# Zohar YosibashTel Aviv University | TAU · School of Mechanical Engineering

Zohar Yosibash

Professor

## About

179

Publications

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## Publications

Publications (179)

Proximal humerus impacted fractures are of clinical concern in the elderly population. Prediction of such fractures by CT-based finite element methods encounters several major obstacles such as heterogeneous mechanical properties and fracture due to compressive strains. We herein propose to investigate a variation of the phase field method (PFM) em...

Pultrusion is a continuous process of forming constant cross-sections of unidirectional composites with a significant long length. This unique process is implemented widely in the composites industry due to its continuous, automated, and highly productive nature. The current research focused on mechanical response characterization at three modes of...

Structures made of steel alloys with V-notches may fracture at the V-notch tip at which a small plastic zone usually evolves. Failure criteria for predicting fracture loads for such quasi-brittle alloys, as a function of the V-notch opening angle are very scarce and have not been validated, to the best of our knowledge, by a set of experimental obs...

Background
Proximal humeri fractures at anatomical and surgical neck (∼5% and ∼50% incidence respectively) are frequent in elderly population. Yet, neither in-vitro experiments nor CT-based finite element analyses (CTFEA) have investigated these in depth. Herein we enhance (Dahan et al., 2019) (addressing anatomical neck fractures) by more experime...

Aims
Type 2 diabetes mellitus (T2DM) impairs bone strength and is a significant risk factor for hip fracture, yet currently there is no reliable tool to assess this risk. Most risk stratification methods rely on bone mineral density, which is not impaired by diabetes, rendering current tests ineffective. CT-based finite element analysis (CTFEA) cal...

Three-dimensional part-elliptic crack fronts are common in engineering practice. Herein we formulate a computational method, known as the quasidual function method (QDFM) for the functional representation of edge stress intensity functions (ESIFs) along such cracks in 3D domains. It is an efficient post-processing algorithm that may use the finite...

Three-dimensional part-elliptic crack fronts are common in engineering practice. Herein we formulate a computational method, known as the quasidual function method (QDFM) for the functional representation of edge stress intensity functions (ESIFs) along such cracks in 3D domains. It is an efficient post-processing algorithm that may use the finite...

Background
Most benign active and latent lesions of proximal femur do not predispose a patient to a pathologic fracture. Nonetheless, there is a tendency to perform internal fixation due to the lack of accurate clinical tools that may reliably confirm low risk of pathologic fracture. As many as 30% of these surgeries may be unnecessary. A patient-s...

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 r...

Aims:
Accurate estimations of the risk of fracture due to metastatic bone disease in the femur is essential in order to avoid both under-treatment and over-treatment of patients with an impending pathological fracture. The purpose of the current retrospective in vivo study was to use CT-based finite element analyses (CTFEA) to identify a clear qua...

Background: Long-term survival of hip implants is of increasing relevance due to the rising life expectancy. The biomechanical effect of strain shielding as a result of the implant insertion may lead to bone resorption, thus increase risk for implant loosening and periprosthetic fractures. Patient-specific quantification of strain shielding could a...

Finite element analysis (FEA), introduced more than half a century ago, requires a (qualified) analyst to generate the necessary input data, verify the output and post process the analysis results for a meaningful conclusion. The required expertise and labor efforts have precluded the use of FEA in daily medical practice by orthopedic surgeons for...

Take home message A retrospective in-vivo study on 41 patients with femoral MBD shows that CTFEA predicts the risk of an impending fracture by far better compared to Mirels' score (sensitivity of 100% and specificity of 67%). CTFEA predicts well the fracture location. The CTFEA is quick and automated and may be easily incorporated into CT sca...

Finite element analyses (FEAs) of human femurs are mostly validated by ex-vivo experimental observations. Such validations were largely performed by comparing local strains at a small subset of points to the gold standard strain gauge (SG) measurements. A comprehensive full field validation of femoral FEAs including both strains and displacements u...

A new numerical method to model the active response of arteries is proposed. Vasoconstrictors and vasodilators in the bloodstream diffuse from the lumen into the arterial wall through the intima and cause the smooth muscle cells, mostly in the media, to contract. We combine the diffusion process with the mechanical model in Yosibash and Priel (Comp...

Elliptical cracks are common in practice, as most cracks tend to propagate along semi-elliptical fronts. Herein we extend the quasidual function method (QDFM) for the computation of edge flux intensity functions (EFIFs) along elliptical cracks and generalized EFIFs along elliptical V-notches in 3-D domains. This QDFM is used to extract EFIFs from f...

