Nonlinear fiber-bundle-cells-based phenomenological modeling of human tissue samples

Certain assemblies of fibers, called fiber bundles, play a crucial role in the statistical macroscale properties of fibrous structures like natural or artificial materials. Based on the concept of using idealized statistical fiber bundle cells (FBCs) as model elements, the software named FiberSpace was developed by us earlier for the phenomenological modeling of the tensile test process of real fibrous structures. The model fibers of these FBCs had been considered linear elastic, which was suitable for modeling certain textiles and composites. However, the biological tissues are multilevel structures with fiber-like building elements on every structural level where the fiber elements on the dominant level are statistical bundles of elementary fibers. Hence, their modeling required us to introduce model fibers of nonlinear mechanical behavior and derive the proper mathematical formulas for the calculation of the expected tensile force processes of the FBCs. Accordingly, we developed a new version of FiberSpace. The proposed nonlinear FBCs-based modeling method is essentially phenomenological that decomposes the measured and averaged stress-strain curve into the weighted sum of the responses of different idealized nonlinear FBCs. However, this decomposition can give certain information about the fibrous structure and some details of its damage and failure sub-processes. A special application of nonlinear E-bundles, where the measured stress-strain curve is expanded into a product-function series, may give another type of description for the failure process and can be applied to single measurements of structured failure process containing significant peaks and drops as well. The fitted phenomenological FBC models provide a decomposition of the measured force-strain curve, which enables to construct informative damage and failure maps. The applicability of the phenomenological modeling method and the fitting procedure is demonstrated with the tensile test data of some human and animal tissues, such as facial nerves and tendons.