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Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: In this article, the authors compare the energy barriers predicted by continuum mechanics models for homogeneous dislocation nucleation in copper with explicit atomistic calculations and find that a relatively simple continuum model can agree with full atomistic calculation if the dislocation Burgers vector is allowed to increase continuously during nucleation.
89 citations
TL;DR: In this paper, the authors reviewed the continuum theories of straight adhesion at a spherically tipped asperity and presented a "map" to indicate the conditions under which the different theories apply.
Abstract: Fundamental studies of friction between solid surfaces are bedevilled by their inevitable roughness. However recent developments in nanotribology through molecular dynamics, the surface force apparatus, and the atomic force microscope have made possible direct examination of adhesion and friction at a single asperity in which the real and apparent contact areas coincide. In this paper the continuum theories of straight adhesion at a spherically tipped asperity are reviewed and a “map” presented which indicates the conditions under which the different theories apply. The interaction between friction and adhesion is then considered from the point of view of “fracture mechanics”. This approach has the advantage of clearly separating the roles of continuum mechanics and physics. The former is used to calculate the “elastic energy release rate” G as the adhesion is broken; the work of adhesion Gc can only be found from physical considerations.
89 citations
Book•
03 Oct 1995
TL;DR: In this article, the continuance of an analytical solution across the elastic-plastic boundary of a mode I fracture mechanics problem was studied, as predicted by linear elastic fracture mechanics.
Abstract: Equations of continuum mechanics equations of elasticity equations of plasticity plane problems of elasticity theory linear elastic fracture mechanics strip models of crack tip plasticity exact elastoplastic solutions for mode III plane stran problems involving plastic material plane stress involving plastic material numerical solutions of the mode I elastoplastic problem miscellaneous mathematical topics on the continuance of an analytical solution across the elastic-plastic boundary of a mode I fracture mechanics problem plastic zone transitions environmental cracking small-scale yielding versus exact linear elastic solutions elastic-plastic loci as predicted by linear elastic fracture mechanics.
89 citations
TL;DR: A new type of deformable model which combines the realism of physically-based continuum mechanics models and the usability of frame-based skinning methods and is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations.
Abstract: We present a new type of deformable model which combines the realism of physically-based continuum mechanics models and the usability of frame-based skinning methods. The degrees of freedom are coordinate frames. In contrast with traditional skinning, frame positions are not scripted but move in reaction to internal body forces. The displacement field is smoothly interpolated using dual quaternion blending. The deformation gradient and its derivatives are computed at each sample point of a deformed object and used in the equations of Lagrangian mechanics to achieve physical realism. This allows easy and very intuitive definition of the degrees of freedom of the deformable object. The meshless discretization allows on-the-fly insertion of frames to create local deformations where needed. We formulate the dynamics of these models in detail and describe some precomputations that can be used for speed. We show that our method is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations. To encourage its use, the software will be freely available in the simulation platform SOFA.
89 citations
Book•
13 Feb 2012TL;DR: In this article, the authors present the fundamentals of multiscale materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering, and provide a self-contained treatment of topics directly related to nonlinear materials modeling.
Abstract: Continuum mechanics and thermodynamics are foundational theories of many fields of science and engineering. This book presents a fresh perspective on these fundamental topics, connecting micro- and nanoscopic theories and emphasizing topics relevant to understanding solid-state thermo-mechanical behavior. Providing clear, in-depth coverage, the book gives a self-contained treatment of topics directly related to nonlinear materials modeling. It starts with vectors and tensors, finite deformation kinematics, the fundamental balance and conservation laws, and classical thermodynamics. It then discusses the principles of constitutive theory and examples of constitutive models, presents a foundational treatment of energy principles and stability theory, and concludes with example closed-form solutions and the essentials of finite elements. Together with its companion book, Modeling Materials, (Cambridge University Press, 2011), this work presents the fundamentals of multiscale materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.
88 citations