Finite strain parametric HFGMC micromechanics of soft tissues.

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.

A new multiscale micromechanical model of vertebral trabecular bones.

A new three-dimensional (3D) multiscale micromechanical model has been suggested as adept at predicting the overall linear anisotropic mechanical properties of a vertebral trabecular bone (VTB) highly porous microstructure. A nested 3D modeling analysis framework spanning the multiscale nature of the VTB is presented herein. This hierarchical analysis framework employs the following micromechanical methods: the 3D parametric high-fidelity generalized method of cells (HFGMC) as well as the 3D sublaminate model. At the nanoscale level, the 3D HFGMC method is applied to obtain the effective elastic properties of a representative unit cell (RUC) representing the mineral collagen fibrils composite. Next at the submicron scale level, the 3D sublaminate model is used to generate the effective elastic properties of a repeated stack of multilayered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron scale level, the 3D HFGMC method is used again on a RUC of the highly porous VTB microstructure. The VTB-RUC geometries are taken from microcomputed tomography scans of VTB samples harvested from different vertebrae of human cadavers [Formula: see text]. The predicted anisotropic overall elastic properties for native VTBs are, then, examined as a function of age and sex. The predicted results of the VTBs longitudinal Young's modulus are compared to reported values found in the literature. The proposed 3D nested modeling analysis framework provides a good agreement with reported values of Young's modulus of single trabeculae as well as for VTB-RUC in the literature.

Aneurysm strength can decrease under calcification.

Aneurysms are abnormal dilatations of vessels in the vascular system that are prone to rupture. Prediction of the aneurysm rupture is a challenging and unsolved problem. Various factors can lead to the aneurysm rupture and, in the present study, we examine the effect of calcification on the aneurysm strength by using micromechanical modeling. The calcified tissue is considered as a composite material in which hard calcium particles are embedded in a hyperelastic soft matrix. Three experimentally calibrated constitutive models incorporating a failure description are used for the matrix representation. Two constitutive models describe the aneurysmal arterial wall and the third one - the intraluminal thrombus. The stiffness and strength of the calcified tissue are simulated in uniaxial tension under the varying amount of calcification, i.e. the relative volume of the hard inclusion within the periodic unit cell. In addition, the triaxiality of the stress state, which can be a trigger for the cavitation instability, is tracked. Results of the micromechanical simulation show an increase of the stiffness and a possible decrease of the strength of the calcified tissue as compared to the non-calcified one. The obtained results suggest that calcification (i.e. the presence of hard particles) can significantly affect the stiffness and strength of soft tissue. The development of refined experimental techniques that will allow for the accurate quantitative assessment of calcification is desirable.

The analysis of localized effects in composites with periodic microstructure.

Several methods for the analysis of composite materials with periodic microstructure in which localized effects (such as concentrated loads, cracks and stationary/progressive damage) occur are resented. Owing to the loss of periodicity caused by these localized effects, it is no longer possible to identify and analyse a repeating unit cell that characterizes the periodic composite. For elastostatic problems, these methods are based on the combination of the representative cell method (RCM), the higher-order theory for functionally graded materials and often the high-fidelity generalized method of cells (HFGMC) micromechanical model. For elastodynamic problems, the combination of the dynamic RCM with a theory for wave propagation in heterogeneous media is used for the prediction of the time-dependent response of the periodic composite with localized effects. In the framework of the RCM, the problem for a periodic composite that is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher-order theory and the theory of wave propagation in composites, the resulting governing equations and interfacial conditions in the transform domain are solved by dividing the single cell into subcells and imposing the latter in an average (integral) sense. The HFGMC is often used for the prediction of the proper far-field boundary conditions based on the response of the unperturbed composite. The inverse of the Fourier transform provides the real elastic field at any point of a composite with localized effects. This research summarizes a series of investigations for the prediction of the behaviour of periodic composites with localized loading, fibre loss, damage and cracks subjected to static and dynamic loadings under isothermal and full thermomechanical coupling conditions.

Behavior of Elastoplastic Auxetic Microstructural Arrays.

A continuum-based micromechanical model is employed for the prediction of the elasto-plastic behavior of periodic microstructural arrays that can generate negative values of Poisson's ratios. The combined effects of the negative Poisson's ratio generated by the array microstructure and the elastoplastic behavior of the constituents are studied. A design methodology for the determination of the constituents' properties of two-phase arrays that generate required values of negative Poisson's ratio is considered.