A Bifurcation Approach Modeling Cavitation in Anisotropic Nonlinearly Elastic Solids
Abstract
In this thesis, material anisotropy and the phenomena of void formation and growth (cavitation) in nonlinearly elastic incompressible solids are considered. We first discuss materials which are transversely isotropic in the contexts of linear and nonlinear hyperelasticity, and derive important constitutive restrictions on the nonlinear stored-energy function, W, by relating W to the associated infinitesimal elastic moduli. We then propose a class of stored-energy functions satisfying these conditions to model incompressible transversely isotropic nonlinearly elastic materials. The effect of material anisotropy on void nucleation and growth in incompressible nonlinearly elastic solids is then examined. A bifurcation problem is considered for a solid sphere composed of an incompressible homogeneous nonlinearly elastic material that is transversely isotropic about the radial direction. Under a uniform radial tensile dead-load, a branch of radially symmetric configurations involving a traction-free internal cavity bifurcates from the undeformed configuration at sufficiently large loads.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1993
- Accession Number
- ADA342697
Entities
People
- Debra A. Polignone
Organizations
- University of Virginia