| 1. |
- Ståhle, Per, et al.
(författare)
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Interface instabilities of growing hydrides
- 2016
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Ingår i: Procedia Structural Integrity. - : Elsevier BV. - 2452-3216. ; 2, s. 589-596
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Tidskriftsartikel (refereegranskat)abstract
- Formation of metal hydrides is a serious complication that occur when hydride forming metals such as zirconium, niobium, vanadium and magnesium are exposed to long term hydrogen environment. The main concern is that the hydride, as being a brittle material, has very poor fracture mechanical properties. Formation of hydride is associated with transportation of hydrogen along the gradients of increasing hydrostatic stress, which leads to crack tips and other stress concentrators, where it forms the hydride. In the present study the thermodynamics of the evolving hydrides is studied. The process is driven by the release of free strain, chemical, and gradient energies. A phase field model is used to capture the driving forces that the release of the free energy causes. The study gives the conditions that lead to hydride advancement versus retreat and under which conditions the metal-hydride interface becomes unstable and develops a waviness. The spatial frequency spectrum leading to instability is found to depend on the ratio of the elastic strain energy density and parameters related to the interface energy.
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| 2. |
- Olsson, Pär, et al.
(författare)
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Ab initio and classical atomistic modelling of structure and defects in crystalline orthorhombic polyethylene : Twin boundaries, slip interfaces, and nature of barriers
- 2017
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Ingår i: Polymer. - : Elsevier Ltd. - 0032-3861 .- 1873-2291. ; 121, s. 234-246
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Tidskriftsartikel (refereegranskat)abstract
- We study the stability of twin boundaries and slip in crystalline orthorhombic polyethylene by means of density functional theory (DFT), using a nonempirical, truly nonlocal density function, and by means of classical molecular dynamics (MD). The results show that, in accordance with experimental observations, there is a clear preference to chain slip over transverse slip for all considered slip planes. The activation energy for pure chain slip lies in the range 10–20 mJ/m2 while that for transverse slip corresponds to 40–280 mJ/m2. For the (11¯0)-slip plane the energy landscape is non-convex with multiple potential energy minima, indicating the presence of stable stacking faults. This suggests that dissociation of perfect dislocations into partials may occur. For the two low-energy twin boundaries considered in this work, {110} and {310}, we find that the former is more stable than the latter, with ground state energies corresponding to 8.9 and 28 mJ/m2, respectively. We have also evaluated how well the empirical MD simulations with the all-atom optimized potential for liquid MD simulations (OPLS-AA) and the coarse-grained united atom (UA) potential concur with the DFT results. It is found that an all-atom potential is necessary to partially capture the γ-surface energy landscapes obtained from the DFT calculations. The OPLS-AA predicts chain slip activation energies comparable with DFT data, while the transverse slip energy thresholds are low in comparison, which is attributed to weak close ranged monomer repulsion. Finally, we find that the H-H interaction dominates the slip activation. While not explicitly represented in the UA potential, its key role is revealed by correlating the DFT energy landscape with changes in the electron distributions and by MD simulations in which components of the OPLS-AA intermolecular potential are selectively silenced. © 2017 Elsevier Ltd
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| 3. |
- Hedberg, Claes, et al.
(författare)
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Collisions, mutual losses and annihilation of pulses in a modular nonlinear medium
- 2017
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Ingår i: Nonlinear dynamics. - : Springer Netherlands. - 0924-090X .- 1573-269X. ; 90:3, s. 2083-2091
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Tidskriftsartikel (refereegranskat)abstract
- One of the most important sections of nonlinear wave theory is related to the collisions of single pulses. These often exhibit corpuscular properties. For example, it is well known that solitons described by the Korteweg–de Vries equation and a few other conservative model equations exhibit properties of elastic particles, while shock waves described by dissipative models like Burgers’ equation stick together as absolutely inelastic particles when colliding. The interactions of single pulses in media with modular nonlinearity considered here reveal new physical features that are still poorly understood. There is an analogy between the single pulses collision and the interaction of clots of chemical reactants, such as fuel and oxidant, where the smaller component disappears and the larger one decreases after a reaction. At equal “masses” both clots can be annihilated. In this work various interactions of two and three pulses are considered. The conditions for which a complete annihilation of the pulses occurs are indicated. © 2017 The Author(s)
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| 4. |
- Khamitova, Raisa
(författare)
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Symmetries and conservation laws
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided.Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws.One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.
