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  • Open Access

    REVIEW

    Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

    Artur V. Dmitrenko1,2,*, Vladislav M. Ovsyannikov2

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

    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 >

  • Open Access

    ARTICLE

    An Eulerian-Based Formulation for Studying the Evolution of the Microstructure under Plastic Deformations

    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 >

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