412,663 research outputs found
Assumed-strain finite element technique for accurate modelling of plasticity problems
In this work a linear hexahedral element based on an assumed-strain finite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double- step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions
Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network
A new class of micromechanically motivated chain network models for soft
biological tissues is presented. On the microlevel, it is based on the
statistics of long chain molecules. A wormlike chain model is applied to
capture the behavior of the collagen microfibrils. On the macrolevel, the
network of collagen chains is represented by a transversely isotropic eight
chain unit cell introducing one characteristic material axis. Biomechanically
induced remodeling is captured by allowing for a continuous reorientation of
the predominant unit cell axis driven by a biomechanical stimulus. To this end,
we adopt the gradual alignment of the unit cell axis with the direction of
maximum principal strain. The evolution of the unit cell axis' orientation is
governed by a first-order rate equation. For the temporal discretization of the
remodeling rate equation, we suggest an exponential update scheme of
Euler-Rodrigues type. For the spatial discretization, a finite element strategy
is applied which introduces the current individual cell orientation as an
internal variable on the integration point level. Selected model problems are
analyzed to illustrate the basic features of the new model. Finally, the
presented approach is applied to the biomechanically relevant boundary value
problem of an in vitro engineered functional tendon construct.Comment: LaTeX2e, 19 pages, 9 figure
Modernizing science&engineering software systems
As the demands for modernized legacy systems rise, so does the need for
frameworks for information integration and tool interoperability. The Object Management
Group (OMG) has adopted the Model Driven Architecture (MDA), which is an evolving
conceptual architecture that aligns with this demand. MDA could help solve coupling
problems of multidisciplinary character in science and engineering that consist of one or more
applications, supported by one or more platforms. The objective of this paper is to describe
rigorous techniques to control the evolution from science & engineering software legacy
systems to MDA technologies. We propose a rigorous framework to reverse engineering code
in the context of MDA. Considering that validation, verification and consistency are crucial
activities in the modernization of systems that are critical to safety, security and economic
profits, our approach emphasizes the integration of MDA with formal methods
Alternating Direction Implicit Method for Two-Dimensional Fokker-Planck Equation of Dense Spherical Stellar Systems
The Fokker-Planck (FP) model is one of the commonly used methods for studies
of the dynamical evolution of dense spherical stellar systems such as globular
clusters and galactic nuclei. The FP model is numerically stable in most cases,
but we find that it encounters numerical difficulties rather often when the
effects of tidal shocks are included in two-dimensional (energy and angular
momentum space) version of the FP model or when the initial condition is
extreme (e.g., a very large cluster mass and a small cluster radius). To avoid
such a problem, we have developed a new integration scheme for a
two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI)
method given in the Douglas-Rachford split form. We find that our ADI method
reduces the computing time by a factor of ~2 compared to the fully implicit
method, and resolves problems of numerical instability.Comment: Published in J. Korean Astron. Soc., 40, 91 (2007
Projective and Coarse Projective Integration for Problems with Continuous Symmetries
Temporal integration of equations possessing continuous symmetries (e.g.
systems with translational invariance associated with traveling solutions and
scale invariance associated with self-similar solutions) in a ``co-evolving''
frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with
the evolving solution) leads to improved accuracy because of the smaller time
derivative in the new spatial frame. The slower time behavior permits the use
of {\it projective} and {\it coarse projective} integration with longer
projective steps in the computation of the time evolution of partial
differential equations and multiscale systems, respectively. These methods are
also demonstrated to be effective for systems which only approximately or
asymptotically possess continuous symmetries. The ideas of projective
integration in a co-evolving frame are illustrated on the one-dimensional,
translationally invariant Nagumo partial differential equation (PDE). A
corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is
used to illustrate the coarse-grained method. A simple, one-dimensional
diffusion problem is used to illustrate the scale invariant case. The
efficiency of projective integration in the co-evolving frame for both the
macroscopic diffusion PDE and for a random-walker particle based model is again
demonstrated
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