Part-elliptical crack fronts are common in real life, especially at free surfaces and at fastener holes. For such cases we herein extend the quasidual function method (QDFM) presented in Schapira and Yosibash (2019) to allow the extraction of edge flux intensity functions (EFIFs) from finite element solutions. We consider the Laplace operator, whic...

The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to de...

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 r...

A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This c...

Background
Proximal humerus fractures which occur as a result of a fall on an outstretched arm are frequent among the elderly population. The necessity of stabilizing such fractures by surgical procedures is a controversial matter among surgeons. Validating a personalized FE analysis by ex-vivo experiments of humeri and mimicking such fractures by...

The asymptotic solution of the elasticity equations in the vicinity of an elliptical singular edge is derived and presented explicitly for an elliptical crack with traction free BCs. It is composed of edge stress intensity functions (ESIFs), which are functions along the singular edge, eigenfunctions and their shadows. The recursive equations to de...

Patient-specific QCT-based finite element (QCTFE) analyses enable highly accurate quantification of bone strength. We evaluated CT scanner influence on QCTFE models of long bones. A femur, humerus, and proximal femur without the head were scanned with K 2 HPO 4 phantoms by seven CT scanners (four models) using typical clinical protocols. QCTFE mode...

Realistic material properties, as the Young modulus E and Poisson ratio ν (isotropic materials), are measured by experimental observations and are inherently stochastic. Having their stochastic representation E(ξ) or ν(ξ) where ξ is a random variable, we formulate the elastic solution of the stochastic elasticity system in the vicinity of a crack t...

The T-stress in a three dimensional elastic domain containing a straight crack is considered. First the complete asymptotic expansion in the vicinity of the crack front, including the T-stress, is presented explicitly. Having obtained the asymptotic expansion, we compute the dual solution associated with the T-stress, and prove it must contain loga...

This paper presents an image-based method aimed at generating a mesh of high-order finite elements on a tubular structure. The method assumes that the object is immersed in a liquid with known refractive coefficients and the images are recorded by moving the camera on a circular path around the object. Both the refractive effects and the camera mot...

Background:
Over 1.6 million hip replacements are performed annually in Organisation for Economic Cooperation and Development countries, half of which involve cemented implants. Quantitative computer tomography based finite element methods may be used to assess the change in strain field in a femur following such a hip replacement, and thus determ...

Physician recommendation for prophylactic surgical fixation of a femur with metastatic bone disease (MBD) is usually based on Mirels' criteria and clinical experience, both of which suffer from poor specificity. This may result in a significant number of these health compromised patients undergoing unnecessary surgery. CT-based finite element analy...

Even though many studies have been conducted to understand and model the passive response of arteries, very few studies have been performed to develop constitutive equation for the active response of arteries and to perform numerical simulations. In this paper, the diffusion of the neurotransmitter, for example noradrenaline, is combined with the a...

At V-notched tips in specimens made of quasi-brittle materials a small damaged or plastic zone is evident that cannot not be neglected in terms of dissipated energy and stress state, although it is small. Herein, to predict the failure initiation at the notch tip, we extend the finite fracture mechanics (FFM) coupled criterion, which requires a sim...

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblo...

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) 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...

The singular solution of the Laplace equation with a straight crack is represented by a series of eigenpairs, shadows, and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM). The QDFM is based on the dual eigenpairs and shad...

Identification of unique material parameters for the media and adventitia in the case of arteries involves many challenges. Tension-inflation experiments were performed on the internal mammary artery and the axial force and the radial displacements were used to identify the material parameters. It will be shown that these experimental data are not...

This article discusses the passive response of arteries, with a particular focus on the material parameter identification process of constitutive model of anisotropic hyperelasticity. The arterial wall is composed of three layers: tunica intima, tunica media and tunica adventitia. However, only the media and the adventitia are assumed to be mechani...

The solution to the elasticity problem in three-dimensional polyhedral domains in the vicinity of an edge around which the material properties depend on the angular angle is addressed. This asymptotic solution involves a family of eigenpairs and their shadows which are being computed by means of p-finite element methods. In particular the examples...

Further experimental evidence on the compressibility of arteries under normal physiological pressure range is provided using the experimental apparatus introduced in Yosibash et al., JMBBM 39(2014):339–354. We enlarged the experimental database by including almost twice the number of experiments, we considered a different artery – the porcine commo...

A three-dimensional failure initiation criterion in brittle materials containing a sharp V-notch is presented and validated by experiments. It is based on simultaneous fulfilment of the stress requirement and a finite fracture mechanics energy release rate (ERR) requirement.
Since the ERR cannot determine failure initiation direction for dominant m...

Background:
Although ~200,000 emergency room visits per year in the US alone are associated with fractures of the proximal humerus, only limited studies exist on their mechanical response. We hypothesise that for the proximal humeri (a) the mechanical response can be well predicted by using inhomogeneous isotropic material properties, (b) the rela...

