ISSN:
eISSN:
1450-5584
2406-0925

Theoretical and Applied Mechanics

Теоријска и примењена механика

Articles in Press


A pileup of screw dislocations against an inclined bimetallic interface
Vlado A. Lubarda
Available online 07 September 2017

Abstract
Pileups of screw dislocations against an inclined bimetallic interface are considered. It is assumed that differently oriented pileups are either under the same remote uniform loading, or under the same resolved shear stress along the pileup direction for any orientation of the interface. The distributions of dislocations and the lengths of pileups are substantially different for differently oriented interfaces, particularly in the case of the same remote loading. The interface stresses are also strongly depended on the pileup orientation. The maximum stress can be higher for a pileup along an inclined direction than along the direction orthogonal to the interface. The back stress behind a pileup is evaluated and discussed.

Mathematics Subject Classification
74B99; 74L99

Keywords
back stress, bimetallic interface, dislocation pileup, screw dislocation, stress concentration

DOI
https://doi.org/10.2298/TAM170504007L


The Routh theorem for mechanical systems with unknown first integrals
Alexander V. Karapetyan and Alexander S. Kuleshov
Available online 18 September 2017

Abstract
In this paper we discuss problems of stability of stationary motions of conservative and dissipative mechanical systems with first integrals. General results are illustrated by the problem of motion of a rotationally symmetric rigid body on a perfectly rough plane.

Mathematics Subject Classification
70K20; 70E50; 70E18

Keywords
mechanical systems, first integrals, stability

DOI
https://doi.org/10.2298/TAM170512008K


(In)Compressibility and parameter identification in phase field models for capillary flows
M. Dehsara, H. Fu, S. Dj. Mesarović, D. P. Sekulić, and M. Krivilyov
Available online 26 September 2017

Abstract
Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibility within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the CC model against sharp interface theory and experimental kinetics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.

Mathematics Subject Classification
76T10

Keywords
diffusive triple line motion, no-slip boundary condition, quasi-compressibility, computational instabilities

DOI
https://doi.org/10.2298/TAM170803009D


A note on the complete instability of linear non-conservative undamped systems
Ranislav M. Bulatović
Available online 02 November 2017

Abstract
The note is concerned with the problem of determining the completely unstable linear non-conservative undamped (circulatory) dynamical systems. Several conditions that provide the complete instability for such systems are derived using the direct method of Lyapunov and the concept of controllability. The conditions are expressed directly via the matrices describing the dynamical system.

Mathematics Subject Classification
70J25; 70H14

Keywords
non-conservative system, degree of instability, complete instability

DOI
https://doi.org/10.2298/TAM170620010B


Ut Vis Sic Tensio
Giuseppe Saccomandi
Available online 03 November 2017

Abstract
The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

Mathematics Subject Classification
74B20

Keywords
hyper-elasticity, simple extension, phenomenological reduction, non-Gaussian effects

DOI
https://doi.org/10.2298/TAM170703011S


Variational model of scoliosis
Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, and Stepan Bober
Available online 07 November 2017

Abstract
Scoliosis, being one of the most widespread spine diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of three-dimensional deformation of human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. The numerical properties of the first stage of scoliosis are investigated, which is shown to have the highest influence on the development of the disease.

Mathematics Subject Classification
92C10; 74L15

Keywords
spine, model, variational method

DOI
https://doi.org/10.2298/TAM170818012P


On geometrization of some nonholonomic systems
Aleksandar Bakša
Available online 14 November 2017

Abstract

Mathematics Subject Classification
37J60; 70F25; 53C22; 53B05

Keywords
Chaplygin systems, affine connections, the Jacobi metric

DOI
https://doi.org/10.2298/TAM171110013B