scholarly journals Damage Mechanics of Carbon Nanotubes

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
George Z. Voyiadjis ◽  
◽  
Peter I. Kattan ◽  
Keyword(s):  
Carbon Nanotubes ◽  
Damage Mechanics ◽  
Three Dimensional ◽  
Damage Variable ◽  
Dimensional Case ◽  
Third Order ◽  
Cross Sectional ◽  
Energy Equivalence ◽  
The One

A robust mathematical method for the characterization of damage in carbon nanotubes is presented the presentation here is limited to elasticity. In this regard, the second and third order elastic stiffnesses are employed. All this is based on damage mechanics. The hypotheses of elastic strain equivalence and elastic energy equivalence are utilized. A new damage variable is proposed that is defined in terms of the surface area. This is in contrast to the classical damage variable which is defined in terms of the cross-sectional area. In the presentation, both the one-dimensional case (scalars) and the three-dimensional case (tensors) are illustrated.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

scholarly journals THE ETIOLOGIC RELEVANCE OF 3-D PATHOANATOMY OF ADOLESCENT IDIOPATHIC SCOLIOSIS

2017 ◽  
Vol 16 (4) ◽  
pp. 302-307
Author(s):  
Tom Schlösser ◽  
Rob Brink ◽  
René Castelein
Keyword(s):  
Adolescent Idiopathic Scoliosis ◽  
Idiopathic Scoliosis ◽  
Three Dimensional ◽  
Imaging Studies ◽  
Cross Sectional ◽  
Ongoing Research ◽  
Biomechanical Loading ◽  
Cross Sectional Imaging ◽  
Sectional Imaging ◽  
The One

ABSTRACT Despite many years of dedicated research into the etiopathogenesis of adolescent idiopathic scoliosis, there is still no single distinct cause for this puzzling condition. In this overview, we attempt to link knowledge on the complex three-dimensional pathoanatomy of AIS, based on our ongoing research in this field, with etiopathogenic questions. Evidence from multiple recent cross-sectional imaging studies is provided that supports the hypothesis that AIS has an intrinsic biomechanical basis: an imbalance between the biomechanical loading of the upright human spine due to its unique sagittal configuration on the one hand, and the body’s compensating mechanisms on the other. The question that remains in the etiology of AIS, and the focus of our ongoing research, is to determine what causes or induces this imbalance.

Mechanics of damage, healing, damageability, and integrity of materials: A conceptual framework

2016 ◽  
Vol 26 (1) ◽  
pp. 50-103 ◽  
Author(s):  
George Z Voyiadjis ◽  
Peter I Kattan
Keyword(s):  
Damage Mechanics ◽  
Healing Process ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Variable Section ◽  
Damage Healing ◽  
Characterization Of Materials ◽  
New Formulation

In this work several new and fundamental concepts are proposed within the framework of continuum damage mechanics. These concepts deal primarily with the nature of the two processes of damage and healing along with introducing a consistent and systematic definition for the concepts of damageability and integrity of materials. Toward this end, seven sections are presented as follows: “The logarithmic damage variable” section introduces the logarithmic and exponential damage variables and makes comparisons with the classical damage variable. In “Integrity and damageability of materials” section a new formulation for damage mechanics is presented in which the two angles of damage–integrity and healing–damageability are introduced. It is shown that both the damage variable and the integrity variable can be derived from the damage–integrity angle while the healing variable and damageability variable are derived from the healing–damageability angle. “The integrity field” section introduces the new concept of the integrity field while “The healing field” section introduces the new concept of the healing field. These two fields are introduced as a generalization of the classical concepts of damage and integrity. “Unhealable damage and nondamageable integrity” section introduces the new and necessary concept of unrecoverable damage or unhealable damage. In this section the concept of permanent integrity or nondamageable integrity is also presented. In “Generalized nonlinear healing” section generalized healing is presented where a distinction is clearly made between linear healing and nonlinear healing. As an example of nonlinear healing the equations of quadratic healing are derived. Finally in “Dissection of the healing process” section a complete and logical/mathematical dissection is made of the healing process. It is hoped that these new and fundamental concepts will pave the way for new, consistent, and holistic avenues in research in damage mechanics and characterization of materials.

Verification of a Finite Element Method for Solving One-Dimensional Equations of Blood Flow Incorporating a Viscoelastic Wall Model

2009 ◽  
Author(s):  
Rashmi Raghu ◽  
Charles A. Taylor
Keyword(s):  
Blood Flow ◽  
Surgical Planning ◽  
Computational Cost ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Cross Sectional ◽  
One Dimensional ◽  
The One ◽  
Modeling Flow ◽  
Three Dimensional Simulations

The one-dimensional (1-D) equations of blood flow consist of the conservation of mass equation, balance of momentum equation and a wall constitutive equation with arterial flow rate, cross-sectional area and pressure as the variables. 1-D models of blood flow enable the solution of large networks of blood vessels including wall deformability. Their level of detail is appropriate for applications such as modeling flow and pressure waves in surgical planning and their computational cost is low compared to three-dimensional simulations.

Constitutive Inequalities for the Damage of Elastic-Brittle Materials

2011 ◽  
Vol 675-677 ◽  
pp. 891-899
Author(s):  
Qi Chang He ◽  
J.Z. Zhou
Keyword(s):  
Three Dimensional ◽  
Brittle Materials ◽  
Dimensional Case ◽  
Continuum Damage ◽  
One Dimensional ◽  
Damage Models ◽  
Constitutive Inequalities ◽  
The One

Starting from the requirement that the principle of determinism be satisfied, two constitutive inequalities are derived for one-dimensional strain- and stress-based continuum damage models. The one-dimensional constitutive inequality corresponding to the strain-based formulation turns out to be much less restrictive than the one associated to the stress-based formulation and is extended to the three-dimensional case. This extension gives a general constitutive inequality for the damage of elastic-brittle materials.