We revise the failure criterion by Yosibash, Priel and Leguillon for V-notched 2-D domains made of brittle elastic materials (Yosibash et al., 2006) under mixed-mode loading. It is based on a finite fracture mechanics (FFM) concept that requires the determination of a finite virtual crack that simultaneously satisfies the normal stress criterion an...

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$\epsilon$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue $\lambda$($\epsilon$) and the eigenvector angular frequency k($\epsilon$) for shells with Dirichlet bou...

Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\'e} 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 param...

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered...

The energy release rate (ERR) proposed by Irwin based on a theory by Griffith (1920) and Irwin (1957) has been extensively used as a fracture criterion in 2D for brittle domains. Under in-plane mixed mode loading (modes I+II), the direction of crack initiation from cracks and sharp V-notches was determined by the orientation at which the ERR attain...

Numerical solutions of non-linear stochastic thermo-hyperelastic problems at finite strains are addressed. These belong to a category of non-linear coupled problems that impose challenges on their numerical treatment both in the physical and stochastic spaces. Combining the high order finite element methods (FEMs) for discretizing the physical spac...

We compared the flow rates, reactivity, and morphology of the distal internal thoracic artery and its branches, the superior epigastric and musculophrenic arteries, to test their applicability as possible conduits in coronary artery bypass grafting surgeries.
Skeletonized internal thoracic artery and subdivisions of patients undergoing coronary art...

Uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element (FE) models in clinical applications. Reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor. We therefore analyze the in-vivo available data of seven individuals from H...

Explicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic...

Verified and validated simulations of the mechanical response of femurs, based on CT scans, have been recently presented. These simulations, based on high-order finite element methods (p-FEMs), may be used to diagnose the risk or fracture when used in clinical orthopedic practice. The first part of this chapter describes the methods used to create...

Background:
Predicting patient specific risk of fracture in femurs with metastatic tumors and the need for surgical intervention are of major clinical importance. Recent patient-specific high-order finite element methods (p-FEMs) based on CT-scans demonstrated accurate results for healthy femurs, so that their application to metastatic affected fe...

A definitive answer to the question whether artery walls are incompressible is to our opinion not yet categorically provided. Experimental-based evidence on the level of compressibility in artery walls is not easily achieved because of the difficulties associated with the measurement of very small differences in volumes under physiological pressure...

The difference in the potential energy in an elastic three-dimensional domain with a V-notch with and without a small crack (δΠδΠ) under a general mixed mode I+II+III loading is provided as an asymptotic series. It involves the V-notch edge stress intensity functions, the area of the formed crack, and special geometrical functions that can be pre-c...

Creep phenomenon at the scale of bone tissue (small specimens) is known to be present and demonstrated for low strains. Here creep is demonstrated on a pair of fresh-frozen human femurs at the organ level at high strains. Under a constant displacement applied on femur`s head, surface strains at the upper neck location increase with time until fract...

A newly developed method, named the quasi-dual function method (QDFM) is proposed for extracting edge stress intensity functions (ESIFs) along circular crack fronts from finite element solutions, in a general three-dimensional domain and boundary conditions. The mathematical machinery developed in the framework of the Laplace operator in [17] is ex...

The mechanical response of human metatarsal bones is of importance in both research and clinical practice, especially when associated with the correction of Hallux Valgus. Verified and validated patient-specific finite-element analysis (FEA) based on CT scans developed for human femurs are extended here to the first and second metatarsal bones. Two...

Explicit asymptotic series describing solutions to the Laplace equation in the vicinity of a circular edge in a three-dimensional domain was recently provided in Yosibash et al. (Int J Fract 168:31–52, 2011). Utilizing it, we extend the quasidual function method (QDFM) for extracting the generalized edge flux intensity functions (GEFIFs) along circ...

Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a ‘monolithic’ hig...

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.

The p-version of the finite element method (p-FEM) is extended to problems in the field of biomechanics: the mechanical response of bones and arteries. These problems are extremely challenging, partly because the constitutive models governing these materials are very complex and have not been investigated by sufficiently rigorous methods. Furthermo...

The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of high-order Finite Elements. While previous publications concentrated on single-field applications, this paper demonstrates that the advantages of the method carry over to the multi-physical context of linear thermoelasticity. The ability of the...

Background:
Verified and validated CT-based high-order finite element (FE) methods were developed that predict accurately the mechanical response of patient-specific intact femurs. Here we extend these capabilities to human femurs undergoing a total hip replacement using cemented prostheses.
Methods:
A fresh-frozen human femur was CT-scanned and...

