Geodesic
Global solvability of the regularized problem of the volumetric growth of hyperelastic materials
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 3, pp. 11-23

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a model of volumetric growth of biological materials in the framework of finite elasticity. Surface effects on the boundary with the environment are taken into account. New mathematical results are obtained for the model, the main of which is a complete proof of global existence of a solution. The results can be used in further scientific developments at the juncture of biology and mechanics.
Keywords: volumetric growth
Mots-clés : existence of global solutions. 
A. V. Beskrovnykh. Global solvability of the regularized problem of the volumetric growth of hyperelastic materials. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 3, pp. 11-23. http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a1/
@article{SJIM_2017_20_3_a1,
     author = {A. V. Beskrovnykh},
     title = {Global solvability of the regularized problem of the volumetric growth of hyperelastic materials},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {11--23},
     year = {2017},
     volume = {20},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a1/}
}
TY  - JOUR
AU  - A. V. Beskrovnykh
TI  - Global solvability of the regularized problem of the volumetric growth of hyperelastic materials
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 11
EP  - 23
VL  - 20
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a1/
LA  - ru
ID  - SJIM_2017_20_3_a1
ER  - 
%0 Journal Article
%A A. V. Beskrovnykh
%T Global solvability of the regularized problem of the volumetric growth of hyperelastic materials
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 11-23
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a1/
%G ru
%F SJIM_2017_20_3_a1

[1] Rodriguez E. K., Hoger A., McCulloch A. D., “Stress-dependent finite growth in soft elastic tissues”, J. Biomechanics, 27:4 (1994), 455–467 | DOI

[2] Epstein M., Maugin G. A., “Thermomechanics of volumetric growth in uniform bodies”, Internat. J. Plasticity, 16:7 (2000), 951–978 | DOI | Zbl

[3] Epstein M., Elzanowski M., Material Inhomogeneities and Their Evolution: A Geometric Approach, Springer, Berlin, 2007 | MR

[4] Falk F., “Elastic phase transitions and nonconvex energy functions”, Free Boundary Problems: Theory and Applications, 1 (1990), 45–59 | MR

[5] Sprekels J., Zheng S., “Global solutions to the equations of a Ginzburg–Landau theory for structural phase transitions in shape memory alloys”, Physica D: Nonlinear Phenomena, 39:1 (1989), 59–76 | DOI | MR | Zbl

[6] Ciarletta P., Ambrosi D., Maugin G. A., “Mass transport in morphogenetic processes: a second gradient theory for volumetric growth and material remodeling”, J. Mech. Phys. Solids, 60:3 (2012), 432–450 | DOI | MR | Zbl

[7] Plotnikov P., Ganghoffer J. F., Sokolowski J., “Volumetric growth of solid bodies: mechanical framework and mathematical aspects”, Computer Methods in Mechanics (9–12 May 2011)

[8] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Editorial URSS, M., 2002 | MR

[9] Simon J., “Compact sets in the space $L^p(0,T;B)$”, Ann. Math. Pure Appl., 146 (1988), 65–96 | DOI | MR