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Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.
Pubmed ID: 29867581
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Multi paradigm numerical computing environment and fourth generation programming language developed by MathWorks. Allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, Fortran and Python. Used to explore and visualize ideas and collaborate across disciplines including signal and image processing, communications, control systems, and computational finance.
View all literature mentionsThe ARCHER project is built upon the prototype software developed by the DART (http://dart.edu.au) and ARROW (http://arrow.edu.au) projects to produce a robust set of software tools. These tools: - may be customised to suit the needs of diverse research areas - automate the collection and management of instrument generated data - enable the repository storage of research data and associated metadata - enable collection and tagging of research data in a collaborative environment, and - provide these capabilities in a secure end-to-end proces. :ARCHER developed a ''production-ready'' software tools, operating in a secure environment, to assist researchers to: - collect, capture and retain large data sets from a range of different sources including scientific instruments - deposit data files and data sets to eResearch storage repositories - populate these eResearch data repositories with associated metadata - permit data set annotation and discussion in a collaborative environment, and - support next-generation methods for research publication, dissemination and access.
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