A classification of higher-order strain-gradient models in damage mechanics

2003 ◽  
Vol 73 (5-6) ◽  
pp. 448-465 ◽  
Author(s):  
H. Askes ◽  
L. J. Sluys
2002 ◽  
Vol 72 (2-3) ◽  
pp. 171-188 ◽  
Author(s):  
H. Askes ◽  
A. S. J. Suiker ◽  
L. J. Sluys

2017 ◽  
Vol 25 (7) ◽  
pp. 1429-1449 ◽  
Author(s):  
Samuel Forest ◽  
Karam Sab

Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presented, together with its relation to the second-order micromorphic model. The linearization of the combination of stress and strain gradient models is then shown to deliver formulations related to Eringen’s and Aifantis’s well-known gradient models involving the Laplacians of stress and strain tensors. Finally, the structures of the dynamical equations are given for strain and stress gradient media, showing fundamental differences in the dynamical behaviour of these two classes of generalized continua.


2020 ◽  
Vol 36 (14) ◽  
pp. 4130-4136
Author(s):  
David J Burks ◽  
Rajeev K Azad

Abstract Motivation Alignment-free, stochastic models derived from k-mer distributions representing reference genome sequences have a rich history in the classification of DNA sequences. In particular, the variants of Markov models have previously been used extensively. Higher-order Markov models have been used with caution, perhaps sparingly, primarily because of the lack of enough training data and computational power. Advances in sequencing technology and computation have enabled exploitation of the predictive power of higher-order models. We, therefore, revisited higher-order Markov models and assessed their performance in classifying metagenomic sequences. Results Comparative assessment of higher-order models (HOMs, 9th order or higher) with interpolated Markov model, interpolated context model and lower-order models (8th order or lower) was performed on metagenomic datasets constructed using sequenced prokaryotic genomes. Our results show that HOMs outperform other models in classifying metagenomic fragments as short as 100 nt at all taxonomic ranks, and at lower ranks when the fragment size was increased to 250 nt. HOMs were also found to be significantly more accurate than local alignment which is widely relied upon for taxonomic classification of metagenomic sequences. A novel software implementation written in C++ performs classification faster than the existing Markovian metagenomic classifiers and can therefore be used as a standalone classifier or in conjunction with existing taxonomic classifiers for more robust classification of metagenomic sequences. Availability and implementation The software has been made available at https://github.com/djburks/SMM. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.


2019 ◽  
Vol 57 ◽  
pp. 175-191 ◽  
Author(s):  
Wafa Adda Bedia ◽  
Mohammed Sid Ahmed Houari ◽  
Aicha Bessaim ◽  
Abdelmoumen Anis Bousahla ◽  
Abdelouahed Tounsi ◽  
...  

In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns


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