On the nonlinear viscoelastic deformations of composites with prestressed inclusions

Zhu, Huanlin; Muliana, Anastasia; Rajagopal, K. R.

doi:10.1016/j.compstruct.2016.03.008

Cited by 11 publications

(6 citation statements)

References 19 publications

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“…In a rather different limiting scenario, when the outer radius of the hollow sphere tends to infinity, the canonical hollow sphere problem becomes highly relevant to understanding the response of porous viscoelastic elastomers under hydrostatic pressure [28][29][30][31]. In closed-cell materials, voids are distributed throughout an elastomer, resulting in a compressible medium even when the host elastomer is incompressible.…”

Section: Introductionmentioning

confidence: 99%

The inflation of viscoelastic balloons and hollow viscera

et al. 2018

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For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders . While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.

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Section: Introductionmentioning

confidence: 99%

The inflation of viscoelastic balloons and hollow viscera

et al. 2018

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“…where the material moduli âi , i = 0, 1, 2 depend on r, trT, trT 2 , trT 3 , and by virtue of the mass balance (as in ( 14)). The model (20) has been studied in several investigations involving cracks in elastic bodies exhibiting strain-limiting behavior, 24,[28][29][30]53 quasi-static crack evolution, 43,44 thermo-elastic bodies, 34,35 quasi-linear viscoelastic bodies, [54][55][56] and nonlinear constitutive model for rock. 57,58 Another subclass of models of the above general class of relations (19) wherein the constitutive relation is linear in both e and T is given by (see also Itou et al 59 )…”

Section: Implicit Constitutive Relationsmentioning

confidence: 99%

“…where the material moduli α ^ i , i = 0 , 1 , 2 depend on ρ , tr T , tr T 2 , tr T 3 , and by virtue of the mass balance (as in (14)). The model (20) has been studied in several investigations involving cracks in elastic bodies exhibiting strain-limiting behavior, 24,28–30,53 quasi-static crack evolution, 43,44 thermo-elastic bodies, 34,35 quasi-linear viscoelastic bodies, 54–56 and nonlinear constitutive model for rock. 57,58…”

Section: Formulation Of the Density-dependent Materials Moduli Modelmentioning

confidence: 99%

Finite element solution of crack-tip fields for an elastic porous solid with density-dependent material moduli and preferential stiffness

Yoon,

Mallikarjunaiah,

Bhatta

2024

Advances in Mechanical Engineering

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In this paper, the finite element solutions of crack-tip fields for an elastic porous solid with density-dependent material moduli are presented. Unlike the classical linearized case in which material parameters are globally constant under a small strain regime, the stiffness of the model presented in this paper can depend upon the density with a modeling parameter. The proposed constitutive relationship appears linear in the Cauchy stress and linearized strain independently. From a subclass of the implicit constitutive relation, the governing equation is bestowed via the balance of linear momentum, resulting in a quasi-linear partial differential equation (PDE) system. Using the classical damped Newton’s method, the sequence of linear problems is then obtained, and the linear PDEs are discretized through a bilinear continuous Galerkin-type finite element method. We perform a series of numerical simulations for material bodies with a single edge-crack subject to a variety of loading types (i.e. the pure mode-I, II, and mixed-mode). Numerical solutions demonstrate that the modeling parameter in our proposed model can control preferential mechanical stiffness with its sign and magnitude along with the change of volumetric strain. This study can provide a mathematical and computational foundation to further model the quasi-static and dynamic evolution of cracks, utilizing the density-dependent moduli model and its modeling framework.

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“…Such a feature is very important to study problems of initiation and growth of both cracks and fractures in elastic medium. There have been a lot of investigations undertaken to revisit the classical problems of solid mechanics using Rajagopal's theory of elasticity, e.g., the static single-crack [26][27][28], the v-notch problems [29,30], the elliptical hole [31,32], deformation of viscoelastic solids [33][34][35], unsteady problems [36][37][38], and rigorous mathematical analysis for existence and uniqueness of solutions [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Finite element study of V-shaped crack-tip fields in a three-dimensional nonlinear strain-limiting elastic body

Gou,

Mallikarjunaiah

2023

Mathematics and Mechanics of Solids

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We study the crack-tip fields in a three-dimensional (3D) plate with a V-shaped crack employing Rajagopal’s theory of elasticity with the strain-limiting effect. The classical linear elastic fracture mechanics (LEFM) theory bears a well-documented inconsistency, i.e., for a static crack problem under the traction-free boundary condition, the LEFM theory predicts singular crack-tip strains. Such results are inconsistent with the constitutive relation derived using the assumption of uniform bound for the strain values. Instead, Rajagopal’s recent theory of elasticity provides implicit constitutive relations between the linearized strain and Cauchy stress in which one can impose an a-priori upper bound for strains. We formulate the strain-limiting theory comprehensively in this article. The linearized strain is expressed as a nonlinear function of the Cauchy stress. The equation for the equilibrium of the linear momentum under a special type of nonlinear constitutive relation reduces to a second-order quasilinear elliptic boundary value problem (BVP). Using a Picard-type linearization and a continuous Galerkin-type finite element technique, we solve several BVPs with tensile and shear displacement loading. The numerical results for the strains, the stresses, the stress intensity factor (SIF), and strain energy density (SED) are obtained for different Poisson values, strain-limiting parametric values, and the V-shaped angles. The growth of the near-tip strains is far less than that of stresses, and the results for both the SIF and SED are also consistent with the results from LEFM. Our work demonstrates that the framework of Rajagopal’s theory of elasticity can provide a basis for developing physically meaningful and mathematically well-posed BVPs to study evolution of cracks, damage, nucleation, or failure in elastic bodies.

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On the nonlinear viscoelastic deformations of composites with prestressed inclusions

Cited by 11 publications

References 19 publications

The inflation of viscoelastic balloons and hollow viscera

The inflation of viscoelastic balloons and hollow viscera

Finite element solution of crack-tip fields for an elastic porous solid with density-dependent material moduli and preferential stiffness

Finite element study of V-shaped crack-tip fields in a three-dimensional nonlinear strain-limiting elastic body

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