Indentation Tests on Elastomer Blocks

A CONSTITUTIVE MODEL FOR BOTH LOW AND HIGH STRAIN NONLINEARITIES IN HIGHLY FILLED ELASTOMERS AND IMPLEMENTATION WITH USER-DEFINED MATERIAL SUBROUTINES IN ABAQUS

Strain energy functions (SEFs) are used to model the hyperelastic behavior of rubberlike materials. In tension, the stress–strain response of these materials often exhibits three characteristics: (i) a decreasing modulus at low strains (<20%), (ii) a constant modulus at intermediate strains, and (iii) an increasing modulus at high strains (>200%). Fitting an SEF that works in each regime is challenging when multiple or nonhomogeneous deformation modes are considered. The difficulty increases with highly filled elastomers because the small strain nonlinearity increases and finite-extensibility occurs at lower strains. One can compromise by fitting an SEF to a limited range of strain, but this is not always appropriate. For example, rubber seals in oilfield packers can exhibit low global strains but high localized strains. The Davies–De–Thomas (DDT) SEF is a good candidate for modeling such materials. Additional improvements will be shown by combining concepts from the DDT and Yeoh SEFs to construct a more versatile SEF. The SEF is implemented with user-defined material subroutines in Abaqus/Standard (UHYPER) and Abaqus/Explicit (VUMAT) for a three-dimensional general strain problem, and an approach to overcome a mathematically indeterminate stress condition in the unstrained state is derived. The complete UHYPER and VUMAT subroutines are also presented.

ANALYTICAL RELATIONSHIPS FOR NANOINDENTATION-BASED ESTIMATION OF MECHANICAL PROPERTIES OF BIOMATERIALS

Nanoindentation is an (almost) non-invasive method for obtaining material properties of different types of materials from the interpretation of experimental data related to indenter load (P) and penetration depth (h). In most cases, the material properties that are obtained by nanoindentation are elastic modulus (E), shear modulus (G) and hardness (H). The main advantages of this method are that no extensive preparation of the test specimen is required and that the mechanical properties can be probed at small scales. Moreover, nanoindentation test procedure is automated and the test equipment is easy to use. In this paper, we review different analytical methods that could be used for obtaining the mechanical properties of biomaterials based on the force-displacement curves generated by nanoindentation machines. Some practical issues including different types of machines and tips, calibration of nano-indentation machines, sources of error and specimen preparation are also briefly discussed. The main interest of this paper is the elastic behavior of biological tissues and biomaterials. Nevertheless, there is one section on elasto-plasticity, because purely elastic deformation of linearly elastic materials is difficult to achieve. The analytical solutions found in the literature for different material models are presented including the relationships found for linear elastic, elasto-plastic, hyperelastic, viscoelastic and poroelastic materials. These material models are relevant material models for studies of biological tissues and biomaterials.

In situ Materials Characterization using the Tissue Diagnostic Instrument

An understanding of the mechanical behavior of polymers is critical towards the design, implementation, and quality control of such materials. Yet experiments and method for the characterization of material properties of polymers remain challenging due the need to reconcile constitutive assumptions with experimental conditions. Well-established modes of mechanical testing, such as unconfined compression or uniaxial tension, require samples with specific geometries and carefully controlled orientations. Moreover, producing specimens that conform to such specifications often requires a considerable amount of sample material. In this study we validate a micromechanical indentation device, the Tissue Diagnostic Instrument (TDI), which implements a cyclic indentation method to determine the material properties of polymers and elastomeric materials. Measurements using the TDI require little or no sample preparation, and they allow the testing of sample materials in situ. In order to validate the use of the TDI, we compared measurements of modulus determined by the TDI to those obtained by unconfined compression tests and by uniaxial tension tests within the limit of small stresses and strains. The results show that the TDI measurements were significantly correlated with both unconfined compression (p<0.001; r(2) = 0.92) and uniaxial tension tests (p<0.001; r(2)=0.87). Moreover, the measurements across all three modes of testing were statistically indistinguishable from each other (p=0.92; ANOVA) and demonstrate that TDI measurements can provide a surrogate for the conventional methods of mechanical characterization.