TY - JOUR
T1 - A path-following simulation-based study of elastic instabilities in nearly-incompressible confined cylinders under tension
AU - Giovanardi, Bianca
AU - Śliwiak, Adam A.
AU - Koshakji, Anwar
AU - Lin, Shaoting
AU - Zhao, Xuanhe
AU - Radovitzky, Raúl
PY - 2019
Y1 - 2019
N2 - Recent experiments on hydrogels subjected to large elongations have shown elastic instabilities resulting in the formation of geometrically intricate fringe and fingering deformation patterns. In this paper, we present a robust numerical framework addressing the challenges that emerge in the simulation of this complex material response from the onset of instability to the post-bifurcation behavior. We observe that the numerical difficulties stem from the non-convexity of the strain energy density in the near-incompressible, large-deformation regime, which is responsible for the coexistence of multiple equilibrium paths with vastly-different, sinuous deformation patterns immediately after bifurcation. We show that these numerical challenges can be overcome by using sufficiently-high order of interpolation in the finite element approximation, an arc-length-based nonlinear solution procedure that follows the entire equilibrium path of the system, and an implementation enabling parallel, large-scale simulations. The resulting computational approach provides the ability to conduct highly-resolved, truly quasi-static simulations of complex elastic instabilities. We present numerical results illustrating the ability of the path-following approach to describe the full evolution of fringe and fingering instabilities observed experimentally in recent experiments of confined cylindrical specimens of soft hydrogels subject to tension. Importantly, we observe that the robustness of the static solution procedure enables complete access to the multiplicity of solutions occurring immediately after the onset of bifurcation, as well as to the settled post-bifurcation states.
AB - Recent experiments on hydrogels subjected to large elongations have shown elastic instabilities resulting in the formation of geometrically intricate fringe and fingering deformation patterns. In this paper, we present a robust numerical framework addressing the challenges that emerge in the simulation of this complex material response from the onset of instability to the post-bifurcation behavior. We observe that the numerical difficulties stem from the non-convexity of the strain energy density in the near-incompressible, large-deformation regime, which is responsible for the coexistence of multiple equilibrium paths with vastly-different, sinuous deformation patterns immediately after bifurcation. We show that these numerical challenges can be overcome by using sufficiently-high order of interpolation in the finite element approximation, an arc-length-based nonlinear solution procedure that follows the entire equilibrium path of the system, and an implementation enabling parallel, large-scale simulations. The resulting computational approach provides the ability to conduct highly-resolved, truly quasi-static simulations of complex elastic instabilities. We present numerical results illustrating the ability of the path-following approach to describe the full evolution of fringe and fingering instabilities observed experimentally in recent experiments of confined cylindrical specimens of soft hydrogels subject to tension. Importantly, we observe that the robustness of the static solution procedure enables complete access to the multiplicity of solutions occurring immediately after the onset of bifurcation, as well as to the settled post-bifurcation states.
KW - Arc-length nonlinear solver
KW - Elastic instabilities
KW - Fringe and fingering in solids
KW - Large-scale simulation
KW - Soft materials
UR - http://www.scopus.com/inward/record.url?scp=85068877247&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2019.06.020
DO - 10.1016/j.jmps.2019.06.020
M3 - Article
AN - SCOPUS:85068877247
SN - 0022-5096
VL - 131
SP - 252
EP - 275
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
ER -