“…The position of the dipoles is determined using the Metropolis algorithm. [15][16][17] In this paper, in contrast to those presented, the distribution of the angle θ depends on the elongation degree of the chain and its value lies in the interval [Àθ 0 ; θ 0 ]. (3) The diameter of the tube is calculated at which the free energy of the system takes a minimum value at a given temperature.…”
In this work, shear strain modeling in materials consisting of a thin polymer layer ([Formula: see text][Formula: see text]nm), adhesive bonded to a rigid substrate, considered not to be impacted by deformation, was performed. A discrete-continuum model of chains system with a given stiffness with polar groups is developed. The polymer chain was considered in the framework of the persistene model, and the polar groups were based on the lattice model on the tetragonal lattice. It was assumed that the main contribution to the energy of interchain interactions is due to the potential of the polar groups and was calculated using the Metropolis algorithm. The potential interactions between the nearest polar groups of chains included the energy of dipole–dipole interactions (Keesom energy) and the Lennard–Jones potential. It is taken into account that the possible orientations of the polar groups are determined by the average elongation of the chain. Calculations showed that the dependence of free energy on the interchain distance has two minima. The first minimum is characterized by the orientational ordering of the polar groups, the second — by their disordered state. The depth and position of the minima depend on temperature, bending stiffness of the chain, the modulus of the dipole moment of the polar groups and the depth of the potential well in the Lennard–Jones energy. A step-by-step simulation of shear strain in a polymer layer in an orientationally disordered state was carried out. The obtained stress–strain diagrams make it possible to estimate the value of the elastic limit and also to determine the stresses at the points of phase transitions from a disordered to an orientationally ordered state.
“…The position of the dipoles is determined using the Metropolis algorithm. [15][16][17] In this paper, in contrast to those presented, the distribution of the angle θ depends on the elongation degree of the chain and its value lies in the interval [Àθ 0 ; θ 0 ]. (3) The diameter of the tube is calculated at which the free energy of the system takes a minimum value at a given temperature.…”
In this work, shear strain modeling in materials consisting of a thin polymer layer ([Formula: see text][Formula: see text]nm), adhesive bonded to a rigid substrate, considered not to be impacted by deformation, was performed. A discrete-continuum model of chains system with a given stiffness with polar groups is developed. The polymer chain was considered in the framework of the persistene model, and the polar groups were based on the lattice model on the tetragonal lattice. It was assumed that the main contribution to the energy of interchain interactions is due to the potential of the polar groups and was calculated using the Metropolis algorithm. The potential interactions between the nearest polar groups of chains included the energy of dipole–dipole interactions (Keesom energy) and the Lennard–Jones potential. It is taken into account that the possible orientations of the polar groups are determined by the average elongation of the chain. Calculations showed that the dependence of free energy on the interchain distance has two minima. The first minimum is characterized by the orientational ordering of the polar groups, the second — by their disordered state. The depth and position of the minima depend on temperature, bending stiffness of the chain, the modulus of the dipole moment of the polar groups and the depth of the potential well in the Lennard–Jones energy. A step-by-step simulation of shear strain in a polymer layer in an orientationally disordered state was carried out. The obtained stress–strain diagrams make it possible to estimate the value of the elastic limit and also to determine the stresses at the points of phase transitions from a disordered to an orientationally ordered state.
“…If we consider the simple structural scheme sketched in figure 12 , it is simple to prove that, for a pantographic lattice with orthogonal fibres, which reveals the auxiliary rods’ contribution to contrast the shear mode of the square formed by the four pantographic rods ( figure 2 b ). This relationship could be useful to calibrate the stiffness of the auxiliary rods, following, for example, the guidelines reported in [ 36 – 38 ]. Figure 11.…”
Section: Pantographic Lattice With King Post Truss Building Blockmentioning
confidence: 99%
“…which reveals the auxiliary rods' contribution to contrast the shear mode of the square formed by the four pantographic rods (figure 2b). This relationship could be useful to calibrate the stiffness of the auxiliary rods, following, for example, the guidelines reported in [36][37][38].…”
Section: Behaviour Of King Post Pantographic Unitmentioning
One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by ‘standard’ materials. In dell’Isola et al. (2015 Zeitschrift für angewandte Mathematik und Physik
66, 3473–3498. (doi:10.1007/s00033-015-0556-410.1007/s00033-015-0556-4)), it was proved that, with a pantographic microstructure constituted by ‘long’ micro-beams it is possible to obtain metamaterials whose elastic range spans up to an elongation exceeding 30%. In this paper, we demonstrate that the same behaviour can be obtained by means of an internal microstructure based on a king post motif. This solution shows many advantages: it involves only microbeams; all constituting beams are undergoing only extension or compression; all internal constraints are terminal pivots. While the elastic deformation energy can be determined as easily as in the case of long-beam microstructure, the proposed design seems to have obvious remarkable advantages: it seems to be more damage resistant and therefore to be able to have a wider elastic range; it can be realized with the same three-dimensional printing technology; it seems to be less subject to compression buckling. The analysis which we present here includes: (i) the determination of Hencky-type discrete models for king post trusses, (ii) the application of an effective integration scheme to a class of relevant deformation tests for the proposed metamaterial and (iii) the numerical determination of an equivalent second gradient continuum model. The numerical tools which we have developed and which are presented here can be readily used to develop an extensive measurement campaign for the proposed metamaterial.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
