Standard Tests for Ex Vivo Material Testing

Figure5.1shows some schematic drawings of standard tests to characterise materials.

For a uniaxial test (Fig.5.1a) a long slender dogbone shaped bar is clamped in a mechanical testing machine. The dogbone shape reduces clamping effects in the long slender part of the bar. If the material has homogeneous properties and the bar is indeed a long slender structure, with a length much higher than the cross-sectional dimensions, stretching of the bar will lead to a uniaxial stress state in the bar. The stress can be derived by dividing the measured force by the cross-sectional area. Usually the length change of the bar is measured with a contactless measurement system in the middle section of the bar (avoiding effects of slipping in the clamps) and sometimes the reduction of the cross-sectional area is measured, so the Poisson’s ratio can also be derived from the test. This all works quite well for homogeneous, isotropic, stiff materials and for small deformations. In mechanical and civil engineering, for technical materials, this test is standardised and if performed well is a good way to determine material properties. The stress as well as the strain state can be derived directly from the measurements and the material properties:

Young’s modulus and Poisson’s ratio can be determined easily.

The biaxial test in Fig.5.1b is based on a similar idea. A square sample is clamped in a testing machine enabling to stretch the material in two directions independently.

The clamping system is designed such that the square sample remains a square

Fig. 5.1 Examples of standard testsauniaxial extensionbbiaxial testcshear test

after it is being stretched. However, when the sample has anisotropic properties, the forces in the two directions will be different and anisotropic material properties can be derived. Like in the uniaxial test, for homogeneous material samples the stress and strain field is constant in a large part of the sample at a certain distance of the clamps, and can be measured directly, independent of the material properties of the used sample. From this stress and strain field the material parameters can be derived easily. One of the problems encountered in this type of test is the required uniformity in a part of the sample. The biaxial deformation is obtained using hooks that penetrate the skin. These hooks are usually attached to strings or slender bars that are stiff in tension, but can bend very easily to accommodate movement in the direction perpendicular to the pulling direction. The penetration locations lead to stress and strain concentrations around the hooks, which may lead to tearing of the tissue and a partly inhomogeneous strain field in the sample. This means that specimen design and attachment significantly affect the uniformity of the strain field produced in biaxial tests [1].

A final example is the shear test that is used for viscoelastic materials and fluids.

The sample is placed between a plate and a cone or between two plates. The cone

is rotated. This can either be with a constant rotation speed, a rotation to a certain degree and then held constant (relaxation test) or using a harmonic oscillation. For small deformations at each time point the shear strain rate is approximately the same in the entire sample and can be determined from the cone rotation. The torque on the lower plate is measured and the viscosity of the fluid can be derived. Usually the test is performed at a large range of strain amplitudes to find the linear region and for a very large range of frequencies. This frequency range can often be extended by performing the experiment at different temperatures and using time-temperature superposition to create a master curve over a very large range of frequencies. Typical outcomes are storage and loss modulus as a function of frequency [2].

These are just three examples of standard tests to characterise materials, but there are many more. For most of these tests standards are defined on how to perform the test properly. What is common in all the standard tests is the possibility to derive the stress as well as the strain directly from the experiment, independent of the type of material that is being tested.

For many technical materials it is relatively easy to make test samples according to the agreed standards, but for most biological materials this is much more difficult.

Below a number of reasons are given why standard tests for biological materials are difficult

• To create a sample it has to be taken out of a body. If it concerns human tissue it is either left over material of surgery or post mortem material. An other option is to use tissue from animals. In all situations the material is taken out of the body, so it loses part of its integrity, the pretension found in the living system is (partly) gone or difficult to maintain, the tissue is no longer supplied with blood and will start to deteriorate quickly. However, when isolated and preserved in a proper way the negative effects of making samples of biological materials can be reduced considerably and the parameters may change, but the physical behaviour will be similar to the behaviour in vivo. Also during testing the physical and chemical environment of the material has to be controlled (humidity, temperature).

• It is extremely difficult to make samples according to the standards (e.g. a dogbone shape of a soft biological material). The amount of material available is usually small or very small. Clamping is a big issue.

• Often the material has inhomogeneous properties, so the assumption in standard tests that the stress strain field is homogeneous is not a valid assumption.

• Especially for soft biological materials the samples can be stretched to very high deformations, they behave highly nonlinear and viscoelastic so the strain and strain rate history play an important role.

Despite the difficulties given above, standard tests are done quite often because they are well defined and they constitute the only way to gain a good understanding of the physical behaviour of the material and to define constitutive equations. Some of the above problems can be circumvented or partly solved using mixed numer-ical/experimental or inverse methods. These inverse methods are the only way to determine in vivo material parameters of biological materials. This method will be discussed in the next section.