From molecular systems to continuum solids: A multiscale structure and dynamics (original) (raw)
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A multiscale modeling technique for bridging molecular dynamics with finite element method
In computational mechanics, molecular dynamics (MD) and finite element (FE) analysis are well developed and most popular on nanoscale and macroscale analysis, respectively. MD can very well simulate the atomistic behavior, but cannot simulate macroscale length and time due to computational limits. FE can very well simulate continuum mechanics (CM) problems, but has the limitation of the lack of atomistic level degrees of freedom. Multiscale modeling is an expedient methodology with a potential to connect different levels of modeling such as quantum mechanics, molecular dynamics, and continuum mechanics. This study proposes a new multiscale modeling technique to couple MD with FE. The proposed method relies on weighted average momentum principle. A wave propagation example has been used to illustrate the challenges in coupling MD with FE and to verify the proposed technique. Furthermore, 2-Dimensional problem has also been used to demonstrate how this method would translate into real world applications.
Perspectives in mechanics of heterogeneous solids
Acta Mechanica Solida Sinica, 2011
The Micro-and Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives, trends, and directions in mechanics of heterogeneous materials in January 2010. The international journal, Acta Mechanica Solida Sinica, is devoted to all fields of solid mechanics and relevant disciplines in science, technology, and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. On the occasion of the 30 th anniversary of Acta Mechanica Solida Sinica, its editor-in-chief, Professor Q.S. Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids, with a particular emphasis on the recent research development results of Chinese scientists. Their reviews are organized into five research areas as reported in different sections of this paper. §I firstly brings in focus on micro-and nano-mechanics, with regards to several selective topics, including multiscale coupled models and computational methods, nanocrystal superlattices, surface effects, micromechanical damage mechanics, and microstructural evolution of metals and shape memory alloys. §II shows discussions on multifield coupled mechanical phenomena, e.g., multi-fields actuations of liquid crystal polymer networks, mechanical behavior of materials under radiations, and micromechanics of heterogeneous materials. In §III, we mainly address the multiscale mechanics of biological nanocomposites, biological adhesive surface mechanics, wetting and dewetting phenomena on microstructured solid surfaces. The phononic crystals and manipulation of elastic waves were elaborated in §IV. Finally, we conclude with a series of perspectives on solid mechanics. This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development. Supports from NSFC and MOST are acknowledged. · 2 · ACTA MECHANICA SOLIDA SINICA 2011 I. MICRO-AND NANO-MECHANICS 1.1
Multiscale modelling of nanomechanics and micromechanics: an overview
Philosophical Magazine, 2003
Recent advances in analytical and computational modelling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum are reviewed. It is shown that multiscale modelling of materials approaches relies on a systematic reduction in the degrees of freedom on the natural length scales that can be identified in the material. Connections between such scales are currently achieved either by a parametrization or by a 'zoom-out' or 'coarse-graining' procedure. Issues related to the links between the atomistic scale, nanoscale, microscale and macroscale are discussed, and the parameters required for the information to be transferred between one scale and an upper scale are identified. It is also shown that seamless coupling between length scales has not yet been achieved as a result of two main challenges: firstly, the computational complexity of seamlessly coupled simulations via the coarse-graining approach and, secondly, the inherent difficulty in dealing with system evolution stemming from time scaling, which does not permit coarse graining over temporal events. Starting from the Born-Oppenheimer adiabatic approximation, the problem of solving quantum mechanics equations of motion is first reviewed, with successful applications in the mechanics of nanosystems. Atomic simulation methods (e.g. molecular dynamics, Langevin dynamics and the kinetic Monte Carlo method) and their applications at the nanoscale are then discussed. The role played by dislocation dynamics and statistical mechanics methods in understanding microstructure self-organization, heterogeneous plastic deformation, material instabilities and failure phenomena is also discussed.
