The present research introduces a model of surface growth of bone tissue based on the principles of thermodynamics and mechanics of configurational forces. In this work, a kinetic equation is formulated and an expression of the normal component of the surface growth tensor governing surface growth is derived. Surface growth tensor controls the growth and adaptation of bone tissue and determines the rate of these processes depending on the applied loads and the initial characteristics of the body. The developed approach takes into account the growth strains and stresses in the growing layer. The analysis of the applicability of the model is carried out for problems of surface growth of a body under axial compression and bending.
REFERENCES
1.
J.
Wolff
, Das Gesetz der Transformation der Knochen
(A. Hirschwald
, Berlin
, 1892
), p. 300
.2.
3.
A.
Goriely
, The Mathematics and Mechanics of Biological Growth
(Springer-Verlag
, New York
, 2017
).4.
S. A.
Lychev
and A. V.
Manzhirov
, Journal of Applied Mathematics and Mechanics
77
(4
), 421
–432
(2013
).5.
J.-F.
Ganghoffer
and I.
Goda
, International Journal of Engineering Science
127
, 53
–79
(2018
).6.
A. B.
Freidin
and E. N.
Vilchevskaya
, “Chemical Affinity Tensor in Coupled Problems of Mechanochemistry”, in Encyclopedia of Continuum Mechanics
, edited by H.
Altenbach
, and A.
Öchsner
(Springer
, Berlin, Heidelberg
, 2020
).7.
A. B.
Freidin
, E. N.
Vilchevskaya
and I. K.
Korolev
, International Journal of Engineering Science
83
, 57
–75
(2014
).8.
A. B.
Freidin
, Mechanics of Solids
50
(3
), 260
–285
(2015
).9.
A. B.
Freidin
and Y. O.
Izmaylova
, Materials Physics and Mechanics
42
, 582
–595
(2019
).
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