Summary
We present a three‐dimensional vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM ...adopting discontinuous linear enrichment functions in place of the asymptotic near‐tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, ie, the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach, significantly simplifies implementation and reduces the computational cost associated with numerical integration, while providing nonoptimal convergence rates similar to standard finite elements. The 2 dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for nonplanar crack propagation problems.
The knee meniscus is a highly porous structure which exhibits a grading architecture through the depth of the tissue. The superficial layers on both femoral and tibial sides are constituted by a fine ...mesh of randomly distributed collagen fibers while the internal layer is constituted by a network of collagen channels of a mean size of 22.14
μ
m aligned at a
30
∘
inclination with respect to the vertical. Horizontal dog-bone samples extracted from different depths of the tissue were mechanically tested in uniaxial tension to examine the variation of elastic and viscoelastic properties across the meniscus. The tests show that a random alignment of the collagen fibers in the superficial layers leads to stiffer mechanical responses (
E
= 105 and 189 MPa) in comparison to the internal regions (
E
= 34 MPa). All regions exhibit two modes of relaxation at a constant strain (
τ
1
=
6.4
to 7.7 s,
τ
2
= 49.9 to 59.7 s).
The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how ...to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper.
We introduce in this article a unified algorithm which allows the selection of collocation stencils, based on the visibility criterion, for convex, concave, and singular problems solved using a ...collocation method. The algorithm can be applied to any 2D or 3D problem. We show the importance of using a threshold angle, in conjunction with the visibility criterion, to assess of the inclusion of a node in the support of a collocation center. We also show how the algorithm can be used to assess the presence of a node in a defined domain. Such algorithm is particularly useful in the context of model refinement.
Understanding complex materials at different length scales requires reliably accounting for van der Waals (vdW) interactions, which stem from long-range electronic correlations. While the important ...role of many-body vdW interactions has been extensively documented for the stability of materials, much less is known about the coupling between vdW interactions and atomic forces. Here we analyze the Hessian force response matrix for a single and two vdW-coupled atomic chains to show that a many-body description of vdW interactions yields atomic force response magnitudes that exceed the expected pairwise decay by 3-5 orders of magnitude for a wide range of separations between perturbed and observed atoms. Similar findings are confirmed for carbon nanotubes, graphene, and delamination of graphene from a silicon substrate previously studied experimentally. This colossal force enhancement suggests implications for phonon spectra, free energies, interfacial adhesion, and collective dynamics in materials with many interacting atoms.
The meniscus is an integral part of the human knee, preventing joint degradation by distributing load from the femoral condyles to the tibial plateau. Recent qualitative studies suggested that the ...meniscus is constituted by an intricate net of collagen channels inside which the fluid flows during loading. The aim of this study is to describe in detail the structure in which this fluid flows by quantifying the orientation and morphology of the collagen channels of the meniscal tissue. A 7 mm cylindrical sample, extracted vertically from the central part of a lateral porcine meniscus was freeze-dried and scanned using the highest-to-date resolution Microscopic Computed Tomography. The orientation of the collagen channels, their size and distribution was calculated. Comparisons with confocal multi-photon microscopy imaging performed on portions of fresh tissue have shown that the freeze-dried procedure adopted here ensures that the native architecture of the tissue is maintained. Sections of the probe at different heights were examined to determine differences in composition and structure along the sample from the superficial to the internal layers. Results reveal a different arrangement of the collagen channels in the superficial layers with respect to the internal layers with the internal layers showing a more ordered structure of the channels oriented at 30
∘
with respect to the vertical, a porosity of 66.28% and the mean size of the channels of 22.14
μ
m
.
This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, ...(ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity.
Pulsar wind nebulae (PWNe) produced from supersonic runaway pulsars can render extended X-ray structures in the form of tails and prominent jets. In this Letter, we report on the analysis of ∼130 ks ...observations of the PWN around PSR J1135–6055 that were obtained with the
Chandra
satellite. The system displays bipolar jet-like structures of uncertain origin, a compact nebula around the pulsar likely formed by the bow shock ahead of it, and a trailing tail produced by the pulsar fast proper motion. The spectral and morphological properties of these structures reveal strong similarities with the PWNe in other runaway pulsars, such as PSR J1509–5850 and Geminga. We discuss their physical origin considering both canonical PWN and jet formation models as well as alternative scenarios that can also yield extended jet-like features following the escape of high-energy particles into the ambient magnetic field.
Parametrized reduced order modeling for cracked solids Agathos, Konstantinos; Bordas, Stéphane P. A.; Chatzi, Eleni
International journal for numerical methods in engineering,
30 October 2020, Letnik:
121, Številka:
20
Journal Article
Recenzirano
Odprti dostop
Summary
A parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and ...size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding to specific crack configurations and a basis for a lower dimensional solution space is created. Then in the online phase, this basis is used to obtain solutions for configurations that do not lie in the training set. The use of the same basis for different crack geometries is rendered possible by defining a reference configuration and employing mesh morphing to map the reference to different target configurations. To enable the application to complex geometries, a mesh morphing technique is introduced, based on inverse distance weighting, which increases computational efficiency and allows for special treatment of boundaries. Applications in linear elastic fracture mechanics are considered, with the extended finite element method being used to represent discontinuous and asymptotic fields.
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