This work develops a hybrid analytical–numerical framework to investigate the dynamic response of functionally graded nanoplates resting on general viscoelastic foundations within the modified nonlocal strain gradient theory. The formulation simultaneously integrates nonlocal softening and strain-gradient hardening mechanisms, enabling a consistent representation of size-dependent effects at the nanoscale. A four-parameter viscoelastic foundation model is employed to account for both elastic and damping contributions at the Winkler and Pasternak layers. The equations of motion are derived from Hamilton’s principle based on a higher-order plate kinematics. Closed-form Navier solutions are combined with Newmark–β time integration to establish a computationally efficient and accurate solution procedure. The established algorithm is realized in Matlab to conduct systematic parametric investigations. Results reveal complex interactions among foundation stiffness, damping coefficients, material gradation, thickness ratio, and scale parameters. The frequency-response characteristics are evaluated to identify resonance peaks and attenuation zones, providing quantitative insight into vibration amplification mechanisms. The results provide valuable insight into the influence of foundation interaction and size-dependent effects on the dynamic behavior of nano-engineered structures supported by viscoelastic media, serving as a theoretical reference for future investigations and design-oriented studies.
In this work, a nonlinear dynamics of a rotary jointed single-link flexible manipulator system is investigated. The arm is made of a fibre-reinforced composite material. The extended Hamilton's principle is applied to derive the governing differential equations of the system based on classical laminated beam theory. The system equations are discretized by the finite element method, and Newmark’s technique is employed for time integration. Nonlinearity is considered due to the effect of shortening of the beam caused by transverse bending of beam. Shortening effects consideration in the formulation is called the first order approximation coupling (FOAC) model and while neglecting this effects is called the zeroth order approximation (ZOAC) model. The FOAC model provides more accurate predictions of dynamic characteristics of the flexible manipulator than the ZOAC model. The effect of the rotational torques, torque profiles, fibre orientations, material orthotropy and ply thicknesses on the system responses is studied. Response of system based on FOAC model and ZOAC model are compared. Also, the effects of the different torque profiles, fibre orientations, and material orthotropic and ply thicknesses on the system dynamics are observed through numerical experiments. The manipulator is actuated at a single revolute joint whose axis passes through the centre of a rigid hub, the hub rotation being the only rigid-body degree of freedom of the system.
This work employs geometric fractional deflection modeling in tangent space to analyze the bending of spatial fractional beams using the Green’s function method. The fractional model is based on tangent-curve geometry and spatial fractional beam elasticity within Euler-Bernoulli beam theory to formulate the problem. The fractional Green’s function method is employed to solve the problem. Several numerical applications are presented to demonstrate the method’s effectiveness and accuracy. Results show that the curvature behavior of fractional beams varies significantly with the degree of freedom, static indeterminacy, length, and fractional order of derivatives. A novel two-sided derivative interpolation approach has been applied to solve the governing equations for symmetric beams. Moreover, the model accommodates a variety of boundary conditions, and the effect of different types of boundary conditions on beam supports is studied in detail.
Using large-scale, three-dimensional discrete element simulations, we investigate the kinematic properties of granular chute flows of cohesionless grains, together with the evolution of the coordination number and the fraction of sliding contacts. Our results reveal that, under certain conditions, increasing the grain–grain friction coefficient leads to a decrease in the global dissipation of the system. This finding highlights that the overall dissipation is not solely governed by the energy lost during sliding contacts, but also by the probability that such contacts occur, a probability that decreases markedly as the friction coefficient increases. Together, these effects demonstrate the subtle and nontrivial interplay between grain-scale frictional interactions and macroscopic flow behavior in dense and cohesionless granular materials.
