A microsphere-based remodelling formulation for anisotropic biological tissues

2009 ◽  
Vol 367 (1902) ◽  
pp. 3499-3523 ◽  
Author(s):  
Andreas Menzel ◽  
Tobias Waffenschmidt
Keyword(s):  
Evolution Equations ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Internal Variables ◽  
Chain Model ◽  
Chain Molecules ◽  
Numerical Studies ◽  
Algorithmic Treatment ◽  
The One ◽  
Unit Vectors

Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material’s anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

MRS Advances ◽  
2016 ◽  
Vol 1 (24) ◽  
pp. 1791-1796 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Slip System ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Structure Evolution ◽  
Internal Variables ◽  
Plastic Shear ◽  
Continuum Dislocation Dynamics ◽  
Dynamics Simulations

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

Strain-Rate Sensitive Constitutive Modeling of Anisotropic Visco-Hyperelastic Materials

2012 ◽  
Author(s):  
Sahand Ahsanizadeh ◽  
LePing Li
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Internal Variables ◽  
Current Configuration ◽  
Hyperelastic Materials ◽  
History Of ◽  
Viscoelastic Constitutive Model

Integral-based formulations of viscoelasticity have been widely used to describe the mechanical behavior of soft biological tissues and polymers. However, it is suggested that they are not suitable to be used under high strain rates. On the other hand, strain-rate sensitive models with an explicit dependence on the strain-rate have been developed for a certain class of materials. They predict the viscoelastic behavior during ramp loading more accurately while fail to account for the relaxation response. In order to overcome these drawbacks, a viscoelastic constitutive model has been proposed in this study based on the concept of internal variables. While the behavior of elastic materials is uniquely determined by the current state of deformation or external variables, the mechanical response of inelastic materials are regulated also by internal variables. The internal variables are associated with the dissipative mechanisms in the material and along with the evolution equations introduce the effect of history of the deformation to the current configuration. The current study employs short-term and long-term internal variables to account for the viscoelastic response during loading and relaxation respectively.

Modeling the Mullins effect of rubber-like materials

2016 ◽  
Vol 26 (6) ◽  
pp. 933-948 ◽  
Author(s):  
Yihui Pan ◽  
Zheng Zhong
Keyword(s):  
Free Energy ◽  
Energy Dissipation ◽  
Evolution Equations ◽  
Helmholtz Free Energy ◽  
Mass Conservation ◽  
Internal Variables ◽  
Bond Rupture ◽  
Chain Model ◽  
Mullins Effect ◽  
Physical And Chemical

In this paper, the Mullins effect that is a stress-softening phenomenon of rubber-like materials during cyclic loadings is studied, by considering the energy dissipation process of weak physical and chemical bond rupture. The eight-chain model is used to construct the Helmholtz free energy, with two network structure parameters (the chain density n and the average number of monomer segments of a polymer chain N) being taken as internal variables, which can be derived in terms of a given stretch at the start point of each unloading by analyzing the stored Helmholtz free energy and the unloading stress–stretch relation. Furthermore, a novel method is developed to determine the evolution equations of these internal variables through the analysis of mass conservation and energy dissipation, and then the Mullins effect of rubber-like materials can be theoretically predicted and agree with experimental results, not only for the unloading curves, but also for the first loading curve.

A comparative study of a multi-surface and a non-quadratic plasticity model with application to the in-plane anisotropic elastoplastic modelling of paper and paperboard

2018 ◽  
Vol 53 (6) ◽  
pp. 753-767 ◽  
Author(s):  
Rex Bedzra ◽  
Yujun Li ◽  
Stefanie Reese ◽  
Jaan-Willem Simon
Keyword(s):  
Constitutive Model ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Euler Method ◽  
Internal Variables ◽  
Surface Model ◽  
Plasticity Model ◽  
Tension Tests ◽  
Backward Euler ◽  
Numerical Performance

