Mots-clés : existence of global solutions.
@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 -
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/
[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