scholarly journals A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

2020 ◽  
Author(s):  
Jörg Schröder ◽  
Thomas Wick ◽  
Stefanie Reese ◽  
Peter Wriggers ◽  
Ralf Müller ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Applied Mathematics ◽  
Benchmark Problems ◽  
Material Interfaces ◽  
German Research Foundation ◽  
Simulation Techniques ◽  
Classical Fields ◽  
Computational Solid Mechanics ◽  
Selection Of ◽  
Quantities Of Interest

Abstract In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

scholarly journals GEORGE KEITH BATCHELOR 8 March 1920–30 March 2000 Founding Editor, Journal of Fluid Mechanics, 1956

2000 ◽  
Vol 421 ◽  
pp. 1-14 ◽  
Author(s):  
HERBERT E. HUPPERT
Keyword(s):  
Fluid Mechanics ◽  
International Organizations ◽  
Solid Mechanics ◽  
Applied Mathematics ◽  
Fluid Flows ◽  
Theoretical Physics ◽  
Founding Editor ◽  
Number Of Factors ◽  
Quantitative Understanding ◽  
The Subject

George Batchelor was one of the giants of fluid mechanics in the second half of the twentieth century. He had a passion for physical and quantitative understanding of fluid flows and a single-minded determination that fluid mechanics should be pursued as a subject in its own right. He once wrote that he ‘spent a lifetime happily within its boundaries’. Six feet tall, thin and youthful in appearance, George's unchanging attire and demeanour contrasted with his ever-evolving scientific insights and contributions. His strongly held and carefully articulated opinions, coupled with his forthright objectivity, shone through everything he undertook.George's pervasive influence sprang from a number of factors. First, he conducted imaginative, ground-breaking research, which was always based on clear physical thinking. Second, he founded a school of fluid mechanics, inspired by his mentor G. I. Taylor, that became part of the world renowned Department of Applied Mathematics and Theoretical Physics (DAMTP) of which he was the Head from its inception in 1959 until he retired from his Professorship in 1983. Third, he established this Journal in 1956 and actively oversaw all its activities for more than forty years, until he relinquished his editorship at the end of 1998. Fourth, he wrote the monumental textbook An Introduction to Fluid Dynamics, which first appeared in 1967, has been translated into four languages and has been relaunched this year, the year of his death. This book, which describes the fundamentals of the subject and discusses many applications, has been closely studied and frequently cited by generations of students and research workers. It has already sold over 45 000 copies. And fifth, but not finally, he helped initiate a number of international organizations (often European), such as the European Mechanics Committee (now Society) and the biennial Polish Fluid Mechanics Meetings, and contributed extensively to the running of IUTAM, the International Union of Theoretical and Applied Mechanics. The aim of all of these associations is to foster fluid (and to some extent solid) mechanics and to encourage the development of the subject.

Recent Development in Multiscale Simulation of Mechanical Properties at Material Interface

2010 ◽  
Vol 146-147 ◽  
pp. 491-494
Author(s):  
Ning Bo Liao ◽  
Miao Zhang ◽  
Rui Jiang
Keyword(s):  
Mechanical Properties ◽  
Multiscale Model ◽  
Multiscale Simulation ◽  
Material Interfaces ◽  
Material Interface ◽  
Multi Scale ◽  
Simulation Techniques ◽  
Hierarchical Nature ◽  
Feature Scale

For nanoscale devices and structures, interface phenomena often dominate their overall thermal behavior. The feature scale of material interfaces usually originate from nanometer length and present a hierarchical nature. Considering to the limitations of the continuum mechanics on the characterization of nano-scale, the multiscale model featuring the interface could be very important in materials design. The purpose of this review is to discuss the applications of multiscale modeling and simulation techniques to study the mechanical properties at materials interface. It is concluded that a multi-scale scheme is needed for this study due to the hierarchical characteristics of interface.

Molecular simulations of protein disorderThis paper is one of a selection of papers published in this special issue entitled “Canadian Society of Biochemistry, Molecular & Cellular Biology 52nd Annual Meeting — Protein Folding: Principles and Diseases” and has undergone the Journal's usual peer review process.

2010 ◽  
Vol 88 (2) ◽  
pp. 269-290 ◽  
Author(s):  
Sarah Rauscher ◽  
Régis Pomès
Keyword(s):  
Intrinsically Disordered Proteins ◽  
Peer Review Process ◽  
Structural Heterogeneity ◽  
Disordered Proteins ◽  
Cellular Biology ◽  
Protein Disorder ◽  
Conformational Ensembles ◽  
Intrinsically Disordered ◽  
Simulation Techniques ◽  
Selection Of

Protein disorder is abundant in proteomes throughout all kingdoms of life and serves many biologically important roles. Disordered states of proteins are challenging to study experimentally due to their structural heterogeneity and tendency to aggregate. Computer simulations, which are not impeded by these properties, have recently emerged as a useful tool to characterize the conformational ensembles of intrinsically disordered proteins. In this review, we provide a survey of computational studies of protein disorder with an emphasis on the interdisciplinary nature of these studies. The application of simulation techniques to the study of disordered states is described in the context of experimental and bioinformatics approaches. Experimental data can be incorporated into simulations, and simulations can provide predictions for experiment. In this way, simulations have been integrated into the existing methodologies for the study of disordered state ensembles. We provide recent examples of simulations of disordered states from the literature and our own work. Throughout the review, we emphasize important predictions and biophysical understanding made possible through the use of simulations. This review is intended as both an overview and a guide for structural biologists and theoretical biophysicists seeking accurate, atomic-level descriptions of disordered state ensembles.

Classical and Computational Solid Mechanics

10.1142/9744 ◽  
2017 ◽  
Author(s):  
Y C Fung ◽  
Pin Tong ◽  
Xiaohong Chen
Keyword(s):  
Solid Mechanics ◽  
Computational Solid Mechanics

scholarly journals Finite Element Framework for Computational Fluid Dynamics in FEBio

2018 ◽  
Vol 140 (2) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Jay J. Shim ◽  
Steve A. Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Element ◽  
Solid Mechanics ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Biological Fluids ◽  
Fluid Velocity ◽  
Benchmark Problems ◽  
Future Extension

The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid–structure interactions (FSIs).

Computational Solid Mechanics

2014 ◽  
Author(s):  
Marco L. Bittencourt
Keyword(s):  
Solid Mechanics ◽  
Computational Solid Mechanics
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