In this paper, a three-dimensional anisotropic multi-surface model for the in-plane elastoplastic deformation of paper and paperboard is developed. The model is based on the concept of structural tensors. It employs three different yield functions and parameterised consistency conditions for three different loading scenarios. The evolution of the yield surface with plastic strain is described by multiple hardening variables. Furthermore, the evolution equations are integrated using the unconditionally stable backward Euler method. Also, the internal variables are updated using a particular form of the elastic predictor/plastic corrector algorithm. The constitutive model is calibrated from a set of simple uniaxial tension tests performed in various directions of the material and is validated against loading in other directions. Additionally, the predictive capability as well as the numerical performance of the constitutive model is accessed against an existing non-quadratic plasticity model. Finally, the applicability of the constitutive model is demonstrated by performing a tensile test on a paperboard with a hole.

Three-Dimensional Visualization of the T-System of Frog Muscle Using High Voltage Electron Microscopy and a Lanthanum Stain

1977 ◽  
Vol 35 ◽  
pp. 570-571 ◽  
Author(s):  
Lee D. Peachey ◽  
Clara Franzini-Armstrong
Keyword(s):  
Electron Microscopy ◽  
High Voltage ◽  
Three Dimensional ◽  
Biological Tissues ◽  
High Voltage Electron Microscopy ◽  
Transverse Tubular System ◽  
Peroxidase Reaction ◽  
Voltage Electron ◽  
High Voltage Electron ◽  
T System

The effective study of biological tissues in thick slices of embedded material by high voltage electron microscopy (HVEM) requires highly selective staining of those structures to be visualized so that they are not hidden or obscured by other structures in the image. A tilt pair of micrographs with subsequent stereoscopic viewing can be an important aid in three-dimensional visualization of these images, once an appropriate stain has been found. The peroxidase reaction has been used for this purpose in visualizing the T-system (transverse tubular system) of frog skeletal muscle by HVEM (1). We have found infiltration with lanthanum hydroxide to be particularly useful for three-dimensional visualization of certain aspects of the structure of the T- system in skeletal muscles of the frog. Specifically, lanthanum more completely fills the lumen of the tubules and is denser than the peroxidase reaction product.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

scholarly journals A computational framework for modeling cell–matrix interactions in soft biological tissues

2021 ◽  
Author(s):  
Jonas F. Eichinger ◽  
Maximilian J. Grill ◽  
Iman Davoodi Kermani ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Soft Tissues ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Computational Framework ◽  
Cell Matrix ◽  
Physiological Processes ◽  
Matrix Interactions ◽  
Mechanical Homeostasis ◽  
Cell Matrix Interactions ◽  
Short Time

AbstractLiving soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

scholarly journals Acoustic Cell Patterning in Hydrogel for Three-Dimensional Cell Network Formation

Micromachines ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 3
Author(s):  
Kyo-in Koo ◽  
Andreas Lenshof ◽  
Le Thi Huong ◽  
Thomas Laurell
Keyword(s):  
Network Formation ◽  
Umbilical Vein ◽  
Three Dimensional ◽  
Extrusion Process ◽  
Fibroblast Cells ◽  
Glass Capillary ◽  
Cell Network ◽  
Significant Difference ◽  
The One ◽  
Umbilical Vein Endothelial Cells

In the field of engineered organ and drug development, three-dimensional network-structured tissue has been a long-sought goal. This paper presents a direct hydrogel extrusion process exposed to an ultrasound standing wave that aligns fibroblast cells to form a network structure. The frequency-shifted (2 MHz to 4 MHz) ultrasound actuation of a 400-micrometer square-shaped glass capillary that was continuously perfused by fibroblast cells suspended in sodium alginate generated a hydrogel string, with the fibroblasts aligned in single or quadruple streams. In the transition from the one-cell stream to the four-cell streams, the aligned fibroblast cells were continuously interconnected in the form of a branch and a junction. The ultrasound-exposed fibroblast cells displayed over 95% viability up to day 10 in culture medium without any significant difference from the unexposed fibroblast cells. This acoustofluidic method will be further applied to create a vascularized network by replacing fibroblast cells with human umbilical vein endothelial cells.

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