Artur V. Dmitrenko^1,2,*, Vladislav M. Ovsyannikov²

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.9, pp. 1925-1939, 2024, DOI:10.32604/fdmp.2024.048389 - 23 August 2024

Abstract The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields. These equations contain derivatives of the first order with respect to time. The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero. Derivatives are used to derive the wave equation. The differential wave equation is second order in time. Therefore, increments of volume and increments of time in continuum mechanics should be considered as small but finite More >

S.Ahmadi¹, B.L.Adams¹ , D.T.Fullwood¹

CMC-Computers, Materials & Continua, Vol.14, No.2, pp. 141-170, 2009, DOI:10.3970/cmc.2009.014.141

Abstract In this paper, a model is introduced to examine the evolution of the microstructure function under plastic deformations. This model is based upon a double continuity relationship that conserves both material particles in the mass space and orientations in the orientation space. An Eulerian description of the motion of material particles and orientations is considered, and continuity relations are derived for both spaces. To show how the proposed model works, two different case studies are provided. In the mass space, the continuity relation is used to examine the evolution of the microstructure function of a More >