13,159 research outputs found
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
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
Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions
The joint probability distribution function (PDF) of the height and its
gradients is derived for a zero tension -dimensional Kardar-Parisi-Zhang
(KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation
shows lack of positivity after a finite time . The properties of zero
tension KPZ equation and its differences with the case that it possess an
infinitesimal surface tension is discussed. Also potential relation between the
time scale and the singularity time scale of the KPZ
equation with an infinitesimal surface tension is investigated.Comment: 18 pages, 8 figure
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