International Journal of Engineering Science最新文献

The study aims to investigate how the mechanics of swelling of a polymer gel is affected by the presence of free-chains due to a partial cross-linking process. The analysis is focused on the equilibrium solution of the mechano-diffusion problem under different as-prepared states, corresponding to different polymer network fractions before diffusion starts. The limit situations of perfectly cross-linked polymer gel and solution of polymeric chains are recovered by the model.

A three-dimensional rate-independent framework consistent with thermodynamics is presented to study the dissipative response of metals. The entropy inequality is transformed into equality by introducing a non-negative, continuous rate of dissipation function. The constitutive relation that relates the Hencky strain and Cauchy stress is parametrized by replacement stress, instead of the plastic strain, for reasons discussed. The evolution equation for the replacement stress is obtained such that among the possible processes, the one that maximizes the rate of dissipation is realized so that thermodynamic equilibrium is achieved in the shortest possible time. Appropriate 3D constitutive functions to model aluminium are prescribed for the dissipation function and a Gibbs-like potential. The variation of the transverse strain as a function of the uniaxial strain differs between the present formulation and classical plasticity. Consistent with some of the experimental observations, the material tends to be compressible in the present formulation during plastic deformations. Thus, further experimental investigations are required to choose the appropriate constitutive relation.

Flows of an incompressible Navier–Stokes fluid are frequently assumed to take place in domains whose boundaries are rigid and that the fluid adheres to them, i.e. there is the “no-slip” on the interface between the rigid solid and the flowing fluid. However, in many interesting problems the walls respond as (visco)-elastic structures and different slipping conditions on the fluid–structure interface seem to be more appropriate. Our main objective is to develop a reliable numerical approach capable of efficiently solving such fluid–structure interaction problems with Navier’s slip interface conditions in three dimensions. We focus on axi-symmetric flow problems; their two-dimensional character allows us to perform systematic testing of the performance of the solver and to study the effects of the (visco)-elasticity of the wall and the value of Navier’s slip-parameter on the properties of the flow including the vorticity, dissipation, pressure drop and wall shear stress. All tests concern steady and time-periodic flows in pipe-like domains with sinuses. It is startling that, in this geometric setting, the effects of (visco)-elasticity of the structure on the flow are minor in comparison to the setting when the walls are rigid.

A perturbation expansion is offered for the micromechanical prediction of the bifurcation buckling of soft viscoelastic composites with imperfections (e.g. wavy fibers). The composites of periodic microstructure are subjected to compressive loading and are undergoing large deformations. The perturbation expansion applied on the imperfect composites results in a zero and first order problems of perfect composites. In the former problem, loading exists and interfacial and periodicity conditions are imposed. In the latter one, however, loading is absent, the interfacial conditions possess complicated terms that have been already established by the zero order problem, and Bloch-Floquet boundary conditions are imposed. Both problems are solved by the high-fidelity generalized method of cells (HFGMC) micromechanical analysis. The ideal critical bifurcation stress can be readily predicted from the asymptotic values of the form of waviness growth with applied loading. This form enables also the estimation of the actual critical stress. The occurrence of the corresponding critical deformation and time is obtained by generating the stress-deformation response of the composite. The offered approach is illustrated for the prediction of bifurcation buckling of viscoelastic bi-layered and polymer matrix composites as well as porous materials. Finally, bifurcation buckling stresses of unidirectional composites in which the matrix is represented by the quasi-linear viscoelasticity theory are predicted. This quasi-linear viscoelasticity model exhibits constant damping which is observed by the actual viscoelastic behavior of biological materials.

Piezoresistive porous elastomers (PPEs) are gaining attention in the field of flexible electronics due to their unique properties including ultra softness, ultra lightness, and high sensitivity. These properties can be precisely adjusted through advanced material synthesis and micro/nanofabrication technologies that control the size, shape, and composition of the functional nanoparticles. Despite various theoretical models of porous materials developed to advance the design of these materials, issues such as reverse piezoresistive response and resistance overshooting remains to be unsolved. Using principles of elastic mechanics and electrical tunnel effects, the present study introduces an analytical model that considers the effects of multimodal buckling of the pore wall, pore closure, microcracks, and mismatch within the pore wall under large deformation. The proposed model achieves a 99.5 % accuracy rate in describing the piezoresistive response (stress and resistance) under 75 % compression deformation by incorporating electrical tunnel theory into the mechanical model. The study also uncovers the mechanism behind high resistance overshooting and its relevant influences, including factors such as loading speed and application temperature. These findings are expected to drive the development of better porous composites and pave the way for practical applications of PPEs in various fields of smart sensors.

The thermo-electro-mechanical vibration characteristics of piezoelectric nanoplates using Kirchhoff and Mindlin plate theories under a two-parameter elastic foundation with general boundary conditions are investigated in this article. Utilizing nonlocal elastic theory, the governing equations of the analytical model, which account for external variable influences, are derived using Hamilton’s principle. In the benchmark case, a wave-based method is employed to analyze the vibration characteristics of the piezoelectric nanoplate with general boundary conditions. Additionally, a series of detailed numerical examples are provided to examine the impact of the nonlocal parameter, external electric voltage, temperature change, biaxial force, Winkler’s modulus parameter, and Pasternak’s modulus parameter on the vibration characteristics of the piezoelectric nanoplate restrained on a two-parameter elastic foundation with general boundary conditions. The accuracy of the calculations is verified, and several conclusions are drawn. This paper aims to expand the numerical analytical range of vibration analysis for nanoplate structures and provide theoretical data for the design of nano-electromechanical systems.

