非線性凝膠材料為高分子網絡所構成，其網絡縫隙中充斥著溶液，而溶液潤脹程度情形影響材料力學行為，於變形量小時材料行為符合線性孔彈理論，而於變形量大則固體網絡之應力應變關係不再遵循線性。
本文分析在平面應變情形下之非線性凝膠中心裂縫問題，考慮裂縫面為可滲透及不可滲透，並於遠端加載應力由σ_0/μ=0.0001逐漸增加至σ_0/μ=0.2，運用有限元素模擬，並使用虛擬裂縫閉合法計算能量釋放率。當遠端應力較小時，能量釋放率符合線性孔彈理論預測；當遠端應力較大時，裂縫尖端產生大變形行為，不僅能量釋放率偏離線性孔彈理論，裂縫尖端行為，包含應力、孔隙水壓及位移量都隨遠端施加應力增加而由線性孔彈行為轉變為大變形行為。
當溶液流入裂縫尖端，易導致尖端之凝膠材料等效剪力模數下降，然而裂縫尖端發生大變形，固體網絡之材料勁度上升，兩者皆影響裂縫尖端之行為與能量釋放率。

Nonlinear gels consist of polymeric network and solvents. The interaction between solid network and solvents affects the mechanical properties. At small deformation, the gels behave as poroelastic materials, whereas at large deformation, the stress-strain relation of solid networks does not follow the linear law.
In this study, a center crack in a nonlinear gel was analyzed under plane strain condition. The crack faces were considered permeable or impermeable. The loading stress was applied remotely from σ_0/μ=0.0001 to σ_0/μ=0.2, where μ is the shear modulus at infinitesimal strain. The analyses were carried out by finite element simulations. The energy release rate was calculated by the virtual crack closure technique (VCCT). When the remote stress is small, the energy release rate agrees with the prediction given by poroelastic theory. When the remote stress is large, not only the energy release rate deviates from the poroelastic theory, but also the near crack tip fields including stress, pore pressure and displacement transform from poroelastic predictions to the behaviors of large deformation.
When solvents flow into the crack tip region, the shear modulus in the region decreases. However, the large deformation occurring near crack tip enhances the property of the solid networks. Both should influence the crack tip behaviors as well as the energy release rate.

Atkinson, C.,Craster, R. V. ,Plane-strain fracture in poroelastic media, Proc R Soc London Ser.A-Math Phys.Eng.Sci.434.605-633,1991

Atkinson, C.,Craster, R.V., A singular perturbation approach to integral equations occurring in poroelasticity. IMA Journal of Applied Mathematics, 52(3), 221-252,1994

Atkinson, C.,Craster, R. V. , Theoretical Aspects of Fracture in Porous Elastic Media, Mechanics of Poroelastic Media ,23-45,1996

Anderson,T.L, Fracture Mechanics:Fundamentaks and Applications, Third Edition,CRC Press,Boca Raton,FL,Pages25-133,2005

Biot M.A.,General Theory of Three‐Dimensional Consolidation,Journal of Applied Physics 12,155,1941

Bouklas, N.,Huang, R., Swelling kinetics of polymer gels: Comparison of linear and nonlinear theories. Soft Matter, 8(31),2012

Bouklas, N., Landis, C. M., Huang, R., Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels. Journal of Applied Mechanics, 82(8),2015

Griffith, A.A., "The Phenomena of Rupture and Flow in Solids," Philosophical Transactions, Series A, Vol. 221, 63-198, 1920.

Geubelle, P. H.,Knauss, W. G.,Finite strains at the tip of a crack in a sheet of hyperelastic material: II. Special bimaterial cases. Journal of Elasticity, 35(1-3), 99-137,1994.

Hui, C., Muralidharan, V.,Gel mechanics: A comparison of the theories of Biot and Tanaka, Hocker, and Benedek. The Journal of Chemical Physics, 123(15), 2005

Hong, W., Zhao, X., Zhou, J.,Suo, Z.,A theory of coupled diffusion and large deformation in polymeric gels,Journal of the Mechanics and Physics of Solids, 56(5),2008

Irwin, G. R., Onset of Fast Crack Propagation in High Strength Steels and Aluminium Alloys, NRL Report 4763 (1956)

Krueger, R. ,Virtual crack closure technique: History, approach, and applications. Applied Mechanics Reviews, 57(2),2004

Long, R., Krishnan, V. R.,Hui, C. ,Finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress. Journal of the Mechanics and Physics of Solids, 59(3), 672-695,2011

Pizzocolo, F., Huyghe, J., Ito, K, Mode I crack propagation in hydrogels is step wise. Engineering Fracture Mechanics, 97, 72-79,2013

Rice, J. R., A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35(2), 379-386, 1968

Rice, J. R.,Cleary, M. P., Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics, 14(2), 227,1976

Scherer, G.W.,Drying gels:VIII.Revision and review . Journal of Non-Crystalline Solids,109(2-3),171-182,1989

Tanaka, T., Hocker, L. O.,Benedek, G. B., Spectrum of light scattered from a viscoelastic gel, The Journal of Chemical Physics, 59(9),1973

Tarantino, A. M.,Thin Hyperelastic sheets of compressible material: Field equations, airy stress function and an application in fracture mechanics. Journal of Elasticity, 44(1), 37-59,1996

Wong, F. S.,Shield, R. T., Large plane deformations of thin elastic sheets of neo-Hookean material. Zeitschrift Für Angewandte Mathematik Und Physik ZAMP, 20(2), 176-199,1969

Wang, X., Hong, W.,Delayed fracture in gels. Soft Matter, 8(31), 2012

楊承學,Analyses on Time-dependent Fracture and Surface Instabilities of Polymeric Gels,國立成功大學博士論文,2018