Theory and identification of a constitutive model of induced anisotropy by the Mullins effect

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.

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A constitutive model for gravelly soils considering shear-induced volumetric deformation

Canadian Geotechnical Journal ◽

10.1139/t09-135 ◽

2010 ◽

Vol 47 (6) ◽

pp. 662-673 ◽

Cited By ~ 21

Author(s):

Bin-Lin Chu ◽

Yeun-Wen Jou ◽

Meng-Chia Weng

Keyword(s):

Hydrostatic Pressure ◽

Constitutive Model ◽

Triaxial Compression ◽

Compression Tests ◽

Induced Anisotropy ◽

Volumetric Deformation ◽

Proposed Model ◽

Gravelly Soils ◽

Deformational Behavior ◽

Stress Induced Anisotropy

This study elucidates the deformational behavior of gravelly soils by analyzing how hydrostatic pressure and pure shearing affect deformational behavior. A series of drained, triaxial compression tests have been performed using large specimens made of gravelly soils, where the grain-size distribution curve was based on the field condition. The volumetric and shear deformations of gravelly soils have been determined by performing experiments with controlled stress paths — hydrostatic pressure was applied first followed by pure shearing. A simple and innovative constitutive model is also proposed. The proposed model is characterized by the following features of gravelly soils: (i) significant shear-induced volumetric deformation prior to failure, (ii) modulus stiffening under hydrostatic loading and degradation under shearing, and (iii) stress-induced anisotropy. In the proposed model, deformational moduli K and G vary according to the stress state. The stiffening and degradation of these moduli result in diverse deformational behavior of gravelly soils. In addition, an anisotropic factor, β, is introduced to represent stress-induced anisotropy. Moreover, the proposed model only requires eight material parameters; each of which can be obtained easily from experiments.

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Biaxial shear behaviour of HDNR with Mullins effect and deformation-induced anisotropy

Engineering Structures ◽

10.1016/j.engstruct.2017.10.060 ◽

2018 ◽

Vol 154 ◽

pp. 78-92 ◽

Cited By ~ 8

Author(s):

Laura Ragni ◽

Enrico Tubaldi ◽

Andrea Dall'Asta ◽

Hamid Ahmadi ◽

Alan Muhr

Keyword(s):

Shear Behaviour ◽

Mullins Effect ◽

Induced Anisotropy

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Pseudo Elastic Analysis of Carbon Reinforced Natural/Styrene-Butadiene Blend Rubber (NSBR) with Ogden Constitutive Model

Materials Science Forum ◽

10.4028/www.scientific.net/msf.928.20 ◽

2018 ◽

Vol 928 ◽

pp. 20-25 ◽

Cited By ~ 1

Author(s):

Li Hong Huang ◽

Xiao Xiang Yang ◽

Jian Hong Gao

Keyword(s):

Constitutive Model ◽

Experimental Results ◽

Mullins Effect ◽

Elastic Analysis ◽

Stress Softening ◽

Styrene Butadiene

In this paper, experimental results that illustrate stress softening in carbon filled natural/styrene-butadiene blend rubber (NSBR) together with Mullins effect are introduced firstly. Then, based on these data, the Ogden constitutive model is derived. The theory of pseudo-elasticity is used in the model. It is found that theory of pseudo-elasticity and Ogden constitutive model is applicable in this composite.

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