arXiv subjects

Andrzej Trzesowski

Publications and source records attributed to Andrzej Trzesowski.

7 recordsLinked to original sources

arXiv2015

On the dynamics and thermodynamics of small Markov-type material systems

The collective properties of small material systems considered as semidynamical systems revealing the Markov-type irreversible evolution, are investigated. It is shown that these material systems admit their treatment as thermodynamic systems in diathermal and isothermal conditions. A kinetic equation describing statistical regularities of the Markov-type material systems and constrained by the compatibility condition with the first and second laws of thermodynamics and with the relaxation postulate, is proposed. The influence of external parameters on the Gibbs distribution of small material systems is discussed.

math-ph↗

arXiv2014

On the material geometry of continuously defective corrugated graphene sheets

Geometrical objects describing the material geometry of continuously defective graphene sheets are introduced and their compatibility conditions are formulated. Effective edge dislocations embedded in the Riemann-Cartan material space and defined by their scalar density and by local Burgers vectors, are considered. The case of secondary curvature-type defects created by this distribution of dislocations is analysed in terms of the material space. The variational geometry of the material space closely related with the existence of a characteristic length parameter is proposed. The formula which describes, in a reference temperature, the influence of dislocations on the material Riemannian metric, is given.

math-ph↗

arXiv2014

On the isothermal geometry of corrugated graphene sheets

Variational geometries describing corrugated graphene sheets are proposed. The isothermal thermomechanical properties of these sheets are described by a 2-dimensional Weyl space. The equation that couples the Weyl geometry with isothermal distributions of the temperature of graphene sheets, is formulated. This material space is observed in a 3-dimensional orthogonal configurational point space as regular surfaces which are endowed with a thermal state vector field fulfilling the isothermal thermal state equation. It enables to introduce a non-topological dimensionless thermal shape parameter of non-developable graphene sheets. The properties of the congruence of lines generated by the thermal state vector field are discussed.

math-ph↗

arXiv2010

Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations

The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congruences of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.

math-ph↗

arXiv2010

Nanothermomechanics

The paper concerns the dependence of thermomechanical properties of three-dimensional solid nanoclusters on the cluster size as well as on its shape. Investigations are restricted to the class of so-called homogeneous thermodynamic processes with kinematics based on affine group and referred to the one whole body, not an infinite system of subbodies. It is shown that then the thermodynamics of nanoclusters is consistent with dynamics of affinely-rigid bodies (constrained or not and elastic as well as admitting viscosity effects). The main discussed top-ics are: (i) a group-theoretical description of structurally stable solid nanoclusters; (ii) a phe-nomenological model of mechanical properties of nanoclusters revealing the coexistence of solid and liquid states in a finite interval of absolute temperature.

cond-mat.mtrl-sci↗

arXiv2008

Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity

A continuous geometric description of Bravais monocrystals with many dislocations and secondary point defects created by the distribution of these dislocations is proposed. Namely, it is distinguished, basing oneself on Kondo and Kroners Gedanken Experiments for dislocated bodies, an anholonomic triad of linearly independent vector fields. The triad defines local crystallographic directions of the defective crystal as well as a continuous counterpart of the Burgers vector for single dislocations. Next, the influence of secondary point defects on the distribution of many dislocations is modeled by treating these local crystallographic directions as well as Burgers circuits as those located in such a Riemannian material space that becomes an Euclidean 3-manifold when dislocations are absent. Some consequences of this approach are discussed.

math-ph↗

arXiv2008

Effective dislocation lines in continuously dislocated crystals. III. Kinematics

A class of congruences of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their dislocation densities (tensorial as well as scalar). Moreover, it shown, basing oneself on a formula defining the mean curvature of glide surfaces for principal edge effective dislocation lines, that the considered kinematics of continuized defective crystals is consistent with some relations appearing in the physical theory of plasticity (e.g. with the Orowan-type kinematic relations and with the treatment of shear stresses as driving stresses of moving dislocations).

math-ph↗