A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy

2006 ◽  
Vol 25 (3) ◽  
pp. 483-496 ◽  
Author(s):  
J. Diani ◽  
M. Brieu ◽  
J.M. Vacherand
2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Yin Liu ◽  
Hongwu Zhang ◽  
Yonggang Zheng

This paper presents a micromechanically based constitutive model within the framework of the continuum mechanics to characterize the inelastic elastomeric and swelling behaviors of double network (DN) hydrogels, such as the stress-softening, necking instability, hardening, and stretch-induced anisotropy. The strain-energy density function of the material is decomposed into two independent contributions from the tight and brittle first network and the soft and loose second network, each of which is obtained by integrating the strain energy of one-dimensional (1D) polymer chains in each direction of a unit sphere. The damage process is derived from the irreversible breakages of sacrificial chains in the first network and characterized by the directional stretch-dependent evolution laws for the equivalent modulus and the locking stretch in the non-Gauss statistical model of a single polymer chain. The constitutive model with the optimized-material evolution law predicts stress–stretch curves in a good agreement with the experimental results during loading, unloading, and reloading paths for both ionic and covalent DN hydrogels. The deformation-induced anisotropy is investigated and demonstrated by the constitutive model for the free swelling of damaged specimen. The constitutive model is embedded into the finite-element (FE) procedure and proved to be efficient to model the necking and neck propagation in the plane-strain uniaxial elongation. Based on the procedure, the effects of imperfection and boundary conditions on the loading path and the material evolution during different stages of deformation are investigated.


Author(s):  
Amir Bahrololoumi ◽  
Roozbeh Dargazany

Abstract The effect of hydrolytic aging on mechanical responses of Rubber likes materials, in particular, Mullins effect and the permanent set has been modeled. Hydrolytic aging is considered as the result of the competition between two phenomena (1) chain scission and (2) cross-link scission/reformation. Both phenomena were modeled and thus, the strain energy of the polymer matrix is written with respect to three independent mechanisms; i) the shrinking original matrix which has not been attacked by water, ii) conversion of the first network to a new network due to the reduction of the crosslinks, and iii) energy loss from network degradation due to water attacks to ester groups. The model is validated with respect to a set of experimental data. Besides accuracy, the simplicity and few numbers of fitting parameters make the model a good choice for further implementations.


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