124. Coleman BD, Noll W (1961) Foundations of linear viscoelasticity. Rev Mod Phys
33:239–249
125. Coleman BD (1964) Thermodynamics of materials with memory. Arch Rational Mech Anal
17:1–46
126. Coleman BD, Gurtin ME (1967) Thermodynamics with Internal State Variables. J Chem
Phys 47:597–613
127. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction
and viscosity. Arch Rational Mech Anal 13:167–178
128. Holzapfel GA (1996) On large strain viscoelasticity: Continuum formulation and finite
element applications to elastomeric structures. Int J Num Methods Eng 39:3903–3926
129. Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at
finite strains: continuum basis, computational aspects and applications. Comput Meth Appl
Mech Eng 190:4379–4403
130. Yoshida J, Abe M, Fujino Y (2004) Constitutive model of high-damping rubber materials.
J Eng Mech 130:129–141
131. Meggyes A (2001) Multiple decomposition in finite deformation theory. Acta Mech
146:169–182
132. Sidoroff F (1974) Nonlinear viscoelastic model with an intermediate configuration.
J Me ´caniques 13:679–713
133. Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12:93–99
134. Green M, Tobolsky A (1946) A new approach to the theory of relaxing polymeric media.
J Chem Phys 14:80–92
135. Bonet J (2001) Large strain viscoelastic constitutive models. Int J Solids Struct 38:2953–2968
136. Hasanpour K, Ziaei-Rad S, Mahzoon M (2009) A large deformation framework for compressible viscoelastic materials: constitutive equations and finite element implementation. Int
J Plast 25:1154–1176
137. Haupt P, Sedlan K (2001) Viscoplasticity of elastomeric materials: experimental facts and
constitutive modelling. Arch Appl Mech 71:89–109
138. Hoo Fatt M, Al-Quraishi A (2008) High strain rate constitutive modeling for natural rubber.
In: Proceedings of the 5th European Conference on Constitutive Models for Rubber, ECCMR
2007. University of Akron, Akron, OH, United States, pp 53–60
139. Huber N, Tsakmakis C (2000) Finite deformation viscoelasticity laws. Mech Mater 32:1–18
140. Lion A (1997) A physically based method to represent the thermo-mechanical behaviour of
elastomers. Acta Mech 123:1–25
141. Vidoli S, Sciarra G (2002) A model for crystal plasticity based on micro-slip descriptors.
Continuum Mech Thermodyn 14:425–435
142. Haupt P, Lion A, Backhaus E (2000) On the dynamic behaviour of polymers under finite
strains: constitutive modelling and identification of parameters. Int J Solids Struct
37:3633–3646
143. Haupt P (1985) On the concept of an intermediate configuration and its application to a
representation of viscoelastic-plastic material behavior. Int J Plast 1:303–316
144. Haupt P, Lion A (2002) On finite linear viscoelasticity of incompressible isotropic materials.
Acta Mech 159:87–124
145. Hoo Fatt MS, Ouyang X (2007) Integral-based constitutive equation for rubber at high strain
rates. Int J Solids Struct 44:6491–6506
146. Huber G, Vilgis TA, Heinrich G (1996) Universal properties in the dynamical deformation of
filled rubbers. J Phys Cond Matter 8:L409–L412
147. Fancello E, Ponthot J, Stainier L (2008) A variational framework for nonlinear viscoelastic
models in finite deformation regime. J Comput Appl Math 215:400–408
148. Green AE, Rivlin RS (1957) The mechanics of non-linear materials with memory. Arch
Rational Mech Anal 1:1–21
149. Fichera G (1979) Avere una memoria tenace crea gravi problemi. Arch Rational Mech Anal
70:101–112
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
269
33:239–249
125. Coleman BD (1964) Thermodynamics of materials with memory. Arch Rational Mech Anal
17:1–46
126. Coleman BD, Gurtin ME (1967) Thermodynamics with Internal State Variables. J Chem
Phys 47:597–613
127. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction
and viscosity. Arch Rational Mech Anal 13:167–178
128. Holzapfel GA (1996) On large strain viscoelasticity: Continuum formulation and finite
element applications to elastomeric structures. Int J Num Methods Eng 39:3903–3926
129. Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at
finite strains: continuum basis, computational aspects and applications. Comput Meth Appl
Mech Eng 190:4379–4403
130. Yoshida J, Abe M, Fujino Y (2004) Constitutive model of high-damping rubber materials.
J Eng Mech 130:129–141
131. Meggyes A (2001) Multiple decomposition in finite deformation theory. Acta Mech
146:169–182
132. Sidoroff F (1974) Nonlinear viscoelastic model with an intermediate configuration.
J Me ´caniques 13:679–713
133. Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12:93–99
134. Green M, Tobolsky A (1946) A new approach to the theory of relaxing polymeric media.
J Chem Phys 14:80–92
135. Bonet J (2001) Large strain viscoelastic constitutive models. Int J Solids Struct 38:2953–2968
136. Hasanpour K, Ziaei-Rad S, Mahzoon M (2009) A large deformation framework for compressible viscoelastic materials: constitutive equations and finite element implementation. Int
J Plast 25:1154–1176
137. Haupt P, Sedlan K (2001) Viscoplasticity of elastomeric materials: experimental facts and
constitutive modelling. Arch Appl Mech 71:89–109
138. Hoo Fatt M, Al-Quraishi A (2008) High strain rate constitutive modeling for natural rubber.
In: Proceedings of the 5th European Conference on Constitutive Models for Rubber, ECCMR
2007. University of Akron, Akron, OH, United States, pp 53–60
139. Huber N, Tsakmakis C (2000) Finite deformation viscoelasticity laws. Mech Mater 32:1–18
140. Lion A (1997) A physically based method to represent the thermo-mechanical behaviour of
elastomers. Acta Mech 123:1–25
141. Vidoli S, Sciarra G (2002) A model for crystal plasticity based on micro-slip descriptors.
Continuum Mech Thermodyn 14:425–435
142. Haupt P, Lion A, Backhaus E (2000) On the dynamic behaviour of polymers under finite
strains: constitutive modelling and identification of parameters. Int J Solids Struct
37:3633–3646
143. Haupt P (1985) On the concept of an intermediate configuration and its application to a
representation of viscoelastic-plastic material behavior. Int J Plast 1:303–316
144. Haupt P, Lion A (2002) On finite linear viscoelasticity of incompressible isotropic materials.
Acta Mech 159:87–124
145. Hoo Fatt MS, Ouyang X (2007) Integral-based constitutive equation for rubber at high strain
rates. Int J Solids Struct 44:6491–6506
146. Huber G, Vilgis TA, Heinrich G (1996) Universal properties in the dynamical deformation of
filled rubbers. J Phys Cond Matter 8:L409–L412
147. Fancello E, Ponthot J, Stainier L (2008) A variational framework for nonlinear viscoelastic
models in finite deformation regime. J Comput Appl Math 215:400–408
148. Green AE, Rivlin RS (1957) The mechanics of non-linear materials with memory. Arch
Rational Mech Anal 1:1–21
149. Fichera G (1979) Avere una memoria tenace crea gravi problemi. Arch Rational Mech Anal
70:101–112
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
269