"Swelling as a notion of free volume change is typically due to some added mass procedures. We use modified constitutive laws that incorporate swelling into a continuum mechanics treatment. By incorporating local volume change (swelling) as a parametric constraint into the conventional theory of hyperelasticity it is possible to model a variety of swelling effects. We consider these effects in the study of certain boundary value problems for spherical and cylindrical finite deformations. In addition to the traditional hyperelastic model, we also employ a relatively new type of constitutive treatment, termed internal balance. The theory of internally balanced materials employs energy minimization to obtain an additional balance principle to treat more complex behaviors. This is useful when conventional elastic behavior is modified by substructural reconfiguration. Hence, we also formulate our problems in the context of the internally balanced material theory for the case of cylindrical deformation where the results are compared to that of the conventional hyperelastic model. For thick spherical shells, the incompressible hyperelastic Mooney-Rivlin constitutive model allows for response to pressure-inflation that could either be globally stable (a monotonic pressure-radius graph) or could instead involve instability jumps of various kinds as pressurization proceeds. The latter occurs when the pressure-radius graph is not monotonic, allowing for a snap-through bifurcation that gives a sudden burst of inflation. Internal swelling of the material that makes up the shell wall will generally change the response. Not only does it alter the quantitative pressure-inflation relation but it can also change the qualitative stability response, allowing burst phenomena for certain ranges of swelling and preventing burst phenomena for other ranges of swelling. These issues are examined both for the case of uniform swelling for the case of a spatially varying swelling field. For cylindrical deformations, we examine the finite strain swelling of a soft solid plug within a rigid tube of circular cross section. The eventual channel wall contact as the swelling proceeds generates a confinement pressure that increases as the plug expands. We consider plug geometries that incorporate an internal channel as well as a simpler case of a solid plug. For the case of a plug with a channel, the wall contact now gives a deformation in which swelling combines axial lengthening with internal channel narrowing. Of particular interest is the closing behavior as the swelling proceeds and we treat the problem using asymptotic expansions. Finally, the same problem is examined in the context of the internal balance constitutive theory."--Pages ii-iii.
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