arXiv subjects

Zohar Yosibash

Publications and source records attributed to Zohar Yosibash.

5 recordsLinked to original sources

arXiv2025

Finite element analysis of very large bone models based on micro-CT scans

High-resolution voxel-based micro-finite element ($μ$FE) models derived from $μ$CT imaging enable detailed investigation of bone mechanics but remain computationally challenging at anatomically relevant scales. This study presents a comprehensive $μ$FE framework for large-scale biomechanical analysis of an intact New Zealand White (NZW) rabbit femur, integrating advanced segmentation, scalable finite element solvers, and experimental validation using predominantly open-source libraries. Bone geometries were segmented from $μ$CT data using the MIA clustering algorithm and converted into voxel-based $μ$FE meshes, which were solved using the open-source MFEM library with algorithms designed for large-scale linear elasticity systems. The numerical solutions were verified by comparing with a commercial finite element solver, and by evaluating the performance of full assembly and element-by-element formulations within MFEM. Models containing over $8\times10^{8}$ DOFs were solved using moderate HPC resources, demonstrating the feasibility of anatomically realistic $μ$FE simulations at this scale. Resolution effects were investigated by comparing models with voxel sizes of 20, 40, and 80 $μ$m, revealing that 40 $μ$m preserves boundary displacement and principal strain distributions with minimal bias while significantly reducing computational cost. Sensitivity analyses further showed that segmentation parameters influence the global mechanical response. Finally, $μ$FE predictions were coupled with Digital Image Correlation measurements on an NZW rabbit femur under compression to calibrate effective bone material properties at the micron scale. The results demonstrate that large-scale, experimentally informed $μ$FE modeling can be achieved using open-source tools, providing a robust foundation for preclinical assessment of bone mechanics and treatment-related risks.

physics.med-ph↗

arXiv2019

A 3D benchmark problem for crack propagation in brittle fracture

We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load-displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced.

cs.CE↗

arXiv2017

Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases

Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{é} system) are determined by an asymptotic analysis as the thickness ($2\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\varepsilon$. Optimizing $k$ for each chosen $\varepsilon$, we find power laws for $k$ in function of $\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding eigenpairs generate quasimodes for the 3D Lam{é} system by means of several reconstruction operators, including boundary layer terms. Numerical experiments demonstrate that in many cases the constructed eigenpair corresponds to the first eigenpair of the Lam{é} system.Geometrical conditions are necessary to this approach: The Gaussian curvature has to be nonnegative and the azimuthal curvature has to dominate the meridian curvature in any point of the midsurface. In this case, the first eigenvector admits progressively larger oscillation in the angular variable as $\varepsilon$ tends to $0$. Its angular frequency exhibits a power law relationof the form $k=γ\varepsilon^{-β}$ with $β=\frac14$ in the parabolic case (cylinders and trimmed cones), and the various $β$s $\frac25$, $\frac37$, and $\frac13$ in the elliptic case.For these cases where the mathematical analysis is applicable, numerical examples that illustrate the theoretical results are presented.

math.NA↗

arXiv2016

High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$ε$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue $λ$($ε$) and the eigenvector angular frequency k($ε$) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k($ε$) is always zero. In contrast to it, for the Lam{é} system of linear elasticity several different types of shells are defined, characterized by their geometry, for which k($ε$) tends to infinity as $ε$ tends to zero. For two families of shells: cylinders and elliptical barrels we explicitly provide $λ$($ε$) and k($ε$) and demonstrate by numerical examples the different behavior as $ε$ tends to zero.

math.NA↗

arXiv2012

Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions

This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular edge with Neumann boundary conditions on the faces that intersect at the singular edge. Two configurations are investigated: a penny-shaped crack and a 90^o V-notch.

math.NA↗