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Effect of Constitutive Parameters on Cavity Formation and Growth in a Class of Incompressible Transversely Isotropic Nonlinearly Elastic Solid Spheres

X.G. Yuan1,2, R.J. Zhang2

The Key Laboratory of Solid Mechanics of the Ministry of Education, Tongji University, Shanghai 200092 , P.R. China. yxg1971@163.com
Department of Mathematics and Informational Science, Yantai University, Yantai 264005 Shandong, P.R. China

Computers, Materials & Continua 2005, 2(3), 201-212. https://doi.org/10.3970/cmc.2005.002.201

Abstract

Cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres are described as a bifurcation problem, for which the strain energy density is expressed as a nonlinear function of the invariants of the right Cauchy-Green deformation tensor. A bifurcation equation that describes cavity formation and growth is obtained. Some interesting qualitative properties of the bifurcation equation are presented. In particular, cavitated bifurcation is examined for a solid sphere composed of an incompressible anisotropic Gent-Thomas material model with a transversely isotropy about the radial direction. The effect of constitutive parameters on cavity formation and growth is then carried out. It is proved that a cavity forms in the interior of the sphere earlier or later than that in the isotropic Gent-Thomas sphere as the anisotropic parameter takes certain values. The condition for the bifurcation to the left or to the right of the cavity solution is proposed. The stability and the catastrophe of the equilibrium solutions are discussed by using the minimal potential energy principle. Whereas, in contrast to other isotropic nonlinear elastic spheres, cavitated bifurcation in the isotropic Gent-Thomas sphere is quite different, it is proved that the cavity solution can bifurcate locally to the left. The growth of a pre-existing micro-void in the sphere is examined, which interprets the physical implications of the preceding bifurcation problem.

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Cite This Article

X. . Yuan and R. . Zhang, "Effect of constitutive parameters on cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres," Computers, Materials & Continua, vol. 2, no.3, pp. 201–212, 2005.



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