The degenerate forced harmonic Duffing oscillator with zero linear stiffness, commonly known as the Ueda oscillator has long been known as a canonical benchmark in nonlinear dynamics and chaos theory. The global dynamics of the Ueda oscillator are investigated through behavioural maps in the forcing amplitude–frequency plane. This methodology not only identifies dangerous and safe parameter combinations with respect to the transmitted acceleration amplitude, but also elucidates how the onset of chaotic dynamics can significantly amplify acceleration levels, offering valuable insights into the complex interplay between chaos and vibration transmission in nonlinear dynamical systems. The results reveal several remarkable phenomena in the structure of the behavioural maps, including: (i) the existence of large, compact regions of chaotic dynamics; (ii) the emergence of sparse (meagre) sets of chaos distributed across broad ranges of forcing frequencies and amplitudes; (iii) the formation of chaotic regions resembling Arnold tongues; and (iv) the presence of distinctive dynamical regimes at small frequency range. This analysis highlights how parameter space basin structures can guide the selection of safe operating regimes for highly nonlinear seismic isolation devices, where low acceleration transmission is critical. The analysis is based on solving the equations of motion by the Adams–Bashforth–Moulton (ABM) predictor-corrector method, enabling numerically stable computations over long time intervals.
In analogy to the famous stress average rule in continuum micromechanics, it has become popular to use a heat flux averaging rule for multiscale thermodynamics: The spatial average of a microscopic heat flux field over a finite microscopic representative volume element (RVE) is set equal to a macroscopic heat flux vector. The latter is associated with a macroscopic infinitesimal volume element dV which is physically equivalent to the RVE. Here we explore the validity range of such a heat flux average rule. Therefore, we introduce microscopic virtual fields dualizing the microscopic heat balance law (i.e., the first law of thermodynamics for stationary iso-deformation conditions). The microscopic virtual fields are then “coarsened” through macroscopic virtual quantities, while requiring equivalence between the microscopic and the macroscopic formulations of the virtual powers expressing heat balance. It turns out that the heat flux average rule holds only in case of vanishing microscopic volume heat sources. Vanishing volume heat sources, together with Fourier’s heat conduction law, imply the RVE to be smaller than the ratio of the first-order to the second-order temperature gradient, which is often referred to as separation-of-scales-condition. Once significant volume heat sources occur, they do not only enter the average law for the macroscopic heat flow, but also necessitate the existence of higher-order macroscopic heat fluxes, which we call hyper-fluxes here. The latter are dual to second-order gradients of the macroscopic virtual field quantities. Associated RVEs do not fulfill the separation-of-scales-conditions, but exhibit a size which is of the order of the ratio of the first-order to the second-order temperature gradient. Hyper-fluxes provide new avenues for modeling the effects of heat sources occurring within the microstructure of a material, on the behavior of structures being built up by such materials. This is illustrated here by two examples which show the difference between concentrated and distributed microscopic heat source terms in terms of the resulting macroscopic hyper-flux quantities. The latter are deemed to be relevant for several practical cases, including wood-based energy sources and timber structures exposed to fire.
Capsule crawling robots offer significant potential for navigating unstructured environments. However, conventional designs based on active anchoring or anisotropic friction generally suffer from complex structures and poor environmental adaptability. Vibro-impact capsule robots eliminate external anchoring mechanisms, but their reliance on high-peak impact forces raises structural fatigue risks and safety concerns in fragile environments. This paper presents a numerical investigation of a novel low-impact capsule robot driven by a bistable dielectric elastomer actuator (DEA). Unlike vibro-impact-driven designs, the proposed robot achieves directional locomotion by exploiting the asymmetric driving force generated during the intra-well oscillations of the bistable DEA. A two-degree-of-freedom electromechanical coupling dynamic model is developed to characterize the nonlinear bistable behaviors and stick–slip locomotion of the system. Extensive numerical simulations are conducted to systematically analyze the effects of key parameters on locomotion performance, including excitation conditions, bistable characteristics, static friction coefficient, and robot mass. The results demonstrate that reliable directional locomotion relies on stable periodic intra-well responses of the DEA. Crucially, increasing the voltage amplitude can improve locomotion velocity within a certain range, while excessive voltage amplitude induces period-doubling bifurcations and chaotic motion, leading to performance degradation. Furthermore, an optimal matching relationship between the nonlinear driving force profile and the static friction threshold is revealed, which minimizes backward slippage and achieves the highest locomotion velocity. This work provides theoretical guidance for the design of low-impact soft capsule robots and is promising for applications requiring delicate contact environments.
