In this work the problem of the in-plane free vibrations (axial and bending) of a Bernoulli–Euler nanobeam using the mixed local/nonlocal Eringen elasticity theory is studied. The natural frequencies ...of vibration have been analytically obtained solving two uncoupled integro-differential eigenvalue problems, which are properly transformed in differential eigenvalue problems. Different kinds of end supports have been considered, and the influence of both mixture parameter and length scale has been analysed. The results show the softening effect of the Eringen’s nonlocality, which is more pronounced as the local phase fraction decreases.
A large number of papers devoted to the dynamics of Bernoulli–Euler beams considering the fully nonlocal Eringen elasticity theory has been previously published. However, as recently stated by Romano, Barretta, Diaco and de Sciarra (2017), the problem is ill-posed in general, and the existence of a solution is an exception, the rule being non-existence. Nevertheless, the presence of a local term in the constitutive equation, leading to the two-phase formulation, renders the problem well-posed. To the best knowledge of the authors, this is the first time an exact solution is presented for a dynamic problem involving structures with constitutive equations corresponding to nonlocal integral Eringen’s elasticity.
In this work, a hyperelastic-thermoviscoplastic constitutive model including thermomechanical coupling is presented to predict the mechanical behavior of semi-crystalline polymers. The constitutive ...model is based on the original approach developed by Polanco-Loria and coauthors (2010) and it accounts for: material hardening due to strain rate sensitivity, temperature evolution during the deformation process due to heat generation induced by plastic dissipation, thermal softening and thermal expansion of the material. The parameters of the constitutive model have been identified for polyether-ether-ketone (PEEK) from experimental data published by Rae and coauthors (2007). In order to analyze the predictive capacity of the model under dynamic conditions, the constitutive model has been implemented in a FE code within a large deformation framework to study two different problems: low velocity impact test on PEEK thin plates and dynamic necking on PEEK slender bar. These problems involve large and irreversible deformations, high strain rates and temperature increment due to plastic dissipation. The analysis determines the interplay between strain rate and thermal effects in the material behavior. The constitutive model presented herein reproduces adequately the mechanical behavior of PEEK under different thermal and loading conditions, demonstrating the importance of considering the coupling between temperature and strain rate.
•A hyperelastic-viscoplastic model for semi-crystalline polymers is developed.•Model includes thermo-mechanical coupling, temperature and rate dependencies.•Model implemented in a FE code is applied to study polyether-ether-ketone (PEEK).•Two dynamic problems were analyzed: low velocity impact test and dynamic necking.•Mechanical behavior under different thermal and strain rate conditions is analyzed.
The nonlocal strain gradient elasticity theory is being widely used to address structural problems at the micro- and nano-scale, in which size effects cannot be disregarded. The application of this ...approach to bounded solids shows the necessity to fulfil boundary conditions, derived from an energy variational principle, to achieve equilibrium, as well as constitutive boundary conditions inherent to the formulation of the constitutive equation through convolution integrals. In this paper we uncover that, in general, is not possible to accomplish simultaneously the boundary conditions, which are all mandatory in the framework of the nonlocal strain gradient elasticity, and therefore, the problems formulated through this theory have no solution. The model is specifically applied to the case of static axial and bending behaviour of Bernoulli-Euler beams. The corresponding governing equation in terms of displacements results in a fourth-order ODE with six boundary conditions for the axial case, and in a sixth-order ODE with eight boundary conditions for the bending case. Therefore, the problems become overconstrained. Three study cases will be presented to reveal that all the boundary conditions cannot be simultaneously satisfied. Although the ill-posedness has been pointed out for an elastostatic 1D problem, this characteristic holds for other structural problems. The conclusion is that the nonlocal strain gradient theory is not consistent when applied to finite structures and leads to problems with no solution in a general case.
The Eringen nonlocal theory of elasticity formulated in differential form has been widely used to address problems in which size effect cannot be disregarded in micro- and nano-structured solids and ...nano-structures. However, this formulation shows some inconsistencies that are not completely understood. In this paper we formulate the problem of the static bending of Euler–Bernoulli beams using the Eringen integral constitutive equation. It is shown that, in general, the Eringen model in differential form is not equivalent to the Eringen model in integral form, and a general method to solve the problem rigorously in integral form is proposed. Beams with different boundary and load conditions are analyzed and the results are compared with those derived from the differential approach showing that they are different in general. With this integral formulation, the paradox that appears when solving the cantilever beam with the differential form of the Eringen model (increase in stiffness with the nonlocal parameter) is solved, which is one of the main contributions of the present work.
A fully inorganic analogue of the nanostructured dye‐sensitized solar cell is fabricated using an electrochemically grown n‐ZnO/CdSe core–shell nanowire array (see Figure). Filling the voids between ...the nanowires with p‐type wide‐bandgap CuSCN by a solution‐deposition technique leads to an extremely thin solar cell exhibiting 2.3 % energy‐conversion efficiency.