Three-Dimensional Anatomic Characterization of the Canine Laryngeal Abductor and Adductor Musculature

2000 ◽  
Vol 109 (5) ◽  
pp. 505-513 ◽  
Author(s):  
Corey W. Mineck ◽  
Roger Chan ◽  
Niro Tayama ◽  
Ingo R. Titze
Keyword(s):  
Vocal Fold ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Cross Sectional ◽  
3 Dimensional ◽  
Moment Arms ◽  
Intrinsic Laryngeal Muscle ◽  
Posterior Cricoarytenoid ◽  
Intrinsic Laryngeal Muscles

The biomechanics of vocal fold abduction and adduction during phonation, respiration, and airway protection are not completely understood. Specifically, the rotational and translational forces on the arytenoid cartilages that result from intrinsic laryngeal muscle contraction have not been fully described. Anatomic data on the lines of action and moment arms for the intrinsic laryngeal muscles are also lacking. This study was conducted to quantify the 3-dimensional orientations and the relative cross-sectional areas of the intrinsic abductor and adductor musculature of the canine larynx. Eight canine larynges were used to evaluate the 3 muscles primarily responsible for vocal fold abduction and adduction: the posterior cricoarytenoid, the lateral cricoarytenoid, and the interarytenoid muscles. Each muscle was exposed and divided into discrete fiber bundles whose coordinate positions were digitized in 3-dimensional space. The mass, length, relative cross-sectional area, and angle of orientation for each muscle bundle were obtained to allow for the calculations of average lines of action and moment arms for each muscle. This mapping of the canine laryngeal abductor and adductor musculature provides important anatomic data for use in laryngeal biomechanical modeling. These data may also be useful in surgical procedures such as arytenoid adduction.

Aneurysm presence at the anterior communicating artery bifurcation is associated with caliber tapering of the A1 segment

2021 ◽  
pp. 1-11
Author(s):  
Alexandra Lauric ◽  
Luke Silveira ◽  
Emal Lesha ◽  
Jeffrey M. Breton ◽  
Adel M. Malek
Keyword(s):  
Three Dimensional ◽  
Parametric Models ◽  
Anterior Communicating Artery ◽  
Predisposing Factor ◽  
Cross Sectional ◽  
Flow Acceleration ◽  
Significant Difference ◽  
Healthy Control ◽  
Mca Aneurysm

OBJECTIVE Vessel tapering results in blood flow acceleration at downstream bifurcations (firehose nozzle effect), induces hemodynamics predisposing to aneurysm initiation, and has been associated with middle cerebral artery (MCA) aneurysm presence and rupture status. The authors sought to determine if vessel caliber tapering is a generalizable predisposing factor by evaluating upstream A1 segment profiles in association with aneurysm presence in the anterior communicating artery (ACoA) complex, the most prevalent cerebral aneurysm location associated with a high rupture risk. METHODS Three-dimensional rotational angiographic studies were analyzed for 68 patients with ACoA aneurysms, 37 nonaneurysmal contralaterals, and 53 healthy bilateral controls (211 samples total). A1 segments were determined to be dominant, codominant, or nondominant based on flow and size. Equidistant cross-sectional orthogonal cuts were generated along the A1 centerline, and cross-sectional area (CSA) was evaluated proximally and distally, using intensity-invariant edge detection filtering. The relative tapering of the A1 segment was evaluated as the tapering ratio (distal/proximal CSA). Computational fluid dynamics was simulated on ACoA parametric models with and without tapering. RESULTS Aneurysms occurred predominantly on dominant (79%) and codominant (17%) A1 segments. A1 segments leading to unruptured ACoA aneurysms had significantly greater tapering compared to nonaneurysmal contralaterals (0.69 ± 0.13 vs 0.80 ± 0.17, p = 0.001) and healthy controls (0.69 ± 0.13 vs 0.83 ± 0.16, p < 0.001), regardless of dominance labeling. There was no statistically significant difference in tapering values between contralateral A1 and healthy A1 controls (0.80 ± 0.17 vs 0.83 ± 0.16, p = 0.56). Hemodynamically, A1 segment tapering induces high focal pressure, high wall shear stress, and high velocity at the ACoA bifurcation. CONCLUSIONS Aneurysmal, but not contralateral or healthy control, A1 segments demonstrated significant progressive vascular tapering, which is associated with aneurysmogenic hemodynamic conditions at the ACoA complex. Demonstration of the upstream tapering effect in the communicating ACoA segment is consistent with its prior detection in the noncommunicating MCA bifurcation, which together form more than 50% of intracranial aneurysms. The mechanistic characterization of this upstream vascular tapering phenomenon is warranted to understand its clinical relevance and devise potential therapeutic strategies.

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

scholarly journals The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wang Guangbao ◽  
Ding Guangtao
Keyword(s):  
Lagrange Function ◽  
Three Dimensional ◽  
Hamiltonian Function ◽  
First Integral ◽  
Dimensional Case ◽  
Analytical Mechanics ◽  
Two Dimensional ◽  
Rectangular Coordinates ◽  
Polar Coordinate ◽  
The One

The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

Sign in / Sign up

Export Citation Format

Share Document