A molecular formulation of the onset of plasticity is proposed to assess temperature and strain rate effects in anisotropic semi-crystalline rubbery films. The presented plane stress criterion is ...based on the strain rate-temperature superposition principle and the cooperative theory of yielding, where some parameters are assumed to be material constants, while others are considered to depend on specific modes of deformation. An orthotropic yield function is developed for a linear low density polyethylene thin film. Uniaxial and biaxial inflation experiments were carried out to determine the yield stress of the membrane via a strain recovery method. It is shown that the 3% offset method predicts the uniaxial elastoplastic transition with good accuracy. Both the tensile yield points along the two principal directions of the film and the biaxial yield stresses are found to obey the superposition principle. The proposed yield criterion is compared against experimental measurements, showing excellent agreement over a wide range of deformation rates and temperatures.
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•The yield stress of a semi-crystalline anisotropic rubbery thin film is investigated.•Uniaxial tensile tests and biaxial inflation experiments are carried out.•Temperature and strain rate effects on the onset of plasticity are evaluated.•The yield criterion is based on the strain rate-temperature superposition principle and the cooperative theory of yielding.
The Eshelbian (or configurational) force is the main concept of a celebrated theoretical framework associated with the motion of dislocations and, more in general, defects in solids. In a similar ...vein, in an elastic structure where a (smooth and bilateral) constraint can move and release energy, a force driving the configuration is generated, which therefore is called by analogy ‘Eshelby-like’ or ‘configurational’. This force (generated by a specific movable constraint) is derived both via variational calculus and, independently, through an asymptotic approach. Its action on the elastic structure is counterintuitive, but is fully substantiated and experimentally measured on a model structure that has been designed, realized and tested. These findings open a totally new perspective in the mechanics of deformable mechanisms, with possible broad applications, even at the nanoscale.
Instability of a penetrating blade Bigoni, D.; Bosi, F.; Dal Corso, F. ...
Journal of the mechanics and physics of solids,
March 2014, 2014-03-00, 20140301, Letnik:
64
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Application of a dead compressive load at the free end of an elastic rod (the ‘blade’) induces its penetration into a sliding sleeve ending with a linear elastic spring. Bifurcation and stability ...analysis of this simple elastic system shows a variety of unexpected behaviors: (i) an increase of buckling load at decreasing of elastic stiffness; (ii) a finite number of buckling loads for a system with infinite degrees of freedom (leading to a non-standard Sturm–Liouville problem); (iii) more than one bifurcation load associated to each bifurcation mode; (iv) a restabilization of the straight configuration after the second bifurcation load associated to the first instability mode; (v) the presence of an Eshelby-like (or configurational) force, deeply influencing stability. Only the first of these behaviors was previously known, the second and third ones disprove common beliefs, the fourth highlights a sort of ‘island of instability’, and the last one shows surprising phenomena and effects on stability.
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Spinel single crystals of 19 compositions along the magnetite-ulvospinel join were synthesized by use of a flux-growth method. To obtain quantitative site populations, the crystals were analyzed by ...single-crystal X-ray diffraction, electron-microprobe techniques, and Mossbauer spectroscopy. All results were processed by using an optimization model. The unit-cell parameter, oxygen fractional coordinate, and tetrahedral bond length increase with increasing ulvospinel component, whereas the octahedral bond length decreases marginally. These changes result in sigmoidal crystal-chemical relationships consistent with cation substitutions in fully occupied sites. As a first approximation, the Akimoto model T(Fe1-X3+ FeX2+)M(Fe2+ Fe1-X3+ TiX)O4 describes the cation substitutions. Deviations from this model can be explained by an electron exchange reaction TFe2++MFe3+ = TFe3++MFe2+, which causes MFe2+≠1 and TFe2+/Ti≠1. The resultant S-shaped trends may be related to a directional change in the electron exchange reaction at Ti≈0.7 apfu. In general, variations in structural parameters over the whole compositional range can be split into two contributions: (1) a linear variation due to the TFe3++MFe3+ = TFe2++MTi4+ chemical substitution and (2) non-linear variations caused by the internal electron exchange reaction. In accordance with bond-valence theory, strained bonds ascribable to steric effects characterize the structure of magnetite-ulvospinel crystals. To relax the bonds and thereby minimize the internal strain under retained spinel space group symmetry, the electron exchange reaction occurs.
