Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations

Influence of rotation and initial stress on Propagation of Rayleigh waves in fiber-reinforced solidanisotropic magneto-thermo-viscoelastic media.

This paper is concerned with giving a mathematical model on the propagation of Rayleigh waves in a homogeneous magneto-thermo-viscoelastic,pre-stressed elastic half – space subjected to theinitial stress and rotation. The dispersion equation has been derived for a half-space, when both media are considered as pre-stressed and the effect of rotation and initial stressshown in earlier investigators.Numerical results have been obtained  in the physical domain. Numerical simulated results are depicted graphically to show the effect of rotation and magnetic field and initial stressonRayleigh wave velocity. Comparison was made with the results obtained in the presence and absence of the rotation , initial stressand magnetic field. The study shows that there is a variational effect of magneto-elasticityand rotation, initial stress on the Rayleigh wave velocity

An Overview of Stress-Strain Analysis for Elasticity Equations

The present chapter contains the analysis of stress, analysis of strain and stress-strain relationship through particular sections. The theory of elasticity contains equilibrium equations relating to stresses, kinematic equations relating to the strains and displacements and the constitutive equations relating to the stresses and strains. Concept of normal and shear stresses, principal stress, plane stress, Mohr’s circle, stress invariants and stress equilibrium relations are discussed in analysis of stress section while strain-displacement relationship for normal and shear strain, compatibility of strains are discussed in analysis of strain section through geometrical representations. Linear elasticity, generalized Hooke’s law and stress-strain relations for triclinic, monoclinic, orthotropic, transversely isotropic, fiber-reinforced and isotropic materials with some important relations for elasticity are discussed

Quasi-static imaged-based immersed boundary-finite element model of human left ventricle in diastole

SUMMARY: Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart

Analysis of no-tension structures under monotonic loading through an energy-based method

An approach is proposed to estimate the collapse load of linear elastic isotropic no-tension 2D solids. The material is replaced by a suitable equivalent orthotropic material with spatially varying local properties. A non-incremental energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material, minimizing the potential energy so as to achieve a compression-only state of stress. The algorithm is embedded within a numerical procedure that evaluates the collapse mechanisms of structural elements under monotonic loading. The accuracy of the method is assessed through comparisons with the “exact” results predicted by limit analysi

Ultimate load analysis and design of stiffened plates in compression

Imperial Users onl

Inverse method for stiffness determination of impact damage in composites

The limited knowledge of stiffness reductions is a major problem in reliably predicting the post-impact strength of composite structures. This work describes development and application of a non-destructive approach for evaluation of the inplane stiffness of impact damage in composites. The approach combines an inverse method linked to a finite element model and non-contact full-field measurements. The material parameters of impact damage are determined by iteratively matching the finite element model to displacement fields measured optically during post-impact loading. A first order, gradient optimization technique coupled with a modified quadratic algorithm is employed. The method is validated on a reference finite element model with axisymmetric damage containing several concentric zones having different properties, and the influence of measurement noise is examined. The approach is applied to in-house experiments with impacted carbon/epoxy laminates to determine their quasi-isotropic mechanical properties in tension and compression. The resulting stiffness distributions are presented and the corresponding nonlinear behaviour of the damage is described. To examine the effect of the type of damage on the mechanical properties a thorough fractographic analysis of the impacted specimens was undertaken. The tensile stiffness is found to be mainly affected by fibre fracture, while the compressive stiffness is strongly linked to delamination buckling. The approach has further been extended for detection and evaluation of multiple impact damage zones at arbitrary locations as well as for stiffness identification of the damage in orthotropic laminates. The accuracy of both extensions is presented and discussed. Finally, possible future applications of the approach are considered

Nonlinear analysis of orthotropic membrane and shell structures including fluid-structure interaction

In this work, membrane and shell structures with large deformations are studied. In the structural part of this work, a new methodology for the analysis of geometrically nonlinear orthotropic membrane and rotation-free shell elements is developed based on the principal fiber orientation of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-of lane prestressed membrane and shell structures. Additionally, since conventional membrane theory allows compression stresses, a wrinkling algorithm based on modifying the constitutive equation is presented. The structure is modeled with finite elements emerging from the governing equations of elastodynamics. the fluid part of this work is governed by the incompressible Navier-Stokes equations, which are modeled by stabilized equal-order interpolation finite elements. Since the monolithic solution for these equations has the disadvantage that take great computer effort to solve large algebraic system of equations, the fractional step methodology is used to take advantage of the computational efficiency given by the uncoupling of the pressure from the velocity field. In addition, the generalized-time integration scheme for fluids is adapted to be used with the fractional step technique.Postprint (published version