A projection method to extract biological membrane models from 3D material models

Journal of Sound and Vibration

2018

Self Cite

The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures. 1 identity tensor in R 3 co-variant tangent vectors of ; = 1, 2 co-variant components of the metric tensor of contra-variant components of the metric tensor of contra-variant tangent vectors of ; = 1, 2 0 reference configuration of the manifold current configuration of the manifold co-variant components curvature tensor of (0) logarithmic surface strain (0) dev deviatoric part of the logarithmic strain Γ Christoffel symbols of the second kind mean curvature of surface area change of 1

mentioning

confidence: 99%

Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities

Ghaffari

Journal of Sound and Vibration

2018

Self Cite

“…g αβ = a αβ and g 33 = λ 2 3 . Thus, a 3D material model can be reduced to a 2D membrane one as (Roohbakhshan et al, 2016)…”

Section: Directly-decoupled (Dd) Shell Modelmentioning

confidence: 99%

“…In many cases, such structures do not resist any bending moments (Humphrey, 1998); thus, a membrane formulation (e.g. Roohbakhshan et al, 2016) is efficient and robust to predict the mechanical response. However, if the bending effects are not negligible, a shell formulation is required.…”

Section: Introductionmentioning

confidence: 99%

“…The finite element modeling and analysis of thin soft tissues has been the subject of extensive research although only the membrane forces are considered in general (e.g. Humphrey et al, 1992;Humphrey, 1998;Prot et al, 2007;Kroon and Holzapfel, 2009;Abdessalem et al, 2011;Kuhl, 2013, 2014;Roohbakhshan et al, 2016) and mostly planar tissues are studied (e.g. Flynn et al, 1998;Sun and Sacks, 2005;Holzapfel and Ogden, 2009;Jacobs et al, 2013;Fan and Sacks, 2014).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient isogeometric thin shell formulations for soft biological materials

Roohbakhshan

Biomech Model Mechanobiol

2017

Self Cite

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.

“…Compared to earlier works, this paper presents a dynamic finite membrane element formulation for liquids that: 1) allows for different concentration-dependent constitutive laws for dynamic surface tension of the liquid-gas interface; 2) can be coupled with structural finite membrane, shell and solid elements; 3) can model thin films, bubbles, liquid droplets and menisci; 4) is able to treat different external forces (like gravity and pressure), contact constraints and various boundary conditions like contact lines with specified contact angles; 5) can include the effect of line tension if needed. Furthermore, in Roohbakhshan (2018), the presented formulation is combined with the computational biological membrane model of Roohbakhshan et al (2016) in order to model surfactantlined alveolar tissue.…”

Section: Introductionmentioning

confidence: 99%

A finite membrane element formulation for surfactants

Roohbakhshan

Colloids and Surfaces A: Physicochemical and Engineering Aspect

2019

Self Cite

Surfactants play an important role in various physiological and biomechanical applications. An example is the respiratory system, where pulmonary surfactants facilitate the breathing and reduce the possibility of airway blocking by lowering the surface tension when the lung volume decreases during exhalation. This function is due to the dynamic surface tension of pulmonary surfactants, which depends on the concentration of surfactants spread on the liquid layer lining the interior surface of the airways and alveoli. Here, a finite membrane element formulation for liquids is introduced that allows for the dynamics of concentration-dependent surface tension, as is the particular case for pulmonary surfactants. A straightforward approach is suggested to model the contact line between liquid drops/menisci and planar solid substrates, which allows the presented framework to be easily used for drop shape analysis. It is further shown how line tension can be taken into account. Following an isogeometric approach, NURBSbased finite elements are used for the discretization of the membrane surface. The capabilities of the presented computational model is demonstrated by different numerical examples -such as the simulation of liquid films, constrained and unconstrained sessile drops, pendant drops and liquid bridges -and the results are compared with experimental data.