An Extended Continuum Mechanics Formulation Enhanced by Direct Coupling with Molecular Dynamics
2015
Based on the notion of micro-structure in linear elasticity presented by Mindlin, a new extended continuum mechanics (ECM) formulation is derived which can be utilized to model the material behavior at atomic scale. An attempt has been made to present a formulation capable of producing the molecular dynamics (MD) simulation results with less computational effort. To this end, some new kinematical variables are defined and some constitutive relations are obtained from MD. To validate the proposed ECM formulation, it is applied to a properly defined sample problem and the response is compared with the MD simulation result and the classical continuum mechanics (CCM) solution. Keywords– Extended continuum mechanics (ECM), generalized continua, molecular dynamics, nanomechanics, dipolar continuum mechanics
The Emerging Role of Multiscale Modeling in Nano- and Micro-mechanics of Materials
Cmes-computer Modeling in Engineering & Sciences, 2002
As a result of surging interest in finding fundamental descriptions for the strength and failure properties of materials, and the exciting prospects of designing materials from their atomic level, an international symposium on Multiscale Modeling was convened in Los Angeles during August 23 25, 2000. In this symposium, 23 speakers with research interests spanning fields as diverse as traditional mechanics, physics, chemistry and materials science have given talks at this symposium. The topics of discussion were focused on sub-continuum modeling of the mechanics of materials, taking into account the atomic structure of solid materials. The main motivation of the symposium was the realization of the limitations of current continuum mechanics modeling approaches (e.g. the finite element method (FEM)) to describe the behavior of materials at scales smaller than tens of microns. The speakers represented the international scientific community in different countries, and utilized diverse s...
Multiscale mechanics of macromolecular materials with unfolding domains
2014
We propose a general multiscale approach for the mechanical behavior of three-dimensional networks of macromolecules undergoing strain-induced unfolding. Starting from a (statistically based) energetic analysis of the macromolecule unfolding strategy, we obtain a three-dimensional continuum model with variable natural configuration and an energy function analytically deduced from the microscale material parameters. The comparison with the experiments shows the ability of the model to describe the complex behavior, with residual stretches and unfolding effects, observed in different biological materials.
arXiv (Cornell University), 2019
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able to generate different outputs when interfacial materials are varied. By considering an atomistic description of matter, theoretical determination of material-specific boundary conditions becomes possible, thereby providing an improved alternative to the completely-invariant no-slip condition. Such a scheme constitutes a multiscale approach to fluid dynamics involving essentially two transitions between space-time scales: the first concerns the derivation of macroscopic boundary conditions by means of molecular assessment of slip lengths; the second concerns the construction of interatomic force fields, required by molecular dynamics simulations, from quantum theory. In this introductory overview we discuss some of the fundamental aspects of these problems.
Extension of continuum mechanics to the nanoscale
Chemical Engineering Science, 2004
This is an extension of continuum mechanics to the nanoscale (not the molecular scale). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. While the presentation is new, it is based upon a long history of important developments beginning with that of Hamaker (Physica 4 (1937) 1058). We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on polydimethylsiloxane. In the case of surface tension and like the best previous theory, one adjustable parameter is required. For the contact angle predictions, no adjustable parameters are used. In both cases, the results are compared with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young's equation for the true, rather than apparent, common line.
Multiscale Modeling of Complex Materials
CISM International Centre for Mechanical Sciences, 2014
The mechanical behaviour of complex materials, characterised at finer scales by the presence of heterogeneities of significant size and texture, strongly depends on their microstructural features. Attention is centred on multiscale approaches which aim to deduce properties and relations at a given macroscale by bridging information at proper underlying microlevel via energy equivalence criteria. Focus is on physically-based corpuscular-continuous models originated by the molecular models developed in the 19 th century to give an explanation per causas of elasticity. In particular, the 'mechanistic-energetistic' approach by Voigt and Poincaré who, when dealing with the paradoxes deriving from the search of the exact number of elastic constants in linear elasticity, respectively introduced molecular models with moment and multi-body interactions is examined. Thus overcoming the experimental discrepancies related to the so-called central-force scheme, originally adopted by Navier, Cauchy and Poisson.