TY - JOUR
T1 - A continuum framework for mechanics of fractal materials I
T2 - from fractional space to continuum with fractal metric
AU - Balankin, Alexander S.
N1 - Publisher Copyright:
© 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
PY - 2015/4/8
Y1 - 2015/4/8
N2 - This paper is devoted to the mechanics of fractally heterogeneous media. A model of fractal continuum with a fractional number of spatial degrees of freedom and a fractal metric is suggested. The Jacobian matrix of the fractal continuum deformation is defined and the kinematics of deformations is elucidated. The symmetry of the Cauchy stress tensor for continua with the fractal metric is established. A homogenization framework accounting for the connectivity, topological, and metric properties of fractal domains in heterogeneous materials is developed. The mapping of mechanical problems for fractal media into the corresponding problems for the fractal continuum is discussed. Stress and strain distributions in elastic fractal bars are analyzed. An approach to fractal bar optimization is proposed. Some features of acoustic wave propagation and localization in fractal media are briefly highlighted.
AB - This paper is devoted to the mechanics of fractally heterogeneous media. A model of fractal continuum with a fractional number of spatial degrees of freedom and a fractal metric is suggested. The Jacobian matrix of the fractal continuum deformation is defined and the kinematics of deformations is elucidated. The symmetry of the Cauchy stress tensor for continua with the fractal metric is established. A homogenization framework accounting for the connectivity, topological, and metric properties of fractal domains in heterogeneous materials is developed. The mapping of mechanical problems for fractal media into the corresponding problems for the fractal continuum is discussed. Stress and strain distributions in elastic fractal bars are analyzed. An approach to fractal bar optimization is proposed. Some features of acoustic wave propagation and localization in fractal media are briefly highlighted.
KW - Solid State and Materials
UR - http://www.scopus.com/inward/record.url?scp=84928251872&partnerID=8YFLogxK
U2 - 10.1140/epjb/e2015-60189-y
DO - 10.1140/epjb/e2015-60189-y
M3 - Artículo
AN - SCOPUS:84928251872
SN - 1434-6028
VL - 88
JO - European Physical Journal B
JF - European Physical Journal B
IS - 4
M1 - 90
ER -