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| 5. |
- Mikhailov, S. G., et al.
(författare)
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A simple nonlinear element model
- 2017
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Ingår i: Acoustical Physics. - : MAIK NAUKA/INTERPERIODICA/SPRINGER. - 1063-7710 .- 1562-6865. ; 63:3, s. 270-274
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Tidskriftsartikel (refereegranskat)abstract
- We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.
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| 6. |
- Nedic, Mitja, et al.
(författare)
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Herglotz functions and applications in electromagnetics
- 2020
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Ingår i: Advances in Mathematical Methods for Electromagnetics. - : Institution of Engineering and Technology. - 9781785613845 - 9781785613852 ; , s. 491-514
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.
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| 7. |
- Rudenko, Oleg
(författare)
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Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities
- 2016
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Ingår i: Doklady Mathematics. - : Maik Nauka/Interperiodica. - 1064-5624. ; 94:3, s. 703-707
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Tidskriftsartikel (refereegranskat)abstract
- A second-order partial differential equation admitting exact linearization is discussed. It contains terms with nonlinearities of three types—modular, quadratic, and quadratically cubic—which can be present jointly or separately. The model describes nonlinear phenomena, some of which have been studied, while others call for further consideration. As an example, individual manifestations of modular nonlinearity are discussed. They lead to the formation of singularities of two types, namely, discontinuities in a function and discontinuities in its derivative, which are eliminated by dissipative smoothing. The dynamics of shock fronts is studied. The collision of two single pulses of different polarity is described. The process reveals new properties other than those of elastic collisions of conservative solitons and inelastic collisions of dissipative shock waves.
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| 8. |
- Rudenko, Oleg
(författare)
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Modular solutions
- 2016
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Ingår i: Doklady Mathematics. - : Maik Nauka/Interperiodica. - 1064-5624. ; 94:3, s. 708-711
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Tidskriftsartikel (refereegranskat)abstract
- Solutions to a partial differential equation of the third order containing the modular nonlinearity are studied. The model describes, in particular, elastic waves in media with weak high-frequency dispersion and with different response to tensile and compressive stresses. This equation is linear for solutions preserving their sign. Nonlinear phenomena only manifest themselves to alternating solutions. Stationary solutions in the form of solitary waves or solitons are found. It is shown how the linear periodic wave becomes nonlinear after exceeding a certain critical value of the amplitude, and how it transforms into a soliton with further increase in the amplitude.
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| 9. |
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| 10. |
- Andreasson, Eskil, et al.
(författare)
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Micro-mechanisms of a laminated packaging material during fracture
- 2014
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Ingår i: Engineering Fracture Mechanics. - : Elsevier BV. - 1873-7315 .- 0013-7944. ; 127, s. 313-326
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Tidskriftsartikel (refereegranskat)abstract
- The micro-mechanisms of fracture in a laminate composed of an aluminium foil and a polymer film are considered in this study. The laminates as well as the individual layers, with and without premade centre-cracks, were tensile tested. Visual inspection of the broken cross-sections shows that failure occurs through localised plasticity. This leads to a decreasing and eventually vanishing cross-section ahead of the crack tip for both the laminate and their single constituent layers. Experimental results are examined and analysed using a slip-line theory to derive the work of failure. An accurate prediction was made for the aluminium foil and for the laminate but not for the freestanding polymer film. The reason seems to be that the polymer material switches to non-localised plastic deformation with significant strain-hardening. (C) 2014 Elsevier Ltd. All rights reserved.
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