Finite strain parametric HFGMC micromechanics of soft tissues
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ORIGINAL PAPER
Finite strain parametric HFGMC micromechanics of soft tissues Uri Breiman1 · Ido Meshi1 · Jacob Aboudi1 · Rami Haj‑Ali1 Received: 2 December 2019 / Accepted: 16 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A micromechanical analysis is offered for the prediction of the global behavior of biological tissues. The analysis is based on the isotropic–hyperelastic behavior of the individual constituents (Collagen and Elastin), their volume fractions, and takes into account their detailed interactions. The present analysis predicts the instantaneous tensors from which the effective current first tangent tensor is established, thus providing the overall anisotropic constitutive behavior of the composite and the resulting field distribution in the composite. This is in contradistinction with the macroanalysis in which the composite internal energy, which involves unknown functions that depend on several strain invariants, must be proposed. The offered micromechanical analysis forms a generalization to the finite strain high-fidelity generalized method of cells (HFGMC) based on the homogenization technique for periodic composites to the parametric finite strain. This involves an arbitrary discretization of the repeating unit-cell of the periodic composites. Results are given for the response of the human abdominal aorta, which consists of three layered tissues: intima, media, and adventitia, all of which are composed out of the Collagen and Elastin. The isotropic–hyperelastic constituents (Mooney–Rivlin and Yeoh) of the composites are calibrated by utilizing available experimental data which describe the response of the tissue. Validation of the results is performed by comparison of the predicted Cauchy stress and stretches with the experimental measurements. In addition, results are given in the form of Cauchy stress and deformation gradient field distributions in the constituents of several tissues. Keywords HFGMC · Finite strain · Micromechanics · Composite · Biological tissues
1 Introduction The mechanical behavior of biological tissues naturally receives considerable attention. These biological materials may be viewed as composites structures consisting of several layers. Arteries, for example, consist of Elastin, Collagen, and other materials, thus forming an orthotropic laminated structure (Humphrey 2013) where the design of each layer contributes to the overall response of the entire tissue. Researches had tried to understand the mechanical response of these composites in order to improve the ability to provide insights for the medical diagnose of the tissues. Moreover, artificial composites with similar or improved properties have been designed and manufactured from biocompatible constituents in order to be stitched on implanted instead of the damaged tissues of the medical patient. These efforts * Rami Haj‑Ali [email protected] 1
School of Mechanical Engineering, Tel Aviv University, Tel Aviv‑Yafo, Israel
include generating tissues using microspun Collagen f
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