An analytical spectral formulation is developed to investigate the influence of surface elasticity on the stress field and image force of a screw dislocation located near a free surface in an isotropic elastic half-space. The analysis is carried out within the framework of the Gurtin–Murdoch surface elasticity theory, where the free surface is modeled as an elastic interface possessing its own constitutive response and intrinsic material length scale. Using a Fourier-transform approach, explicit spectral integral representations are derived for both the reflected stress field and the image force acting on the dislocation. The formulation introduces a wavenumber-dependent reflection coefficient that continuously redistributes the reflected elastic spectrum and replaces the classical discrete image construction by a distributed surface-induced response.The results demonstrate that surface elasticity produces a wavelength-dependent redistribution of the reflected spectral contributions. In particular, the reflection coefficient progressively departs from its classical value with increasing wavenumber and undergoes a sign reversal beyond a characteristic spectral scale. Consequently, both the near-surface stress field and the attractive image force are significantly modified relative to the classical half-space prediction. The deviation from classical elasticity becomes most pronounced when the dislocation depth is comparable to the intrinsic surface elastic length scale, whereas the classical behavior is progressively recovered far from the free surface. Systematic benchmark calculations performed in the limit of vanishing surface elasticity show excellent agreement with the exact classical half-space solution. Additional convergence analyses with respect to spectral cutoff and discretization density confirm the numerical stability and robustness of the spectral implementation. The present work provides a spectral interpretation of nanoscale-elastic effects in terms of wavelength-dependent modification of the reflected elastic response and establishes a direct analytical connection between classical dislocation theory and surface-elastic continuum mechanics.
In this study, the thermo-mechanical vibration and buckling behavior of doubly curved sandwich shells incorporating a TPMS (triply periodic minimal surface) core and porous metal/ceramic face layers is analytically investigated. The face sheets are modeled as Al₂O₃/Ni-based functionally graded porous structures, while the core region is represented by three different TPMS architectures (TPMS-I, TPMS-II, and TPMS-III). Linear, nonlinear, and uniform temperature rises across the plate thickness are considered, and a refined higher-order plate theory including thickness stretching effects is employed to capture the structural response more accurately. The governing equations of motion are derived using Hamilton’s principle and solved via Navier’s method to evaluate the non-dimensional fundamental frequency and critical buckling temperature through an extensive parametric investigation. The results demonstrate that the TPMS core architecture significantly affects not only the initial dynamic stiffness but also the thermo-mechanical buckling response at elevated temperatures. In addition, the metal ratio and void fraction in the face layers are shown to markedly influence the vibration characteristics, while the core thickness and geometric ratios jointly govern the overall structural behavior. These findings provide practical design guidance for lightweight sandwich panels subjected to severe thermal gradients, particularly in aerospace, space, and high-temperature energy applications.
This study aims to develop an enhanced finite element formulation based on the refined first-order shear deformation theory (r-FSDT) for the nonlinear free vibration analysis of 3D-FGM corrugated sandwich plates. The proposed sandwich structure consists of two 3D-FGM face sheets and a 2D-FGM core layer. Geometric nonlinearity associated with large-amplitude deformation and mid-plane stretching is incorporated through the von Kármán kinematic assumption. The governing equations are derived from Hamilton’s principle and discretized using a MITC4 element. The accuracy and reliability of the proposed formulation are verified through comparisons with available benchmark solutions. Comprehensive parametric studies are then conducted to investigate the effects of power-law indices, geometric dimensions, boundary conditions, corrugation characteristics, and layer thickness ratios on the nonlinear frequency of 3D-FGM corrugated sandwich plates. The numerical results reveal that increasing the material gradation indices decreases the nonlinear frequencies owing to the reduction in effective structural stiffness, whereas increasing the core thickness and optimizing the corrugation geometry significantly enhance the structural stiffness and nonlinear frequency characteristics. The proposed formulation provides an efficient and accurate numerical tool for the nonlinear vibration analysis and optimal design of advanced lightweight corrugated sandwich structures for aerospace, marine, and civil engineering applications.
