been proven to be applicable to cases of constant as well as time-varying surcharges. Doi: 10.28991/CEJ-2023-09-01-014 Full Text: PDF

High-fidelity micromechanical modeling of the effects of defects on damage and creep behavior in single tow ceramic matrix composite

Despite the superior properties of ceramic matrix composites (CMCs), their fabrication process generates inevitable defects with high density that significantly influence material integrity and residual useful life. Recent efforts have focused on CMC property prediction and investigation of their different inelastic mechanisms, but very limited work exists on understanding the influence of defects on inelastic responses of CMCs. Here, we introduce a three-dimensional micromechanics computational framework that includes experimentally informed material microstructure and architectural variabilities to investigate CMC response in the presence of manufacturing-induced defects. A developed microstructure generation algorithm is used to generate the representative volume elements in the micromechanics models from complex material morphology information obtained from extensive characterization studies of C/SiNC and SiC/SiNC CMCs. A fracture mechanics-informed matrix damage model is reformulated, in which the model considers the growth of porosity and microcracks in the as-received material. A progressive fiber damage model as well as Orthotropic viscoplasticity creep formulation are also utilized for the study. This methodology is implemented within the micromechanics framework to investigate the complex temperature- and time-dependent load transfer and damage mechanisms of CMCs under operation loading conditions. The developed framework explores the influence of as-received defects on the damage and creep behavior in service conditions. It also provides new insights into the effect of size, shape, distribution, and location of these defects on material response. The framework is then calibrated with unidirectional CMC minicomposite results available in the literature.

Plastic Deformation of High Explosive Projectile 155 mm during Gun Launch Conditions using Finite Element Method

The structural integrity of artillery projectile 155mm high explosive Extended Range Full Bore (ERFB)boat tail designed for 155mm howitzer guns of 39, 45 and 52 calibre plays a key role inside the gun barrel. Thisprojectile comprises a shell body, a driving band, a boat tail, nubs, an explosive, and a fuze. Plastic deformationof the projectile and stripping of driving band are not permitted, when projectile is fired. An investigational study is necessitated to check the plastic deformation of the projectile subjected to maximum propellant charge pressure.The aim of this study is to check the effective plastic deformation and affirm the structural integrity. A 3-D explicit dynamic structural analysis of 155 mm HE ERFB BT during gun launch conditions is carried out by finite element method using FE code ABAQUS/Explicit. To understand the non-linear mechanical behavior of the projectile, the true stress-strain curves of the materials are considered. The plastic behavior of the projectile subjected to the time-dependent loading is studied by using the von Mises plasticity model. The results reveal that the shell body and boat tail have no plastic deformation and the most stressed component is the driving band. The investigation has affirmed the structural integrity of the projectile during gun launch conditions.

An Analytical Solution for 2D Plane Strain Consolidation in Unsaturated Soils with Lateral and Vertical Semipermeable Drainage Boundaries under Time-Dependent Loading

This paper has proposed a closed-form solution for two-dimensional (2D) plane strain consolidation in unsaturated soils with lateral and vertical semipermeable drainage boundaries under time-dependent loading. By using the eigenfunction expansion technique, the governing equations are expanded into coupled ordinary differential equations, and the final solution of pore pressures is obtained by the integral transform method. The degraded proposed solution is then verified with the existing solution. The results show full agreement with the solutions, which indicates the proposed solution and program are completely correct. Meanwhile, the comparison between the analytical solutions and the finite-element simulations also demonstrates the correctness of the proposed solution. Subsequently, the effect of semipermeable parameters and loading parameters on the consolidation behavior has been investigated through the obtained analytical solution. And the distribution of consolidation profiles along two different directions has also been studied. It can be concluded that time-dependent loading changes the dissipation process obviously compared with constant loading.

Internal resonance and bending analysis of thick visco-hyper-elastic arches

In this study, a comprehensive analysis of visco-hyper-elastic thick soft arches under an external time-independent as well as time-dependent loads is presented from bending and internal resonance phenomenon perspectives. Axial, transverse and rotation motions are considered for modelling the thick and soft arch in the framework of the Mooney–Rivlin and Kelvin–Voigt visco-hyper-elastic schemes and third-order shear deformable models. The arch is assumed to be incompressible and is modelled using von Kármán geometric nonlinearity in the strain–displacement relationship. Using a virtual work method, the bending equations are derived. For the vibration analysis, three, coupled, highly nonlinear equations of motions are obtained using force-moment balance method. The Newton–Raphson method together with the dynamic equilibrium technique is used for the bending and vibration analyses. A detailed study on the influence of having visco-hyper-elasticity and arch curvature in the frequency response of the system is given in detail, and the bending deformation due to the applied static load is presented. The influence of having thick, soft arches with different slenderness ratios is shown, and the forced vibration response is discussed. Moreover, internal resonance in the system is studied showing that the curvature term in the structure can lead to three-to-one internal resonances, showing a rich nonlinear frequency response. The results of this study are a step forward in studying the visco-hyper-elastic behaviour of biological structures and soft tissues.Graphic abstract