26,366 research outputs found
Chromatin: a tunable spring at work inside chromosomes
This paper focuses on mechanical aspects of chromatin biological functioning.
Within a basic geometric modeling of the chromatin assembly, we give for the
first time the complete set of elastic constants (twist and bend persistence
lengths, stretch modulus and twist-stretch coupling constant) of the so-called
30-nm chromatin fiber, in terms of DNA elastic properties and geometric
properties of the fiber assembly. The computation naturally embeds the fiber
within a current analytical model known as the ``extensible worm-like rope'',
allowing a straightforward prediction of the force-extension curves. We show
that these elastic constants are strongly sensitive to the linker length, up to
1 bp, or equivalently to its twist, and might locally reach very low values,
yielding a highly flexible and extensible domain in the fiber. In particular,
the twist-stretch coupling constant, reflecting the chirality of the chromatin
fiber, exhibits steep variations and sign changes when the linker length is
varied.
We argue that this tunable elasticity might be a key feature for chromatin
function, for instance in the initiation and regulation of transcription.Comment: 38 pages 15 figure
On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method
Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems, based on bounds on strain energy in both the primal and dual problems. One important feature of SFEM is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation. Upper and lower bounds on two linear outputs and one quadratic output related with elasticity—the local reaction, the local displacement and the J-integral—are computed by the proposed method in two different examples. Some issues with SFEM that remain to be resolved are also discussed
Lattice Resistance and Peierls Stress in Finite-size Atomistic Dislocation Simulations
Atomistic computations of the Peierls stress in fcc metals are relatively
scarce. By way of contrast, there are many more atomistic computations for bcc
metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro
type for fcc metals. One of the reasons for this is the low Peierls stresses in
fcc metals. Because atomistic computations of the Peierls stress take place in
finite simulation cells, image forces caused by boundaries must either be
relaxed or corrected for if system size independent results are to be obtained.
One of the approaches that has been developed for treating such boundary forces
is by computing them directly and subsequently subtracting their effects, as
developed by V. B. Shenoy and R. Phillips [Phil. Mag. A, 76 (1997) 367]. That
work was primarily analytic, and limited to screw dislocations and special
symmetric geometries. We extend that work to edge and mixed dislocations, and
to arbitrary two-dimensional geometries, through a numerical finite element
computation. We also describe a method for estimating the boundary forces
directly on the basis of atomistic calculations. We apply these methods to the
numerical measurement of the Peierls stress and lattice resistance curves for a
model aluminum (fcc) system using an embedded-atom potential.Comment: LaTeX 47 pages including 20 figure
Classical and all-floating FETI methods for the simulation of arterial tissues
High-resolution and anatomically realistic computer models of biological soft
tissues play a significant role in the understanding of the function of
cardiovascular components in health and disease. However, the computational
effort to handle fine grids to resolve the geometries as well as sophisticated
tissue models is very challenging. One possibility to derive a strongly
scalable parallel solution algorithm is to consider finite element tearing and
interconnecting (FETI) methods. In this study we propose and investigate the
application of FETI methods to simulate the elastic behavior of biological soft
tissues. As one particular example we choose the artery which is - as most
other biological tissues - characterized by anisotropic and nonlinear material
properties. We compare two specific approaches of FETI methods, classical and
all-floating, and investigate the numerical behavior of different
preconditioning techniques. In comparison to classical FETI, the all-floating
approach has not only advantages concerning the implementation but in many
cases also concerning the convergence of the global iterative solution method.
This behavior is illustrated with numerical examples. We present results of
linear elastic simulations to show convergence rates, as expected from the
theory, and results from the more sophisticated nonlinear case where we apply a
well-known anisotropic model to the realistic geometry of an artery. Although
the FETI methods have a great applicability on artery simulations we will also
discuss some limitations concerning the dependence on material parameters.Comment: 29 page
Non-regularised inverse finite element analysis for 3D traction force microscopy
The tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.Peer ReviewedPostprint (author's final draft
Optimal boundary geometry in an elasticity problem: a systematic adjoint approach
p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables.
Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654
Multiscale Surrogate Modeling and Uncertainty Quantification for Periodic Composite Structures
Computational modeling of the structural behavior of continuous fiber
composite materials often takes into account the periodicity of the underlying
micro-structure. A well established method dealing with the structural behavior
of periodic micro-structures is the so- called Asymptotic Expansion
Homogenization (AEH). By considering a periodic perturbation of the material
displacement, scale bridging functions, also referred to as elastic correctors,
can be derived in order to connect the strains at the level of the
macro-structure with micro- structural strains. For complicated inhomogeneous
micro-structures, the derivation of such functions is usually performed by the
numerical solution of a PDE problem - typically with the Finite Element Method.
Moreover, when dealing with uncertain micro-structural geometry and material
parameters, there is considerable uncertainty introduced in the actual stresses
experienced by the materials. Due to the high computational cost of computing
the elastic correctors, the choice of a pure Monte-Carlo approach for dealing
with the inevitable material and geometric uncertainties is clearly
computationally intractable. This problem is even more pronounced when the
effect of damage in the micro-scale is considered, where re-evaluation of the
micro-structural representative volume element is necessary for every occurring
damage. The novelty in this paper is that a non-intrusive surrogate modeling
approach is employed with the purpose of directly bridging the macro-scale
behavior of the structure with the material behavior in the micro-scale,
therefore reducing the number of costly evaluations of corrector functions,
allowing for future developments on the incorporation of fatigue or static
damage in the analysis of composite structural components.Comment: Appeared in UNCECOMP 201
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