157 research outputs found
A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact
A unified fluid-structure interaction (FSI) formulation is presented for
solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the
generalized-alpha scheme are used for the spatial and temporal discretization.
The membrane discretization is based on curvilinear surface elements that can
describe large deformations and rotations, and also provide a straightforward
description for contact. The fluid is described by the incompressible
Navier-Stokes equations, and its discretization is based on stabilized
Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming
sharp interface discretization, and the resulting non-linear FE equations are
solved monolithically within the Newton-Raphson scheme. An arbitrary
Lagrangian-Eulerian formulation is used for the fluid in order to account for
the mesh motion around the structure. The formulation is very general and
admits diverse applications that include contact at free surfaces. This is
demonstrated by two analytical and three numerical examples exhibiting strong
coupling between fluid and structure. The examples include balloon inflation,
droplet rolling and flapping flags. They span a Reynolds-number range from
0.001 to 2000. One of the examples considers the extension to rotation-free
shells using isogeometric FE.Comment: 38 pages, 17 figure
A finite membrane element formulation for surfactants
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, NURBS-based 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.Comment: Some typos are removed. Eqs. 13 and 105 are modified. Eqs. 64 and 73
are added; thus, the rest of equations is renumbered. All the numerical
experiments are repeated. The example of Sec. 6.3 is slightly modifie
A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones
A new hyperelastic material model is proposed for graphene-based structures,
such as graphene, carbon nanotubes (CNTs) and carbon nanocones (CNC). The
proposed model is based on a set of invariants obtained from the right surface
Cauchy-Green strain tensor and a structural tensor. The model is fully
nonlinear and can simulate buckling and postbuckling behavior. It is calibrated
from existing quantum data. It is implemented within a rotation-free
isogeometric shell formulation. The speedup of the model is 1.5 relative to the
finite element model of Ghaffari et al. [1], which is based on the logarithmic
strain formulation of Kumar and Parks [2]. The material behavior is verified by
testing uniaxial tension and pure shear. The performance of the material model
is illustrated by several numerical examples. The examples include bending,
twisting, and wall contact of CNTs and CNCs. The wall contact is modeled with a
coarse grained contact model based on the Lennard-Jones potential. The buckling
and post-buckling behavior is captured in the examples. The results are
compared with reference results from the literature and there is good
agreement
Efficient isogeometric thin shell formulations for soft biological materials
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.Comment: Typos are removed. Remark 3.4 is added. Eq. (18) in the previous
version is removed. Thus, the equations get renumbered. Example 5.5 is
updated. Minor typos in Eqs. (17), (80), (145) and (146), are corrected. They
do not affect the result
The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity
This work presents a general unified theory for coupled nonlinear elastic and
inelastic deformations of curved thin shells. The coupling is based on a
multiplicative decomposition of the surface deformation gradient. The
kinematics of this decomposition is examined in detail. In particular, the
dependency of various kinematical quantities, such as area change and
curvature, on the elastic and inelastic strains is discussed. This is essential
for the development of general constitutive models. In order to fully explore
the coupling between elastic and different inelastic deformations, the surface
balance laws for mass, momentum, energy and entropy are examined in the context
of the multiplicative decomposition. Based on the second law of thermodynamics,
the general constitutive relations are then derived. Two cases are considered:
Independent inelastic strains, and inelastic strains that are functions of
temperature and concentration. The constitutive relations are illustrated by
several nonlinear examples on growth, chemical swelling, thermoelasticity,
viscoelasticity and elastoplasticity of shells. The formulation is fully
expressed in curvilinear coordinates leading to compact and elegant expressions
for the kinematics, balance laws and constitutive relations
The irreversible thermodynamics of curved lipid membranes
The theory of irreversible thermodynamics for arbitrarily curved lipid
membranes is presented here. The coupling between elastic bending and
irreversible processes such as intra-membrane lipid flow, intra-membrane phase
transitions, and protein binding and diffusion is studied. The forms of the
entropy production for the irreversible processes are obtained, and the
corresponding thermodynamic forces and fluxes are identified. Employing the
linear irreversible thermodynamic framework, the governing equations of motion
along with appropriate boundary conditions are provided.Comment: 62 pages, 4 figure
A new shell formulation for graphene structures based on existing ab-initio data
An existing hyperelastic membrane model for graphene calibrated from
ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates
and extended to a rotation-free shell formulation based on isogeometric finite
elements. Therefore, the membrane model is extended by a hyperelastic bending
model that reflects the ab-inito data of Kudin et al. (2001). The proposed
formulation can be implemented straight-forwardly into an existing finite
element package, since it does not require the description of molecular
interactions. It thus circumvents the use of interatomic potentials that tend
to be less accurate than ab-initio data. The proposed shell formulation is
verified and analyzed by a set of simple test cases. The results are in
agreement to analytical solutions and satisfy the FE patch test. The
performance of the shell formulation for graphene structures is illustrated by
several numerical examples. The considered examples are indentation and peeling
of graphene and torsion, bending and axial stretch of carbon nanotubes.
Adhesive substrates are modeled by the Lennard-Jones potential and a coarse
grained contact model. In principle, the proposed formulation can be extended
to other 2D materials.Comment: New examples are added and some typos are removed. The previous
results are unchanged, International Journal of Solids and Structures (2017
C1-continuous space-time discretization based on Hamilton's law of varying action
We develop a class of C1-continuous time integration methods that are
applicable to conservative problems in elastodynamics. These methods are based
on Hamilton's law of varying action. From the action of the continuous system
we derive a spatially and temporally weak form of the governing equilibrium
equations. This expression is first discretized in space, considering standard
finite elements. The resulting system is then discretized in time,
approximating the displacement by piecewise cubic Hermite shape functions.
Within the time domain we thus achieve C1-continuity for the displacement field
and C0-continuity for the velocity field. From the discrete virtual action we
finally construct a class of one-step schemes. These methods are examined both
analytically and numerically. Here, we study both linear and nonlinear systems
as well as inherently continuous and discrete structures. In the numerical
examples we focus on one-dimensional applications. The provided theory,
however, is general and valid also for problems in 2D or 3D. We show that the
most favorable candidate -- denoted as p2-scheme -- converges with order four.
Thus, especially if high accuracy of the numerical solution is required, this
scheme can be more efficient than methods of lower order. It further exhibits,
for linear simple problems, properties similar to variational integrators, such
as symplecticity. While it remains to be investigated whether symplecticity
holds for arbitrary systems, all our numerical results show an excellent
long-term energy behavior.Comment: slightly condensed the manuscript, added references, numerical
results unchange
A segmentation-free isogeometric extended mortar contact method
This paper presents a new isogeometric mortar contact formulation based on an
extended finite element interpolation to capture physical pressure
discontinuities at the contact boundary. The so called two-half-pass algorithm
is employed, which leads to an unbiased formulation and, when applied to the
mortar setting, has the additional advantage that the mortar coupling term is
no longer present in the contact forces. As a result, the computationally
expensive segmentation at overlapping master-slave element boundaries, usually
required in mortar methods (although often simplified with loss of accuracy),
is not needed from the outset. For the numerical integration of general contact
problems, the so-called refined boundary quadrature is employed, which is based
on adaptive partitioning of contact elements along the contact boundary. The
contact patch test shows that the proposed formulation passes the test without
using either segmentation or refined boundary quadrature. Several numerical
examples are presented to demonstrate the robustness and accuracy of the
proposed formulation.Comment: In this version, we have removed the patch test comparison with the
classical mortar method and removed corresponding statements. They will be
studied in further detail in future work, so that the focus is now entirely
on the new IGA mortar formulatio
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