Mechanics of prestressed and inhomogeneous bodies

Abstract

In finite elasticity, while developing representation for stress, it is customary to require the reference configuration to be stress free. This study relaxes this requirement and develops representations for stress from a stressed reference configuration. Using the fact that the value of Cauchy stress in the current configuration is independent of the choice of the reference configuration, even though the formula used to compute it depends on the choice of the reference configuration, the sought representation is obtained. It is then assumed that there exists a piecewise smooth mapping between a configuration with prestresses and a configuration that is stress free, and the representation obtained above is used to study the mechanical response of prestressed bodies. The prestress fields are obtained by directly integrating the balance of linear momentum along with the traction free boundary condition. Then, different classes of boundary value problems for the type of inhomogeneous and prestressed bodies of interest are formulated and studied. For the cases studied, it is found that even the global measures like axial-load required to engender a given stretch ratio for a prestressed body vary from the homogeneous stress free bodies, though not significantly. The local measures - stress and deformation - in a prestressed body differ considerably from their homogeneous stress free counterparts. The above gained knowledge is applied to understand the mechanics of circumflex arteries obtained from normotensive and hypertensive micro-mini pigs. It is found that the deformation of these arteries when subjected to inflation and axial extension is not of the form r = r(R), ???? = ????, z = Z. Comparison is also made between the response of an artery at various levels of smooth muscle activation and stretch ratio as well as normotensive and hypertensive specimens, using statistical methods.