Cavitated bifurcation for incompressible hyperelastic material

Abstract

Abs~act: The spherical cavitated bifurcation for a hypereIastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed. Key words: incompressible hyperelastic material; void nucleation and growth; catastrophe and concentration of stress CLC number: O343 Document code: A *

Void formation and growth for a class of compressible hyper-elastic sphere

“…It worth noting here, the Poisson ratio of the strain energy function (10) and the type of the cavitated solution in this paper are quite different from those in [9].…”

“…Analyses on growth of pre-existing micro-void for the particular case of a Blatz-Ko material was carried out by Horgan and Abeyaratne eaJ . Thereafter, many significant investigations have been published, such as [4][5][6][7][8][9][10][11]. The authors have studied the cavitated bifurcation problems for different compressible hyper-elastic materials.…”

Cavitation instability in the plastic IC packaging material due to moisture-induced vapor pressure and thermal stress

“…On the other hand Gent and Lindley [3] observed the sudden formation of voids in hyper-elastic material in their experimental work on rubber cylinders .Ball set up the theoretical frame for cavitation formation and growth and found a class of hyper-potential functions and also gave the conditions of cavitation formation [4]. Ren and Cheng studied the cavitation problem in incompressible or compressible materials too [5,6]. Guo and Cheng established the theory of the unstable void growth in neoHookean plastic IC packaging material [7].In the case of absorbing lots of moisture, the dead load boundary condition is substituted by the constant load boundary condition., which shows that there exists a critical traction, the sum of the internal vapor pressure and the remote thermal stress, which defines the onset of unstable void growth, the presence of large microvoids lowers significantly the critical stress levels for unstable void growth.…”

Research on the Thermal Cavitation Problem of a Preexisting Microvoid in a Viscoelastic Sphere

“…In 1982, Ball [1] created the nonlinear theory of cavitation and gained the explicit expressions of critical loading in the incompressible hyperelastic material for the first time. Sivaloganathan [3], Chou-Wang and Horgan [4], Horgan and Polignone [5], Shang and Cheng [6], and Ren and Cheng [7][8][9] have intensively studied the cavitation problems of hyperelastic materials. Similar studies on hyperelastic materials can be found in Lopez-Pamies [10], Cohen and Durban [11], and Ren and Li [12].…”