Here we demonstrate the application of the SED failure criterion to a “real-life” engineering problem involving thermoelasticity effects in a microscale electronic device discussed in [205]. The fabrication of microelectronic devices (chips) is a multistep process aimed at creating a layered structure made of semiconductors, metals, and insulators.

The active mechanical response of an artery wall resulting from the contraction of the smooth muscle cells (SMCs) is represented by a strain energy function (SEDF) that augments the passive SEDF recently reported in Yosibash and Priel [Z. Yosibash, E. Priel, p-FEMs for hyperelastic anisotropic nearly incompressible materials under finite deformatio...

The focus of this contribution is on the parallelization of the Finite Cell Method (FCM) applied for biomechanical simulations of human femur bones. The FCM is a high-order fictitious domain method that combines the simplicity of Cartesian grids with the beneficial properties of hierarchical approximation bases of higher order for an increased accu...

A mandatory requirement for any reliable prediction of the mechanical response of bones, based on quantitative computer tomography, is an accurate relationship between material properties (usually Young's modulus E) and bone density ρ. Many such E-ρ relationships are available based on different experiments on femur specimens with a large spread du...

Preface.- Introduction.-An Introduction to the p- and hp-versions of the Finite Element Method.-Eigen-pairs Computation for Two-Dimensional Heat Conduction Singularities.-Computation of GFIFs for Two-Dimensional Heat Conduction Problems.-Eigen-pairs for two-dimensional elasticity.-Computing Generalized Stress Intensity Factors.-Thermal Generalized...

Throughout the book we have considered only cases in which the boundaries intersecting at the singular points were straight lines. We show in this appendix by a simple example problem that the leading singular term corresponding to a domain with curved boundaries that intersect at a specific angle are the same as if the boundaries were straight lin...

This last chapter is devoted to our latest results on circular edges, and some open questions that are the aim and scope of future research. In daily practice, in reality, most edges are curved in three-dimensional domains and therefore these are of utmost engineering interest. Here we concentrate on circular edges (a “penny-shaped crack” being a s...

Although singular points in 2-D domains have been extensively investigated, the vertex singularities in 3-D domains have received scant attention due to their complexity. To the best of our knowledge, numerical methods for the investigation of vertices of conical notches, specifically the exponents of the singularity, were first introduced in [23]....

The energy release rate in LEFM was given its name by Irwin in 1956 [86], but was already used in 1920 by Griffith and later shown to be equal to the J-integral by Cherepanov and Rice. In this chapter the various forms of the ERR and their connections are provided.

Let us consider the general scalar elliptic PDE in two dimensions: $$-{\partial }_{\beta }\left ({k}_{\beta \gamma }{\partial }_{\gamma
}\tau \right ) = 0\quad \text{ in}\ \Omega,\quad \quad \beta,\gamma
= 1,2,$$ which can be more conveniently represented as $$-\nabla \cdot \left ([k]\nabla \tau \right ) = 0\quad \text{ in}\ \Omega,$$ where Ω is th...

The two-dimensional elastic solution in the vicinity of a singular point has the same characteristics as presented for the heat conduction solution, namely, it can be expanded as a linear combination of eigenpairs and their coefficients:
$$u = \sum\limits_{i=0}^{I} \sum\limits_{j=0}^{J} \sum\limits_{l=0}^{L} A_{{i}{j}{r}}r^{\alpha_{{i}+j}} 1n^{l}(r...

Here we present a numerical procedure based on the p-version of the finite element method for computing efficiently and reliably approximations to the eigenpairs associated with two-dimensional heat conduction singular points. The proposed method, called the “modified Steklov method,” is general, that is, applicable to singularities associated with...

The various methods described in this monograph for the computation of eigenpairs and GFIF/GSIFs cannot in general be carried out by means of analytical techniques; thus they require the use of numerical methods. We use the p_version of the FE method as the machinery for obtaining the required quantities, therefore, this chapter provides a brief in...

We consider here the exact solution for an elliptic problem with piecewise constant coefficients, representing an anisotropic 2-D domain. Analytical methods are applied to compute the eigenpairs by transformation of the coordinate system.

Having computed the eigenpairs associated with a 2-D singular point, the next task is the computation of the coefficients of the series expansion Ai ’s, called for the heat conduction equation “generalized flux intensity functions” (GFIFs). The eigenpairs may be viewed as characterizing the straining modes, and their amplitudes (the GFIFs) quantify...

In the previous chapter we described the asymptotic solution to heat conduction problems in the vicinity of edges, where EFIFs are functions along the edge. In this chapter we discuss two different pointwise extraction methods for EFIFs, and then introduce a novel method, called the quasidual function method, that extracts the functional representa...