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Despite real applications having complex triaxial loading, current physical test methods to predict component behaviour are mainly uniaxial. But previous work has indicated that there may be substantial differences between the rubber's uniaxial and biaxial behaviour and hence through incompressibility, its triaxial properties. In order to quantify these differences equipment was developed to assess the biaxial performance of selected rubber compounds using inflated circular diaphragms. Although allowing higher extensions than stretching a sheet in its own plane, such tests do not allow stress and strain to be measured directly, requiring careful marking of the sample, or calculation through simulation. On the grounds of perceived accuracy, the latter was chosen, requiring accurate, general, elastic constants to high extensions. In this thesis the development of this apparatus, along with the associated techniques is described, along with the development of a new elastic theory. The tests on this new apparatus indicated significant differences between the uniaxial and biaxial strength and fatigue of rubber. In a unimdal test natural rubber (NR) is much stronger than styrene butadiene rubber (SBR) below 35pphr of carbon black. In a biaxial test though the converse is true, although there is some evidence of crystallinity in NR during the biaxial test. Distinct differences were also found in fatigue between the two load cases. When plotted against extension ratio the biaxial life of SBR was found to increase, while the converse is true for NR. However if life is plotted against a function of strain energy, the biaxial life of both polymers increases for a given energy.

Elastic deformation has wide applications in medical simulations, therefore when it comes to designing physical behavior of objects for realistic training applications, determining material parameters so that objects behave in a desired way becomes a crucial. In this work we consider the problem of elasticity parameter estimation for deformable bodies, which is important for accurate medical simulations. Our work has two major steps: the first step is the data acquisition and preparation, and the second step is the parameter estimation. The experimental setup for data acquisition consists of depth and force sensors. Surface deformations are acquired as a series of images along with the corresponding applied forces. The contact point of the force sensor on the surface is found visually and the corresponding applied forces are acquired directly from the force sensor. A complete mesh deformation which is obtained from a surface tracking method is employed along with force measurements in the elasticity parameter estimation method. Our approach to estimate the physical material properties is based on an inverse linear finite element method. We have experimented with two approaches to optimize the elasticity parameters: a linear iterative method and a force-displacement error minimization method. The two methods were tested on the simulation data, and the second method was tested on three deformable objects. The results are presented for the data captured by two different depth sensors. The result is a set of two parameters, the Young's modulus and the Poisson's ratio, which represents the stiffness of the object under test.

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