A study on Poynting effect in brain white matter: A hyperelastic 3D micromechanical model

A novel 3D micromechanical Finite Element Model (FEM) has been developed to depict the Poynting effect in bi-phasic Representative volume element (RVE) with axons embedded in surrounding extra-cellular matrix (ECM) for simulating the brain white matter response under simple and pure shear. In the proposed 3D FEM, nonlinear Ogden hyper-elastic material model describes axons and ECM materials. The modeled bi-phasic RVEs have axons tied to surrounding matrix. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear scenario were simulated. Root mean square deviation (RMSD) were computed for stress and deformation response plots to depict role of axon-ECM orientations & loading condition on the Poynting effect. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane emphasized role of fiber-matrix interactions. At high strains, the stress-strain% plots also indicated modest strain stiffening effects and bending stresses in purely sheared axons

A Fractional Viscoelastic Model Of The Axon In Brain White Matter

Traumatic axonal injury occurs when loads experienced on the tissue-scale are transferred to the individual axons. Mechanical characterization of axon deformation especially under dynamic loads however is extremely difficult owing to their viscoelastic properties. The viscoelastic characterization of axon properties that are based on interpretation of results from in-vivo brain Magnetic Resonance Elastography (MRE) are dependent on the specific frequencies used to generate shear waves with which measurements are made. In this study, we aim to develop a fractional viscoelastic model to characterize the time dependent behavior of the properties of the axons in a composite white matter (WM) model. The viscoelastic powerlaw behavior observed at the tissue level is assumed to exist across scales, from the continuum macroscopic level to that of the microstructural realm of the axons. The material parameters of the axons and glia are fitted to a springpot model. The 3D fractional viscoelastic springpot model is implemented within a finite element framework. The constitutive equations defining the fractional model are coded using a vectorized user defined material (VUMAT) subroutine in ABAQUS finite element software. Using this material characterization, representative volume elements (RVE) of axons embedded in glia with periodic boundary conditions are developed and subjected to a relaxation displacement boundary condition. The homogenized orthotropic fractional material properties of the axon-matrix system as a function of the volume fraction of axons in the ECM are extracted by solving the inverse problem.Comment: Accepted for publication at the 12th International Conference on Mathematical Modeling in Physical Science

FINITE ELEMENT ANALYSIS ON THE RANDOM CHOPPED FIBER COMPOSITES

ABSTRACT A micro-mechanics based finite element analysis method for random chopped fiber composites is applied. A modified random sequential adsorption technique is developed to generate representative volume elements of the composites so to overcome the "jamming limit" in the existing techniques. A homogenization scheme is applied to acquire the effective elastic constants of the composite. Two damage mechanisms are considered, matrix cracking and interfacial debonding, which occur prior to fiber breakage and consequentially leading to catastrophic failure. The incremental plastic model and the cohesive zone model are adopted to account for matrix plasticity and interfacial debonding, respectively. The finite element analysis results are validated by experimental data

Investigation of strength limiting mechanisms in aramid fibers

Aramid fibers owe their high tensile strength and stiffness to their orderly fibrillar structure. The synergistic effect of individual fibrils comprising an aramid fiber, and the interfibrillar interactions determine the strength of an individual fiber. In order to study the existence and role of statistical defects in failure initiation of aramid fibers, quasi-static tensile tests were performed with individual fibers of different molecular compositions and gage lengths in the range of 100 µm–10 mm. The experimental results pointed out to a relative insensitivity of the tensile strength to the fiber gage length, which suggested that failure initiation is governed by processes and/or flaws active at length scales well below micron scale. Therefore, differences in tensile strength between the particular types of aramid fibers discussed in this study were attributed to interfibrillar interactions. The magnitude of the latter was assessed by longitudinal crack growth experiments with individual fibers, as interfibrillar interactions are expected to be similar to the van der Waals interactions between the hydrogen bonded macromolecular sheets comprising the aramid fibers. The initial fracture experiments showed stable crack propagation under relatively constant force taking place for very large lengths of individual fibers. This presentation will provide the current results on the cohesive energy measurements on two types of aramid fibers designed to provide high tensile strength

Delamination growth behavior in cross-ply composites under compressive cyclic (fatigue) loading

Ph.D.George A. Kardomatea

A Data-Driven Framework to Predict Lithium-Ion Battery Cell Imbalance for Real-Time Battery Management Systems

Models that can predict battery cells’ thermal and electrical behaviors are necessary for real-time battery management systems to regulate the imbalance within battery cells. This work introduces a Gaussian Process Regression (GPR)-based data-driven framework that succeeds the Multi-Scale Multi-Dimensional (MSMD) modeling structure. The framework can make highly accurate predictions at the same level as full-order full-distribution simulations based on MSMD. A pseudo-2D model is used to generate training data and is combined with a process that shifts computation burdens from real-time battery management systems to lab data preparation. The testing results highlight the reliability of the GPR-based data-driven framework in terms of accuracy and stability under various operational conditions

A Data-Driven Framework to Predict Lithium-Ion Battery Cell Imbalance for Real-Time Battery Management Systems

Models that can predict battery cells’ thermal and electrical behaviors are necessary for real-time battery management systems to regulate the imbalance within battery cells. This work introduces a Gaussian Process Regression (GPR)-based data-driven framework that succeeds the Multi-Scale Multi-Dimensional (MSMD) modeling structure. The framework can make highly accurate predictions at the same level as full-order full-distribution simulations based on MSMD. A pseudo-2D model is used to generate training data and is combined with a process that shifts computation burdens from real-time battery management systems to lab data preparation. The testing results highlight the reliability of the GPR-based data-driven framework in terms of accuracy and stability under various operational conditions

An Ogden hyperelastic 3D micromechanical model to depict Poynting effect in brain white matter

Shear and torsional load on soft solids such as brain white matter purportedly exhibits the Poynting Effect. It is a typical nonlinear phenomenon associated with soft materials whereby they tend to elongate (positive Poynting effect) or contract (negative Poynting effect) in a direction perpendicular to the shearing or twisting plane. In this research, a novel 3D micromechanical Finite Element Model (FEM) has been formulated to describe the Poynting effect in bi-phasic modeled brain white matter (BWM) representative volume element (RVE) with axons tracts embedded in surrounding extracellular matrix (ECM) for simulating brain matter's response to pure and simple shear. In the presented BWM 3D FEM, nonlinear Ogden hyper-elastic material model is deployed to interpret axons and ECM material phases. The modeled bi-phasic RVEs have axons tied to the surrounding ECM. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear case were analyzed. Root mean square deviation (RMSD) was calculated for stress and deformation response plots to understand the effect of axon-ECM orientations and loading conditions on the degree of Poynting behavior. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane underscored the significance of axonal fiber-matrix interactions. From the simulated ensemble of cases, a transitional dominance trend was noticed, as simple sheared axons showed pronounced Poynting behavior, but shear deformation build-up in the purely sheared brain model exhibited the highest Poynting behavior at higher strain % limits. At lower strain limits, simple shear imparted across and perpendicular to axonal tract directions emerged as the dominant Poynting effect configurations. At high strains, the stress-strain% plots manifested mild strain stiffening effects and bending stresses in purely sheared axons, substantiated the strong non-linearity in brain tissues’ response