Hossein Darban, Ph.D.

Department of Mechanics of Materials (ZMM)
Division of Advanced Composite Materials (PZMK)
position: assistant
telephone: (+48) 22 826 12 81 ext.: 437
e-mail: hdarban

Recent publications
1.Darban H., Luciano R., Caporale A., Fabbrocino F., Higher modes of buckling in shear deformable nanobeams, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/j.ijengsci.2020.103338, Vol.154, pp.103338-1-18, 2020
Abstract:

The size-dependent buckling instability of shear deformable nanobeams rested on a two-parameter elastic foundation is studied through the stress-driven nonlocal theory of elasticity and the kinematic assumptions of the Timoshenko beam theory. The small-scale size effects are taken into account by nonlocal constitutive relationships, which define the strains at each point as integral convolutions in terms of the stresses in all the points and a kernel. In this manner, the nonlocal elasticity formulation is well-posed and does not include inconsistencies usually arising using other nonlocal models. The size-dependent governing differential equations in terms of the transverse displacement and the cross-sectional rotation are decoupled, and closed form solutions are presented for the displacement functions. Proper boundary conditions are imposed and the buckling problem is reduced to finding roots of a determinant of a matrix, whose elements are given explicitly for different classical edge conditions. The closed form treatment of the problem avoids the numerical instabilities usually occurring within numerical techniques, and allows to find also higher buckling loads and shape modes. Several nanobeams rested on the Winkler or Pasternak elastic foundations and characterized by different boundary conditions, shear deformability, and nonlocality are considered and the critical loads and shape modes are presented, including those for the higher modes of buckling. Excellent agreements are found with the available approximate numerical results in the literature and novel insightful findings are presented and discussed, which are in accordance with experimental observations.

Keywords:

nanobeam, buckling, elastic foundation, closed form solution, nonlocal elasticity, size effect

Affiliations:
Darban H.-other affiliation
Luciano R.-other affiliation
Caporale A.-other affiliation
Fabbrocino F.-other affiliation
2.Darban H., Fabbrocino F., Luciano R., Size-dependent linear elastic fracture of nanobeams, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/j.ijengsci.2020.103381, Vol.157, pp.103381-1-13, 2020
Abstract:

A nonlocal linear elastic fracture formulation is presented based on a discrete layer approach and an interface model to study cracked nanobeams. The formulation uses the stress-driven nonlocal theory of elasticity to account for the size-dependency in the constitutive equations, and the Bernoulli-Euler beam theory to define the kinematic field. Two fundamental mode I and mode II fracture nanospecimens with applications in Engineering Science are studied to reveal principal characteristics of the linear elastic fracture of beams at nanoscale. The domains are discretized both through the transverse and longitudinal directions and the field variables are derived by solving systems of the nonlocal equilibrium equations subjected to the variationally consistent and constitutive boundary and continuity conditions. The energy release rates of the fracture nanospecimens are calculated both from the global energy consideration and from the localized fields at the tip of the crack, i.e. the cohesive forces and the displacement jumps. The results are shown to be the same, proving the capability of the interface model to predict localized fields at the crack tip which are important for the cohesive fracture problems. It is found that the nanospecimens with higher nonlocality have higher fracture resistance and load bearing capacity due to higher energy absorptions and lower energy release rates. The crack propagation in the nanospecimens are also studied and load-displacement curves are presented. The nonlocality considerably increases the stiffness of the initial linear response of the nanospecimens. The fracture model is also able to capture the non-linear post-peak response and the unstable crack propagation, the snap-back instability, which is more intense for nanospecimens with higher nonlocality.

Keywords:

cracked nanobeams, nonlocal fracture, energy release rate, cohesive, crack propagation

Affiliations:
Darban H.-IPPT PAN
Fabbrocino F.-other affiliation
Luciano R.-other affiliation
3.Ceroni F., Darban H., Luciano R., Analysis of bond behavior of injected anchors in masonry elements by means of finite element modeling, COMPOSITE STRUCTURES, ISSN: 0263-8223, DOI: 10.1016/j.compstruct.2020.112099, Vol.241, pp.112099-1-18, 2020
Abstract:

Injected anchors made of steel bars embedded in masonry elements by means of cement-based grout represented in the past a wide solution for avoiding out-of-plane mechanisms. Corrosion phenomena in steel bars reduced the effectiveness of such type of intervention over time. Innovative materials, as the Fiber Reinforced Plastic ones, can represent a suitable alternative to increase durability and performance of injected anchors. Since the effectiveness of injected anchors is strictly related to bond behaviour along both the bar-grout and the grout-masonry interfaces, a detailed analysis by means of a Finite Element model was developed for different types of bars embedded in masonry elements. The numerical model was firstly calibrated on some experimental results of pull-out tests available in literature and, then, is used for investigating the effects of several parameters on both local and global behaviour. Load-displacement curves and local distributions of shear stresses are examined in detail. The numerical analyses evidenced that the maximum tensile force in the anchor mainly depends on the shear strength of the bar-grout and the grout-masonry interfaces and on the embedded length, but for very long embedded length, it can be limited by the tensile failure in the anchor or in the masonry.