Torsional locomotion Bigoni, D.; Dal Corso, F.; Misseroni, D. ...
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences,
11/2014, Letnik:
470, Številka:
2171
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One edge of an elastic rod is inserted into a friction-less and fitting socket head, whereas the other edge is subjected to a torque, generating a uniform twisting moment. It is theoretically shown ...and experimentally proved that, although perfectly smooth, the constraint realizes an expulsive axial force on the elastic rod, which amount is independent of the shape of the socket head. The axial force explains why screwdrivers at high torque have the tendency to disengage from screw heads and demonstrates torsional locomotion along a perfectly smooth channel. This new type of locomotion finds direct evidence in the realization of a 'torsional gun', capable of transforming torque into propulsive force.
This paper explores some aspects of the crystal chemistry and structural constraints on tourmaline by examining 127 samples from the literature. According to the bond-valence model, the tourmaline ...structure shows lattice-induced strain at each polyhedron. The overall effect is an expansion of the triangular (BO3) group and compression of the tetrahedron. The X polyhedron can be either compressed or expanded: compression increases with vacancy content, whereas expansion is typical of Ca-rich tourmaline. The Y octahedron changes extensively from compressed through an unstrained to expanded state as a function of increasing Li content. The Z octahedron is almost unstrained in crystals with ΣZR2+<0.40 apfu, whereas it is compressed in crystals with ΣZR2+>0.40 apfu. The configuration of the six-membered tetrahedral ring is strongly affected by {Y-O}, which is the most important parameter linked to the deviation of the tetrahedral ring from hexagonal symmetry. The whole structure is stable when the channels through the Z octahedron framework are able to accommodate the Y cations. As {Y-O} becomes larger, the less puckered the tetrahedral ring and the more the O7 atom is displaced away from Z. Consequently, the difference between {Y-O} and {Z-O} cannot be too large, otherwise {Z-O} will be too small to be commensurate with shifting of the O7 atom. One possible mechanism to reduce the difference between {Y-O} and {Z-O}, is the disordering reaction YAl+ZR→YR+ZAl, which increases {Z-O} and decreases {Y-O}. In ideal dravite, schorl, and "tsilaisite," {Y-O} and {Z-O} are incommensurate.
An elastica arm scale Bosi, F.; Misseroni, D.; Dal Corso, F. ...
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences,
09/2014, Letnik:
470, Številka:
2169
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The concept of a 'deformable arm scale' (completely different from a traditional rigid arm balance) is theoretically introduced and experimentally validated. The idea is not intuitive, but is the ...result of nonlinear equilibrium kinematics of rods inducing configurational forces, so that deflection of the arms becomes necessary for equilibrium, which would be impossible for a rigid system. In particular, the rigid arms of usual scales are replaced by a flexible elastic lamina, free to slide in a frictionless and inclined sliding sleeve, which can reach a unique equilibrium configuration when two vertical dead loads are applied. Prototypes designed to demonstrate the feasibility of the system show a high accuracy in the measurement of load within a certain range of use. Finally, we show that the presented results are strongly related to snaking of confined beams, with implications for locomotion of serpents, plumbing and smart oil drilling.
Self-encapsulation, or the 'dripping' of an elastic rod Bosi, F.; Misseroni, D.; Dal Corso, F. ...
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences,
07/2015, Letnik:
471, Številka:
2179
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A rod covering a fixed span is loaded at the middle with a transverse force, such that with increasing load a progressive deflection occurs. After a certain initial deflection, a phenomenon is ...observed where two points of the rod come in contact with each other. This is defined as the 'dripping point' and is when 'self-encapsulation' of the elastic rod occurs. Dripping seems at a first glance to be impossible and definitely cannot occur in the presence of 'ordinary' constraints (such as simple supports or clamps) at the ends of the span. However, the elastica governs oscillating pendulums, buckling rods and pendant drops, so that a possibility for self-encapsulation might be imagined. This phenomenon is indeed demonstrated (both theoretically and experimentally) to occur when at least one of the constraints at the ends of the rod is a sliding sleeve. This mechanical device generates a configurational force, causing the dripping of the rod, in a fully elastic set-up.
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