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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. [ABSTRACT FROM AUTHOR]

The Parametric High-Fidelity-Generalized-Method-of-Cells (PHFGMC) micromechanical model is extended to include a local cohesive formulation for simulating discontinuities in multiphase composites. The nonlinear PHFGMC governing equations are obtained from a virtual work principle applied to both the local and far-field variables and solved using a new incremental-iterative formulation. The nonlinearity stems from the introduction of the cohesive zones in conjunction with damage evolution. The proposed formulation yields an overall symmetric system of equations and enables the implementation of advanced traction-separation laws available in the literature similar to the displacement-based finite element method (FEM). Two cohesive zone models are integrated with the PHFGMC with a unique nonlinear formulation. These are the non-potential based model proposed by Camanho and Davila (CD) and the potential based Park–Paulino–Roesler (PPR) model. This article presents comparisons with FEM and the applications of this modeling approach. The predictions of damage initiation and evolution, as well as the overall stress–strain response of the cohesive PHFGMC are shown to be in good agreement with those from a finite element analysis for various configurations and loading patterns. [ABSTRACT FROM AUTHOR]

Remarkable mechanical properties of biocomposites (bone, teeth, shell, antler etc.) are usually attributed to their special design where staggered mineral platelets are embedded in a protein matrix. Because of the high aspect ratio of the platelet the soft protein deforms in the shear mode predominantly providing the linkage for the hard inclusions. Mimicking Nature one might design materials with a similar architecture. By employing a micromechanical analysis, we study in the present work the strength of a bio-inspired composite in which hard platelets are embedded in a soft matrix made of the vulcanized natural rubber. We perform simulations of uniaxial tension of the composite material based on a continuum mechanics formulation and the high-fidelity generalized method of cells. The use of the energy limiters in the constitutive model for rubber at finite strains allows us to model failure and arrive at the overall strength of the composite. We find that the overall strength of the composite depends on the deformation and failure of soft matrix in tension and shear. Moreover, we find that the strength of the composite cannot exceed the strength of the matrix. The latter observation is noteworthy because it is qualitatively different from the previous experimental results with biocomposites which show a dramatic (ten times) increase of the strength of the material as compared to the strengths of its constituents. We illustrate these analytical and numerical findings by our experiments on 3D printed composite materials. [ABSTRACT FROM AUTHOR]

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 $$(n=10)$$ . 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. [ABSTRACT FROM AUTHOR]

This paper addresses fiber-matrix debonding in titanium matrix composites (TMCs) using a recently developed micromechanics model known as the high-fidelity generalized method of cells (HFGMC). By employing a higher-order displacement field, this model supercedes its predecessor, the generalized method of cells (GMC), in terms of micro-scale field accuracy. The import of this micro-scale accuracy is amplified in the case of fiber-matrix debonding as the debonding phenomenon is dominated by local field effects. Via inclusion of appropriate constitutive relations for inelastic deformation and fiber-matrix debonding, both HFGMC and GMC have been applied herein to model the transverse deformation of titanium matrix composites, which exhibit obvious effects of interfacial debonding. Results indicate that HFGMC is considerably more quantitatively accurate than GMC for analysis of composites with debonding, enabling realistic predictions of the TMC transverse response. The improved accuracy of the HFGMC local fields also enables investigation of some qualitative aspects of the debonding phenomenon within TMCs. [Copyright &y& Elsevier]

Abstract: This study deals with the mechanical properties of soft polymeric composite laminates made with Ultra-high-molecular-weight polyethylene (UHMWP) fibers, often used for ballistic protection. Two new mechanical test setups, tensile and axial shear, are proposed to characterize the mechanical behavior of a laminated system made of the commercial Dyneema HB26 cross-ply multi-layered plates. The suitable tension setup is found to be close to a bow-tie like geometry while the axial shear is closer to a butterfly shape. The overall linear and nonlinear behaviors under both tension and shear are investigated. Microstructure of the fibers along with results from the mechanical tests, are used to calibrate a micromechanical model for this material system. [Copyright &y& Elsevier]

Abstract: Piezoresistive composites are materials that exhibit spatial and effective electrical resistivity changes as a result of local mechanical deformations in their constituents. These materials have a wide array of applications from non-destructive evaluation to sensor technology. We propose a new coupled nonlinear micromechanical-microelectrical modeling framework for periodic heterogeneous media. These proposed micro-models enable the prediction of the effective piezoresistive properties along with the corresponding spatial distributions of local mechanical–electrical fields, such as stress, strain, current densities, and electrical potentials. To this end, the high fidelity generalized method of cells (HFGMC), originally developed for micromechanical analysis of composites, is extended for the micro-electrical modeling in order to predict their spatial field distributions and effective electrical properties. In both cases, the local displacement vector and electrical potential are expanded using quadratic polynomials in each subvolume (subcell). The equilibrium and charge conservations are satisfied in an average volumetric fashion. In addition, the continuity and periodicity of the displacements, tractions, electrical potential, and current are satisfied at the subcell interfaces on an average basis. Next, a one way coupling is established between the nonlinear mechanical and electrical effects, whereby the mechanical deformations affect the electrical conductivity in the fiber and/or matrix constituents. Incremental and total formulations are used to arrive at the proper nonlinear solution of the governing equations. The micro-electrical HFGMC is first verified by comparing the stand-alone electrical solution predictions with the finite element method for different doubly periodic composites. Next, the coupled HFGMC is calibrated and experimentally verified in order to examine the effective piezoresistivity of different composites. These include conductive polymeric matrices doped with carbon nano-tubes or particles. One advantage of the proposed nonlinear coupled micro-models is its ability to predict the local and effective electro-mechanical behaviors of multi-phase periodic composites with different conductive phases. [Copyright &y& Elsevier]

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., (Copyright © 2015 Elsevier Ltd. All rights reserved.)