This work presents a homogenisation framework to determine the effective mechanical properties of two-phase composites with spring-type imperfect contact whose constituents undergo internal structural evolution. The latter is described within the framework of the multiplicative decomposition of the deformation gradient, accounting for inelastic distortions in each constituent phase. The interaction between the phases is modelled through a spring-type imperfect interface, which allows for displacement discontinuities while maintaining traction continuity across the interface. An asymptotic homogenisation approach is used to derive the macroscopic balance equations together with the corresponding effective coefficients. The general formulation is specialised to periodically laminated composites, leading to explicit analytical expressions for the effective mechanical properties of the homogenised system. These expressions capture the combined influence of elasticity, remodelling-induced inelastic effects, and interfacial stiffness. Finally, by considering a representative remodelling law, we solve the resulting coupled homogenised system in a simplified one-dimensional setting. The results illustrate the influence of remodelling and interfacial stiffness on the homogenised response, showing time-dependent effective coefficients and a nonlinear macroscopic displacement, and recover the perfect-contact case in the appropriate limit.
Multilayer nested re-entrant honeycombs with controllable connection topologies were developed and investigated from single cells to tandem and planar assemblies through quasi-static tensile tests, progressive cyclic loading–unloading tests, and finite element simulations. Nesting preserved the re-entrant geometry of the inner units and enabled staged deformation: the outer units became rectangular, whereas the inner units evolved into spindle-shaped and horizontally inverted Z-shaped forms in two- and three-layer structures, respectively. Alternating connections promoted horizontal-strut bending and concave angles exceeding 90° For the planar structures, nesting increased the initial-stage stiffness by 66.1%–169.7% and the deformation work up to 100% axial strain by 26.1%–64.3%. However, the non-nested structure retained the highest mass-specific values, revealing a trade-off between absolute deformation resistance and material efficiency. The re-entrant angle governed the early-stage response, whereas connection topology affected subsequent load transfer. Under progressive cyclic loading, the same-direction structure exhibited a lower force response than its quasi-static counterpart, whereas the alternating structure showed a transient increase during the first loading segment. No sustained cyclic hardening was identified. These findings clarify the effects of structural hierarchy and connection topology on the large-deformation tensile response of re-entrant honeycombs.
This work presents a one-dimensional Micropolar Mechanics (MM) reduction of Timoshenko beam theory (TBT) in which the cross-section is identified with a rigid microcontinuum endowed with an anisotropic MM constitution. The direct integration of the three-dimensional micropolar balance laws over the section yields a system in which two structurally distinct shear coefficients emerge: κv in the transverse balance, accounting for the total shear flow through the section, and κθ in the angular balance, representing the spin–orbital transfer between translational and rotational channels. Both coefficients are independent and parametrised by the anisotropic shear modulus μ∗ and the anisotropy parameter η. Static consistency of the reduced model determines the micropolar characteristic length and ensures exact recovery of the Euler–Bernoulli bending stiffness for any pair (κv,κθ). Classical TBT is recovered structurally at μ∗=μ, η=κs−2, where κs is Cowper’s coefficient (Cowper, 1996). The general case κv≠κθ provides a structural counterpart to the two-coefficient TBT reported in Franco-Villafañe and Méndez-Sánchez (2014). The isotropic limit η=0 produces the structural identity κθ=2(κv−1), which illuminates the spin–orbital reading of the two channels.