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A novel DMF-free perovskite solar cell fabrication protocol, based on electrodeposited PbI2 films from ionic liquid and subsequent conversion into perovskite is presented. Hexane is ...proposed to be used as an efficient co-solvent in the conversion solution, to affect the film morphology in a controlled way. The effect of the hexane in the CH3NH3-PbI2solvent complex formation and the impact of the complexes in the PbI2 to CH3NH3PbI3 conversion is discussed. Close-packing density nanocrystalline perovskite films from open-packed PbI2 films platelets are successfully obtained after dipping during 10minutes in isopropanol:hexane 90:10v:v conversion solutions. Solar cells based on the obtained perovskite films exhibit a power conversion efficiency of 9%. This finding points out the viability of the reported process in the DMF-free fabrication of perovskite solar cells.
The Na–O2 battery offers an interesting alternative to the Li–O2 battery, which is still the source of a number of unsolved scientific questions. In spite of both being alkali metal–O2 batteries, ...they display significant differences. For instance, Li–O2 batteries form Li2O2 as the discharge product at the cathode, whereas Na–O2 batteries usually form NaO2. A very important question that affects the performance of the Na–O2 cell concerns the key parameters governing the growth mechanism of the large NaO2 cubes formed upon reduction, which are a requirement of viable capacities and high performance. By comparing glyme-ethers of various chain lengths, we show that the choice of solvent has a tremendous effect on the battery performance. In contrast to the Li–O2 system, high solubilities of the NaO2 discharge product do not necessarily lead to increased capacities. Herein we report the profound effect of the Na+ ion solvent shell structure on the NaO2 growth mechanism. Strong solvent–solute interactions in long-chain ethers shift the formation of NaO2 toward a surface process resulting in submicrometric crystallites and very low capacities (ca. 0.2 mAh/cm2 (geom)). In contrast, short chains, which facilitate desolvation and solution-precipitation, promote the formation of large cubic crystals (ca. 10 um), enabling high capacities (ca. 7.5 mAh/cm2 (geom)). This work provides a new way to look at the key role that solvents play in the metal–air system.
A finite element numerical model for carbon/epoxy woven laminates has been used to predict residual velocity and damaged area when subjected to high impact velocities. Experiments using a gas gun ...were conducted to investigate the impact process and to validate the model, measuring the two variables previously indicated. A morphology analysis was also made to investigate the different breakage mechanisms that appear during the penetration process. The influence of the impact velocity and obliquity has been studied using the numerical tool, in a wide range of impact velocities and considering two impact angles, 0° and 45°.
•A constitutive framework for transverse isotropic soft tissues is presented.•Strain rate, temperature and loading direction dependencies are taken into account.•The framework allows for its ...particularisation depending on the specific tissue.•A methodology for the particularisation of the constitutive framework is presented.•Constitutive models have been proposed for white matter and skin tissues.
In this work, a continuum constitutive framework for the mechanical modelling of soft tissues that incorporates strain rate and temperature dependencies as well as the transverse isotropy arising from fibres embedded into a soft matrix is developed. The constitutive formulation is based on a Helmholtz free energy function decoupled into the contribution of a viscous-hyperelastic matrix and the contribution of fibres introducing dispersion dependent transverse isotropy. The proposed framework considers finite deformation kinematics, is thermodynamically consistent and allows for the particularisation of the energy potentials and flow equations of each constitutive branch. In this regard, the approach developed herein provides the basis on which specific constitutive models can be potentially formulated for a wide variety of soft tissues. To illustrate this versatility, the constitutive framework is particularised here for animal and human white matter and skin, for which constitutive models are provided. In both cases, different energy functions are considered: Neo-Hookean, Gent and Ogden. Finally, the ability of the approach at capturing the experimental behaviour of the two soft tissues is confirmed.
This work analyzes the dynamic behavior of cracked Timoshenko beams immersed in a Winkler elastic medium, obtaining their natural frequencies of bending vibration. For this purpose, the beam is ...modeled as two segments connected in the cracked section by two massless springs, one extensional and another one rotational. Their stiffnesses are proportional to the shear force and bending moment transmitted through the cracked section, respectively, considering the discontinuity of vertical displacement and rotation due to bending. The differential equations for the free vibration are solved by applying the corresponding boundary conditions and the compatibility conditions of the cracked section. The proposed methodology allows calculating the natural frequencies of vibration as a function of the type of support, the parameter defining the stiffness of the elastic soil, the crack position and the initial length of the crack. The results obtained are compared with those published by other authors who model the crack in a simplified way, showing the interaction and importance of the parameters considered in the natural frequencies of the system.
•Timoshenko cracked beam requires modeling jump due to shear force.•Complete and simplified crack models are compared.•Simplified crack models overestimate the stiffness of the beam.•Natural frequencies on cracked beams in elastic foundation are analyzed.
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