Mechanics of Growing Solids and Phase Transitions

Abstract

Phase transitions can be usually observed in nature and technology which effectively utilize certain types of these transitions. An approach to modeling phase transition processes on the basis of the mathematical theory of growing solids is developed. Liquid-solid and gas-solid phase transitions are under consideration. Main attention is paid to the processes of solid phase growth and deformation.

A Method for Mechanical Design of AM Fabricated Viscoelastic Parts

“…One can obtain a number of interesting results from (13), (20), (24), (14) and (22) using the property of limited creep of a viscoelastic material (see also [3][4][5][6][7][8][9][10][11][12][13][14][15]). If one assumes that only the surface of the basic solid is subject to a load, the actions are stationary, and accretion does not involve pretension, then the interaction between newly deposited particles and the solid already formed can be neglected starting from some instant t 0 .…”

Mechanical Design of AM Fabricated Prismatic Rods under Torsion

“…The lateral surface 1 Somewhat later, at time 2 3 W t W , accretion may begin again; it may well happen that the new growth boundary is not related in any way to the earlier existing one. Then one can assume that accretion terminates at time 4 W , etc., thus successively arriving at the problem of piecewise continuous accretion of a solid rod with n growth beginning instants and accordingly n growth termination instants.…”

“…From now on, we consider sufficiently slow processes, and so inertial terms in the equilibrium equations can be neglected (also see [1][2][3][4][5][6][7]). …”

Quasistatic problems for piecewise-continuously growing solids with integral force conditions on surfaces expanding due to additional material influx

“…It is made from isotropic homogeneous aging linearly viscoelastic material subordinated to the constitutive equation (1). Take the moment of this material nucleation be the start of timing t. At the moment t = t 0 a load is applied to the ends of the existing solid.…”

“…This is due to the lack of any configuration of the continuously growing solid which could be associated with introduction of the strain measures. An adequate description of mechanical behavior of solids deforming in processes of their continuous growing can be given on the basis of approaches and methods of mechanics of growing solids being actively developed nowadays [1][2][3][4][5][6][7][8][9][10][11].…”