A unifying treatise of variational principles for two types of micropolar continua

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

Download Full-text

Accelerated Simulation of Kinetic Transport Using Variational Principles and Sparsity

10.2172/1417993 ◽

2017 ◽

Author(s):

Russel Caflisch

Keyword(s):

Variational Principles ◽

Accelerated Simulation

Download Full-text

The Physical World

10.1093/oso/9780198795933.001.0001 ◽

2017 ◽

Cited By ~ 1

Author(s):

Nicholas Manton ◽

Nicholas Mee

Keyword(s):

Quantum Mechanics ◽

Particle Physics ◽

Variational Principles ◽

Black Body ◽

Black Body Radiation ◽

Physical World ◽

Atomic Scale ◽

Solid State Physics ◽

Least Action ◽

Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

Download Full-text

Applications of micropolar SPH in geomechanics

Acta Geotechnica ◽

10.1007/s11440-021-01177-x ◽

2021 ◽

Author(s):

Chengwei Zhu ◽

Chong Peng ◽

Wei Wu

Keyword(s):

Strain Localization ◽

Biaxial Compression ◽

Parameter Study ◽

Sand Column ◽

Column Collapse ◽

Micropolar Continua ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Micropolar Model ◽

Geotechnical Problems

AbstractA smoothed particle hydrodynamics code based on micropolar continua for geomaterials is developed for problems involving large deformation and shear strain localization. Two typical geotechnical problems, i.e., biaxial compression test and sand column collapse, are simulated using classical and micropolar model to demonstrate the performance of the newly proposed method. A parameter study is given on the scale effect in the micropolar continua.

Download Full-text

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

Journal of Applied Analysis ◽

10.1515/jaa-2018-0017 ◽

2018 ◽

Vol 24 (2) ◽

pp. 175-183

Author(s):

Jean-Claude Ndogmo

Keyword(s):

Explicit Form ◽

Nonlinear Equations ◽

Variational Principles ◽

Symmetry Algebra ◽

First Integrals ◽

Maximal Symmetry ◽

General Order ◽

Linear And Nonlinear ◽

Variational Symmetries ◽

Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

Download Full-text

Comparative 3D DEM simulations of sand–structure interfaces with similarly shaped clumps versus spheres with contact moments

Acta Geotechnica ◽

10.1007/s11440-021-01255-0 ◽

2021 ◽

Author(s):

A. Grabowski ◽

M. Nitka ◽

J. Tejchman

Keyword(s):

Particle Shape ◽

Friction Angle ◽

Rigid Wall ◽

Numerical Results ◽

Contact Forces ◽

Interface Roughness ◽

Interface Shear ◽

Dem Simulations ◽

Micropolar Continua ◽

Interface Behaviour

AbstractThree-dimensional simulations of a monotonic quasi-static interface behaviour between initially dense cohesionless sand and a rigid wall of different roughness during tests in a parallelly guided direct shear test under constant normal stress are presented. Numerical modelling was carried out by the discrete element method (DEM) using clumps in the form of convex non-symmetric irregularly shaped grains. The clumps had an aspect ratio of 1.5. A regular grid of triangular grooves (asperities) along the wall with a different height at the same distance was assumed. The numerical results with clumps were directly compared under the same conditions with our earlier DEM simulations using pure spheres with contact moments with respect to the peak and residual interface friction angle, width of the interface shear zone, ratio between grain slips and grain rotations, distribution of contact forces and stresses. The difference between the behaviour of clumps and pure spheres with contact moments proved to be noticeable in the post-peak regime due to a different particle shape. The rolling resistance model with pure spheres was proved to be limited for capturing particle shape effects. Three different boundary conditions along the interface were proposed for micropolar continua, considering grain rotations and grain slips, wall grain moments and wall grain forces, and normalized interface roughness. The numerical results in this paper offer a better understanding of the interface behaviour of granular bodies in DEM and FEM simulations.

Download Full-text