A mapping technique for enhancing the visualisation and analysis of the flow structure in regions near the wall is presented. After identifying a near-wall region of interest, the output of the proposed mapping technique is an analytical expression of the flow variables, satisfying the governing PDEs and boundary conditions, on a stencil of standardised morphology.

The approach firstly involves selecting a local surface region of interest from the computational domain to be mapped. Subsequently a structured mesh of arbitrary height on top of the cropped surface is generated, thus forming the target volume region, which is termed the physical space. The solution data comprising of flow properties such as velocity and pressure from the computational domain is interpolated onto the physical space. The physical space and the data are consequently mapped onto an unwrapped domain with standard shape, termed the mapped space. For simplicity, the mapped space is chosen here to be a cuboid. Finally, the data is expressed as a best fit polynomial, satisfying the governing PDEs and boundary conditions.

The method is validated by direct pointwise comparison and from the velocity streamlines mapped from the physical space, for a set of test problems. The mapping technique effectiveness is demonstrated firstly on a 90 degree bend pipe as a benchmark investigation and subsequently on a nasal cavity anatomy. For the latter, three scenarios covering different flow structures in the near-wall region are scrutinised, demonstrating the ability of the techniques proposed to uncover the details of the near-wall flow in complex physiological flows. The regions of interest can be identified using near-wall measures such as wall shear stress, shear lines, and wall shear stress critical points.

The mapping technique has potential applications in the fields of fluid dynamics and specifically near-wall flows, as the interface region describing the dynamics of exchanges. It is furthermore capable of inferring the velocity field from reduced data available to enhance the use of deep learning or regression methods.

Strong surface elasticity has been only found in nanoscale materials due to their large surface-to-volume ratio. In this paper, at the macroscale, the strong surface elasticity is revealed in thin metamaterial structures. Moreover, the metamaterial structures filled with complex microstructures often need computationally prohibitive resources if the fully-resolved microstructures are modeled using high-fidelity approaches. Based on the revealed surface elasticity, a surface-based efficient yet accurate homogenization method is developed for thin metamaterial structures. This study explores the role that microstructure plays in determining the macroscopic properties of a metamaterial continuum and reveals the occurrence of the size-dependent surface effect that is strictly related to the microstructure configuration. The contribution of surface elasticity to the mechanical properties of thin metamaterial structures cannot be neglected, particularly when the size of microstructures is comparable to their thickness. The coupling effect of intrinsic length determined by microstructure and extrinsic length (the thickness) on surface elasticity is investigated using the homogenization method. The intrinsic length can be calibrated by the size-dependent effective elasticity tensor. The strength of surface elasticity is determined by the intrinsic length with a specific thickness. The contribution of surface elasticity to the effective elasticity tensor can be determined by the difference between intrinsic length and extrinsic length. Finally, a simple yet representative metamaterial truss under tension is used to illustrate the application of the homogenization method. Our findings not only provide mechanical insights into metamaterial structures but also offer a surface-based computational method for metamaterial structures filled with complex microstructures.

The present study aims to develop a continuum-based model to predict the pseudoelastic behavior of biological composites subjected to finite plane elastostatics. The proposed model incorporates a hyperelastic matrix material reinforced with nonlinear fibers, addressing challenges such as irreversible softening responses, large deformations, and nonlinear stress–strain responses. The kinematics of reinforcing fibers are formulated via the first and second gradient of continuum deformations and, more importantly, damage function and damage variables of Ogden–Roxburgh and Weibull type are integrated into the model to assimilate the various aspects of damage mechanisms present in soft tissues. Adopting the framework of variational principles and a virtual work statement, the Euler equation and admissible boundary conditions are obtained. The proposed model successfully predicts the Mullins effect observed in the human aorta and the Manduca muscle. Experimental validation with elastomeric composites demonstrates its utility to replicate softening and fiber damage phenomena, including deformation profiles. Further, the proposed molecular dynamics scheme offers an enhanced understanding of polymer chain entanglement processes, thereby facilitating the quantification of permanent damage in elastomeric composites. The obtained results may provide valuable insight toward understanding and modeling the mechanical behavior of soft biological tissues with practical implications for the design and analysis of biofabricated composites aimed at mimicking biological tissues.

Implicit elasticity presents the general response of materials without imposing assumptions at the fundamental level. A popular implausible assumption of continuum mechanics is that the reference configuration is stress-free, since residual stress is ubiquitous in Nature. This paper develops large and small deformation implicit elasticity frameworks using residually stressed reference configurations. The general forms of constitutive relations, in finite deformations, are obtained by pull-back or push-forward of all the associated tensors to the same (Eulerian or Lagrangian) configuration. These general forms are used to study the relationship between “residual stress and material symmetry” for implicit elasticity. Further, we use a virtual stress-free body, which is implicit elastic, to exactly determine the response of an initially stressed reference configuration. A number of such exact implicit relations are presented for residually stressed reference configurations, which are further simplified through interesting tensor analysis. The simplified implicit relations directly evaluates strain from a given Cauchy stress and residual stress tensor. One of these constitutive relations are employed for investigating the finite inflation of a residually-stressed, thick sphere. Finally, a small deformation implicit theory is attained by linearizing the developed relations for small strain and small rotation. To represent the small strain from a stressed reference, we need to invert a fourth order tensor. The closed-form inverse is determined in a new approach presented in the paper.