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J Rheol 7:391–410
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Nonlinear Dyn 33:301–321
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J Rheol 27:351–372
171. Metzler R, Nonnenmacher T (2003) Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Int J Plast 19:941–959
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& Sorensen, Inc., Rhode Island
174. Shim VPW, Yang LM, Lim CT, Law PH (2004) A visco-hyperelastic constitutive model to
characterize both tensile and compressive behavior of rubber. J Appl Polym Sci 92:523–531
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Math Mech Solids 12:475–501
151. Fabrizio M, Giorgi C, Morro A (1995) Internal dissipation, relaxation property and freeenergy in materials with fading memory. J Elast 40:107–122
152. Del Piero G, Deseri L (1997) On the concepts of state and free energy in linear viscoelasticity.
Arch Rational Mech Anal 138:1–35
153. Fabrizio M, Morro A (1992) Mathematical problems in linear viscoelasticity. Society for
Industrial and Applied Mathematics, Philadelphia
154. Golden JM (2005) A proposal concerning the physical rate of dissipation in materials with
memory. Q Appl Math 63:117–155
155. Golden JM (2001) Consequences of non-uniqueness in the free energy of materials with
memory. Int J Eng Sci 39:53–70
156. Gurtin ME, Hrusa WJ (1988) On energies for nonlinear viscoelastic materials of singleintegral type. Q Appl Math 46:381–392
157. Ho ¨fer P, Lion A (2009) Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber. J Mech Phys Solids 57:500–520
158. Adolfsson K, Enelund M, Olsson P (2005) On the fractional order model of viscoelasticity.
Mech Time-Depend Mater 9:15–34
159. Hanyga A (2007) Fractional-order relaxation laws in non-linear viscoelasticity. Continuum
Mech Thermodyn 19:25–36
160. Hanyga A, Seredynska M (2007) Multiple-integral viscoelastic constitutive equations. Int J
Non Linear Mech 42:722–732
161. Pipkin AC, Rogers TG (1968) A non-linear integral representation for viscoelastic behaviour.
J Mech Phys Solids 16:59–72
162. Hassani S, Alaoui Soulimani A, Ehrlacher A (1998) A nonlinear viscoelastic model: the
pseudo-linear model. Eur J Mech A Solids 17:567–598
163. Lockett F (1972) Nonlinear viscoelastic solids. Academic, Boston
164. Fung YC (1972) Stress-strain-history relations of soft tissues in simple elongation. In: Fung
NPYC, Anliker M (eds) Biomechanics: its foundations and objectives. Prentice Hall, Englewood Cliffs, pp 181–208
165. Fosdick RL, Yu JH (1998) Thermodynamics, stability and non-linear oscillations of viscoelastic solids. 2. History type solids. Int J Non-Linear Mech 33:165–188
166. Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain.
J Rheol 7:391–410
167. Hanyga A (2005) Viscous dissipation and completely monotonic relaxation moduli. Rheol
Acta 44:614–621
168. Adolfsson K, Enelund M (2003) Fractional derivative viscoelasticity at large deformations.
Nonlinear Dyn 33:301–321
169. Gil-Negrete N, Vinolas J, Kari L (2009) A nonlinear rubber material model combining
fractional order viscoelasticity and amplitude dependent effects. J Appl Mech 76:011009
170. Rogers L (1983) Operators and fractional derivatives for viscoelastic constitutive equations.
J Rheol 27:351–372
171. Metzler R, Nonnenmacher T (2003) Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Int J Plast 19:941–959
172. Fosdick RL, Yu JH (1996) Thermodynamics, stability and non-linear oscillations of viscoelastic solids.1. Differential type solids of second grade. Int J Non-Linear Mech 31:495–516
173. Hibbit D, Karlsson B, Sorensen P (2007) ABAQUS/theory manual, 6th edn. Hibbitt, Karlsson
& Sorensen, Inc., Rhode Island
174. Shim VPW, Yang LM, Lim CT, Law PH (2004) A visco-hyperelastic constitutive model to
characterize both tensile and compressive behavior of rubber. J Appl Polym Sci 92:523–531
175. Hallquist J (1998) LS-DYNA theoretical manual. Livermore Software Technology
Corporation
270
G. Markovic ´ et al.