Keywords:

masonry, FRP bars, injected anchors, bond, pull-out test, FE model

Affiliations:
Ceroni F.-other affiliation
Darban H.-other affiliation
Luciano R.-other affiliation
4.Luciano R., Caporale A., Darban H., Bartolomeo C., Variational approaches for bending and buckling of non-local stress-driven Timoshenko nano-beams for smart materials, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/j.mechrescom.2019.103470, Vol.103, pp.103470-1-7, 2020
Abstract:

In this work, variational formulations are proposed for solving numerically the problem of bending and buckling of Timoshenko nano-beams. The present work belongs to research branch in which the non-local theory of elasticity has been used for analysis of beam-like elements in smart materials, micro-electro-mechanical (MEMS) or nano-electro-mechanical systems (NEMS). In fact, the local beam theory is not adequate to describe the behavior of beam-like elements of smart materials at the nano-scale, so that different non-local models have been proposed in last decades for nano-beams. The nano-beam model considered in this work is a convex combination (mixture) of local and non-local phases. In the non-local phase, the kinematic entities in a point of the nano-beam are expressed as integral convolutions between internal forces and an exponential kernel. The aim is to construct a functional whose stationary condition provides the solution of the problem. Two different functionals are defined: one for the pure non-local model, where the local fraction of the mixture is absent, and the other for the mixture with both local and non-local phases. The Euler equations of the two functionals are derived; then, attention focuses on the mixture model. The functional of the mixture depends on unknown Lagrange multipliers and the Euler equations of the functional provide not only the governing equations of the problem but also the relationships between these Lagrange multipliers and the other variables on which the functional depends. In fact, approximations of the variables of the functional can not be chosen arbitrarily in numerical analyzes but have to satisfy suitable conditions. The Euler equations involving the Lagrange multipliers are essential in the numerical analyzes and suggest the correct approximations that have to be adopted for Lagrange multipliers and the other unknown variables of the functional. The proposed method is verified by comparing numerical solutions with exact solutions in bending problem. Finally, the method is used to determine the buckling load of Timoshenko nano-beams with mixture of phases.

Keywords:

non-local elasticity, variational methods, Timoshenko beam, buckling load, smart materials

Affiliations:
Luciano R.-other affiliation
Caporale A.-other affiliation
Darban H.-other affiliation
Bartolomeo C.-other affiliation
5.Luciano R., Darban H., Bartolomeo C., Fabbrocino F., Scorza D., Free flexural vibrations of nanobeams with non-classical boundary conditions using stress-driven nonlocal model, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/j.mechrescom.2020.103536, Vol.107, pp.103536-1-5, 2020
Abstract:

Free flexural vibrations of nanobeams with non-rigid edge supports are studied by means of the stress-driven nonlocal elasticity model and Euler-Bernoulli kinematics. The elastic deformations of the supports are modelled by transversal and flexural springs, so that, in the limit conditions when the springs stiffnesses tend to zero or infinity, the classical free, pinned, and clamped boundary conditions may be recovered. An analytical procedure is used to derive the closed form solution of the spatial differential equation. The problem of finding the natural frequencies is then reduced to find the roots of the determinant of a matrix, whose elements are explicitly given. The proposed technique, then, avoids the numerical instabilities usually arising when the numerical techniques are used to obtain the solution. The effects of both non-rigid supports elastic deformations and nonlocal parameter on the natural frequencies are studied also for higher vibrations modes. The comparison between the solutions of the proposed model and those available in the literature shows an excellent agreement, and new insightful results and discussions are presented.

Keywords:

elastically constrained beam, nanostructures, natural frequency, size effects, well-posed nonlocal formulation

Affiliations:
Luciano R.-other affiliation
Darban H.-other affiliation
Bartolomeo C.-other affiliation
Fabbrocino F.-other affiliation
Scorza D.-other affiliation
6.Caporale R., Darban H., Luciano R., Exact closed-form solutions for nonlocal beams with loading discontinuities, MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, ISSN: 1537-6494, DOI: 10.1080/15376494.2020.1787565, pp.1-11, 2020
Abstract:

A novel mathematical formulation is presented for the applications of the stress-driven nonlocal theory of elasticity to engineering nano-scale problems requiring longitudinal discretization. Specifically, a differential formulation accompanied with novel constitutive continuity conditions is provided for determining exact closed-form solutions of nonlocal Euler-Bernoulli beams with loading discontinuities, i.e. points of discontinuity for external loads and internal forces. Constitutive continuity conditions have to be satisfied in interior points where a loading discontinuity occurs and contain integral convolutions of the stress over suitable parts of the nonlocal beam. Several results show the effectiveness of the proposed method.

Keywords:

closed-form solutions, discretization, Euler-Bernoulli beams, nanobeams

Affiliations:
Caporale R.-other affiliation
Darban H.-other affiliation
Luciano R.-other affiliation
7.Darban H., Fabbrocino F., Feo L., Luciano R., Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model, MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, ISSN: 1537-6494, DOI: 10.1080/15376494.2020.1739357, pp.1-9, 2020
Abstract:

The instability of nanobeams rested on two-parameter elastic foundations is studied through the Bernoulli-Euler beam theory and the stress-driven nonlocal elasticity model. The size-dependency is incorporated into the formulation by defining the strain at each point as an integral convolution in terms of the stresses in all the points and a kernel. The nonlocal elasticity problem in a bounded domain is well-posed and inconsistencies within the Eringen nonlocal theory are overcome. Excellent agreement is found with the results in the literature, and new insightful results are presented for the buckling loads of nanobeams rested on the Winkler and Pasternak foundations.

Keywords:

buckling, closed form solution, nanobeam, nonlocal elasticity, Pasternak foundation, stress-driven

Affiliations:
Darban H.-other affiliation
Fabbrocino F.-other affiliation
Feo L.-other affiliation
Luciano R.-other affiliation