A central obstruction to well-posedness in nonlinear elasticity is the possible failure of quasiconvexity of the stored-energy density W. When W is not quasiconvex, minimizing sequences develop fine-scale oscillations — rank-one laminates — that prevent strong compactness of the gradients and cause lower semicontinuity to fail. We study the second-gradient functional Eℓ[u]=∫ΩW(∇u)dx+ℓ22∫Ω|∇2u|2dx,ℓ>0,and prove two complementary results under general p-growth hypotheses (p>1) on W:• Compactness (Theorem 3.1) Every sequence (un)⊂W2,2(Ω;Rm) with supnEℓ[un]<∞ has a subsequence whose gradients converge strongly in L2. The proof uses the uniform H2-bound delivered by the second-gradient term together with the Rellich–Kondrachov compact embedding H2(Ω)⋐H1(Ω).• Laminate exclusion (Propositions 4.1–4.2) Smooth (h∈C2) rank-one laminate sequences of wavelength ɛ→0 satisfy Eℓ[uɛ]→+∞ at rate ɛ−2, while piecewise-affine (sawtooth) laminates diverge at the slower rate ɛ−1; either rate suffices, so neither family is energy-bounded.As a consequence (Corollary 5.1), the regularized variational problem admits a minimizer in the affine H2-class even when W itself is not quasiconvex: no quasiconvexification of W is required. We carefully distinguish this compactness-induced well-posedness from an intrinsic quasiconvexity property of W. Throughout, we tie the internal length ℓ to concrete physical mechanisms, to its measurement, and to the higher-order boundary conditions it entails, and we connect the static minimum wavelength to the dynamic dispersion cut-off of second-gradient continua, to gradient-enhanced plasticity, and to variational damage. We close with the open question of the Γ-limit Eℓ→∫QW(∇u)dx as ℓ→0.
Deep shale reservoirs exist in complex thermo-pressure environments, making it difficult to quantitatively characterize their microscopic mechanical behaviors and anisotropic evolution patterns. In this study, molecular dynamics simulations combined with Perl scripts are employed to quantify the tensile mechanical responses of single shale minerals, kerogen and multi-component systems under thermo-pressure conditions, and reveal the underlying microscopic mechanisms. The results show that the mechanical stability of shale ranks as brittle minerals > clay minerals > organic matter. The degree of thermally induced strength degradation follows kaolinite > kerogen > montmorillonite > brittle minerals; kaolinite loses up to 62% strength along the [010] crystal direction, and quartz only loses 2% along the [100] crystal direction. The influence degree of pressure is ranked as clay minerals, organic matter and brittle minerals. The strength of kaolinite rises by up to 90.6% along the [100] crystal direction under pressure, with quartz merely increasing by 0.97% along the [010] crystal direction. In composite models, rigid quartz and kaolinite restrict the plastic flow of kerogen via interfacial confinement. Under thermo-pressure coupling, kerogen enhances thermal softening along the [001] crystal direction without affecting rigid bond-dominated [100]/[010] regions. Quartz enhances directional stability through pressure hardening, and kaolinite induces interlayer anisotropy. The kerogen-quartz-kaolinite composite system undergoes a critical shift from the balance between pressure hardening and thermal softening to thermal softening predominance along the [100] crystal direction. Deformation along the [001] crystal direction is always controlled by thermal softening, while those along the [100]/[010] crystal directions are dominated by pressure hardening. This study is the first to quantitatively characterize the anisotropic evolution of tensile mechanical properties from single minerals, kerogen to multi-component composite systems under temperature-pressure coupling, and reveals the microscopic mechanism of rigid phase interfacial constraint and component synergistic effect.
We first phrase boundary-value problems for a dense, steady, fully developed, gravitational flow of identical inelastic spheres over and within an inclined erodible bed in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical integrations of the governing equations. This contribution is dedicated to the memory of Stuart Savage, who initiated the use of kinetic theory in the study of collisional granular flows.
The dynamics of nonlinear localized strains in a metamaterial due to the thermal effects is studied on the basis of the nonlinear coupled continuum equations. It is shown numerically that the influence of the coefficient of thermoelasticity and the shape of the initial localized thermal initial disturbance provide new effects such as changing of the sign of the amplitude of localized strain wave, generation of two-hump localized waves and arising of a standing localized strain. Particular analytical travelling wave solutions can explain some features of these numerical solutions.
