FE implementations of biphasic theory for cartilage were presented by Spilker and colleagues for small strains ( 17) and finite deformation of the solid matrix ( 18), using penalty methods to enforce incompressibility.
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( 16), who developed a custom code for modeling intervertebral disc segments based on porous media theories. One of the earliest examples of an FE code developed for applications in biomechanics was that by Simon et al. The limitations of commercial codes forced many researchers to develop custom FE packages for solving problems in the biomechanics domain. Commercial codes often do not offer a mechanism for adding new features easily, making it challenging for researchers to implement and test new computational methods or constitutive models. In addition, the closed nature of commercial codes makes it difficult to verify them ( 14, 15) or to compare results across different codes because the implementation details are often unavailable. The commercial packages that are most commonly used by the biomechanics community are not specifically geared toward biological applications.
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However, the lack of FE software that is tailored to the needs of the field has hampered research progress, dissemination of research, and sharing of models and results.
As an example, the development of mixture theory as an accurate approach for modeling the interaction of the solid and fluid components of living tissues has resulted in many new insights ( 7– 13). The field of biomechanics has made tremendous advances over the last few decades as our understanding of the complex structure of biological tissues has grown. Applications have ranged from the molecular level to the cellular, tissue, and organ levels. Since that time, the application of FE analysis in biomechanics research and design has increased exponentially as commercial software and improved computing platforms have made the method more accessible to research communities.
In the field of biomechanics, the FE method was applied to problems as early as the 1970s (e.g., 1– 6). Although it was initially applied to problems in mechanics, since its inception in the 1950s it has been used in virtually every field of engineering and physics, including solid mechanics, fluid flow, heat transfer, electromagnetism, diffusion, and many more. The finite element (FE) method has proven to be one of the most versatile numerical methods for solving computational problems in physics.
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