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Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue.

According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.

Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering.

Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.

The paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.

The fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.

Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.

According to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

The purpose of this paper is to present the basic solution of two collinear mode-I cracks in the orthotropic medium by the use of the non-local theory.

Meanwhile, the generalized Almansi’s theorem and the Schmidt method are used. By the Fourier transform, it is converted to a pair of dual integral equations.

Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks and the lattice parameter on the stress field near the crack tips in the orthotropic medium.

The present solution exhibits no stress singularity at the crack tips in the orthotropic medium.

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

Thermal buckling of double-layered piezoelectric nanoplates has been analyzed by applying an external electric voltage on the nanoplates. The paper aims to discuss this issue.

Double-layered nanoplates are connected to each other by considering linear van der Waals forces. Nanoplates are placed on a polymer matrix. A comprehensive thermal stress function is used for investigating thermal buckling. A linear electric function is used for taking external electric voltages into account. For considering the small-scale effect, the modified couple stress theory has been applied. An analytical solution has been used by taking various boundary conditions.

EEV has a considerable impacted on the results of various half-waves in all boundary conditions. By increasing EEV, the reduction of critical buckling temperature in higher half-waves is remarkably slower than lower half-waves. By considering long lengths, the effect of EEV on the critical temperature will be markedly decreased.

This paper uses electro-thermal stability analysis. Double-layered piezoelectric nanoplates are analyzed. A comprehensive thermal stress function is applied for taking into account critical temperature.

The purpose is to explore the free vibration behaviour of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The goal of this study is to gain a better knowledge of the dynamic response of nanoscale structures made of functionally graded materials and porous features. The Rayleigh-Ritz approach is used in this study to generate realistic mathematical models that take elastic foundation support into account. This research can contribute to the design and optimization of advanced nanomaterials with potential applications in engineering and technology by providing insights into the influence of material composition, porosity and foundation support on the vibrational properties of nanoplates.

A systematic methodology is proposed to evaluate the free vibration characteristics of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The study began by developing the mathematical model, adding material properties and establishing governing equations using the Rayleigh-Ritz approach. Numerical approaches to solve the problem are used, using finite element methods. The results are compared to current solutions or experimental data to validate the process. The results are also analysed, keeping the influence of factors on vibration characteristics in mind. The findings are summarized and avenues for future research are suggested, ensuring a robust investigation within the constraints.

The Rayleigh-Ritz technique is used to investigate the free vibration properties of elastic foundation-supported porous functionally graded nanoplates. The findings show that differences in material composition, porosity and foundation support have a significant impact on the vibrational behaviour of nanoplates. The Rayleigh-Ritz approach is good at modelling and predicting these properties. Furthermore, the study emphasizes the possibility of customizing nanoplate qualities to optimize certain vibrational responses, providing useful insights for engineering applications. These findings expand understanding of dynamic behaviours in nanoscale structures, making it easier to build innovative materials with specific features for a wide range of industrial applications.

The novel aspect of this research is the incorporation of elastic foundation support, porous structures and functionally graded materials into the setting of nanoplate free vibrations, utilizing the Rayleigh-Ritz technique. Few research have looked into this complex combo. By tackling complicated interactions, the research pushes boundaries, providing a unique insight into the dynamic behaviour of nanoscale objects. This novel approach allows for a better understanding of the interconnected effects of material composition, porosity and foundation support on free vibrations, paving the way for the development of tailored nanomaterials with specific vibrational properties for advanced engineering and technology applications.

In this paper, the problem of two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials subjected to an anti‐plane shear loading is investigated by use the Schmidt method. To make the analysis tractable, it is assumed that the material properties varied exponentially with coordinate vertical to the crack. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effect of the geometry of the interacting crack and the functionally graded parameter upon the stress intensity factors. The relations among the electric filed, the magnetic flux field and the stress field are obtained. The shielding effect of two parallel cracks has been discussed.

Building on the intergroup relations perspective on the social identity theory, the authors examine whether firms' environmental, social and governance (ESG) varies when local firms have non-local CEOs. Additionally, the authors examine which contextual factors may strengthen or weaken the effectiveness of ESG in helping non-local CEOs garner trust, legitimacy and resources support from local stakeholders.

Pooled OLS regressions, based on unbalanced panel data and controlling for year and industry fixed effects, were estimated using a sample composed of 836 Chinese A-share listed firms that have Bloomberg ESG disclosure scores data from 2006 to 2019.

Results suggest that companies with non-local CEOs, who are perceived as outgroup members by the local stakeholders, would lead to a higher level of ESG performance to overcome the intergroup bias they face. In addition, results also show that companies with a lower level of previous ESG decoupling and having more slack will mitigate the relationship between non-local CEOs and ESG performance. Conversely, firm visibility at a high level will promote the positive relationship between non-local CEOs and ESG performance.

This study offers theoretical insights that extend the focus of intragroup relation to outgroup identity, by introducing an intergroup relations lens to explore how outgroup (or nonprototypical) leaders utilize ESG to counter intergroup bias they suffer. Moreover, this study also extends current literature focusing on non-local CEOs and ESG performance.

The purpose of this paper is to discover whether factors responsible for the existence of non‐local competences in emerging multinationals are different from those of traditional multinationals.

Survey of 66 subsidiaries of Brazilian multinationals (BrMNes). This represents 70 percent of the 93 subsidiaries originally sampled.

The factors responsible for the development of non‐local competences in BrMNes are: the relationship between subsidiaries and business networks, the initiatives of subsidiaries and the support of the entrepreneurial orientation of subsidiaries by the headquarters.

Even though emerging multinationals require more resources developed abroad and although some studies revealed that different management models had been adopted during the internationalization process, the factors required to develop non‐local competences in BrMNes are very similar to those required by traditional multinationals.

Subsidiary innovation in partnership with the business network in the foreign country is essential to develop non‐local competences.

The paper supports the results of studies of traditional multinationals and demonstrates that despite the differences of Brazilian multinationals the factors required to develop non‐local competences are very similar. This is an interesting result to consolidate knowledge about global competitive advantages in multinationals: the management model to develop non‐local competences seems to be the same, in order of importance, regardless of multinational origin.