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Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

Siavash Jafarzadeh, Adam Larios, Florin Bobaru
2020 Journal of Peridynamics and Nonlocal Modeling  
We introduce an efficient boundary-adapted spectral method for peridynamic transient diffusion problems with arbitrary boundary conditions.  ...  The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier space, resulting in computations that scale as O(N log N).  ...  Dynamic brittle fracture [17] [18] [19] , fatigue and thermally induced cracking [16, 20] , fracture in porous and granular materials [21] [22] [23] , failure of composites [24, 25] , and corrosion  ... 
doi:10.1007/s42102-019-00026-6 fatcat:ykqkg6vm5rdy7ez4libbafurfq

Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods [article]

Siavash Jafarzadeh, Adam Larios, Florin Bobaru
2019 arXiv   pre-print
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions.  ...  The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier space, resulting in computations that scale as O(NlogN).  ...  Acknowledgments This work has been supported by the AFOSR MURI Center for Materials Failure Prediction through Peridynamics (program managers Jaimie Tiley, David Stargel, Ali Sayir, Fariba Fahroo, and  ... 
arXiv:1905.03875v1 fatcat:aqnmqxhaxncqth4rerxbg4pjca

Index [chapter]

2015 Structural Integrity and Durability of Advanced Composites  
Although, this chapter deals mainly with computer methods applied to fibre reinforced composites based on a polymeric matrix, many of them are applicable to a broader range of composite materials as well  ...  This chapter presents some of the most recent and relevant computational techniques for modelling and simulation of damage and/or failure on composite materials.  ...  • Peridynamics is a type of particle method and, hence, meshfree with all the advantages that it carries, e.g. fracture is modelled in terms of the distance generated among particles. • For completeness  ... 
doi:10.1016/b978-0-08-100137-0.18001-0 fatcat:vfz23hpog5foxbf2w5kzgx3iy4

On the application of the method of difference potentials to linear elastic fracture mechanics

W. H. Woodward, S. Utyuzhnikov, P. Massin
2015 International Journal for Numerical Methods in Engineering  
Acknowledgements ACKNOWLEDGEMENTS The authors are grateful to the unknown referees for very useful remarks that lead to an essential improvement of the paper quality.  ...  This work is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under DTA award and EDF.  ...  34 A On the application of the method of difference potentials to linear elastic fracture mechanics 49 B The method of difference potentials for linear elastic fracture me- chanics problems  ... 
doi:10.1002/nme.4903 fatcat:662irxkabvesdprjmyprdo2764

Dual-horizon peridynamics and Nonlocal operator method

Huilong Ren
All three peridynamic formulations, namely bond based, ordinary state based and non-o [...]  ...  By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD.  ...  General numerical method is applicable for different physical problems, while non-general methods have very narrow field of application.  ... 
doi:10.25643/bauhaus-universitaet.4403 fatcat:vvvs3kwhrvhk5kr36xzrdml4yy

Strain injection techniques in dynamic fracture modeling

O. Lloberas-Valls, A.E. Huespe, J. Oliver, I.F. Dias
2016 Computer Methods in Applied Mechanics and Engineering  
Following the Continuum Strong Discontinuity Approach (CSDA), stress-strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to  ...  The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains  ...  Acknowledgments The research leading to these results has received funding from the European Research Council under the European Union  ... 
doi:10.1016/j.cma.2016.05.023 fatcat:56ihcoxf4ffkjiru7e5ndeyzqq

Scientific Program

2014 Procedia IUTAM  
, China Convolution quadrature boundary element method for 3D elastodynamic analysis of general anisotropic elastic solids FS02-032 Akira Furukawa * , Yukumo Tanaka, Takahiro Saitoh, Sohichi Hirose, Chuanzeng  ...  elastic peridynamic body SM04-042 Adair R.  ...  Thickness-shear vibrations of rectangular plates with free edges by the extended kantorovich method FS07-019 Ji  ... 
doi:10.1016/j.piutam.2014.01.011 fatcat:osy4egnuufdophopfpj75e24jm

A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale

T. Sendova, J.R. Walton
2010 Mathematics and mechanics of solids  
The dissertation focuses on the analysis, through combined analytical and numerical techniques, of the partial differential equations arising from a new approach to modeling brittle fracture, based on  ...  profile at the crack tip, in contrast to the classical theory of brittle fracture.  ...  Fracture of brittle materials has been modeled over a broad range of approachesfrom classical continuum theories like linear elastic fracture mechanics (LEFM) to particulate theories such as molecular  ... 
doi:10.1177/1081286510362457 fatcat:ghf26nei5vdazemchz3koqv2g4


Moonseop Kim
The strain in increased for a specified number of times in a loop and the stress is calculated at eac [...]  ...  First is based on the empirical potentials development in silicon nanowires for theory parts of molecular dynamics.  ...  He not only helped me a lot in my research but also gave me a chance to do my research well during my doctorate. I want to repeat thanks. Also, I would like to say thanks to my committee members,  ... 
doi:10.25394/pgs.9768107.v1 fatcat:6zrwfmjug5crrimw2xih5pmkle

Morphed vertical tailplane assessment for certification requirements

Miguel Angel Castillo-Acero
2015 Zenodo  
The results, opinions, conclusions, etc. presented in this work are those of the author(s) only and do not necessarily represent the position of the JU; the JU is not responsible for any use made of the  ...  The JU receives support from the European Union's Horizon 2020 research and innovation programme and the Clean Sky 2 JU members other than the Union.  ...  The research leading to these results received funding from the European Union's Seventh Framework Programme (FP7/2007(FP7/ -2013  ... 
doi:10.5281/zenodo.3905083 fatcat:jegirrd5jbgeho7qtr7o3sfzpi

APM 2016. Book of Abstracts [article]

"Advanced Problems In Mechanics" (APM 2016), International Conference (44; 2016; St. Petersburg), Russian Academy Of Sciences. Institute For Problems In Mechanical Engineering, University, Peter The Great St. Petersburg Polytechnic
The authors kindly acknowledge funding from the project TAMER, Trans-Atlantic Micromechanics Evolving Research "Materials containing inhomogeneities of diverse physical properties, shapes and orientations  ...  The solution of general peridynamic diffusive problems can be constructed base on the solution of a point source; thus the Green's functions can be used to develop a method to solve diffusive problems  ...  We develop special mathematical tool, a method of radial multipliers, for the high-precision approximation of fast variables functions in the asymptotic homogenization method for gradient elasticity equations  ... 
doi:10.18720/spbpu/2/k16-40 fatcat:yegzycnwbrco7dwsdnsjxvwbc4

Numerical simulation of fracture in high-velocity impact [article]

Marvin Becker, Universität Stuttgart
The algorithms to process the motion of parallax and noise containing images are described. In terms of (ii) we compare the FEM and SPH method and propose improved choices for modelling the impact.  ...  This thesis contains (i) experimental and (ii) numerical techniques to improve the description of fracture.  ...  However, initially, the method was developed for brittle fracture, and the previous result mainly shows that the range of applications is much more extensive.  ... 
doi:10.18419/opus-11547 fatcat:4umttsqffzg3bocphnrbyfrnlu