scholarly journals Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity

2019 ◽  
Vol 29 (06) ◽  
pp. 1079-1138
Author(s):  
Riccarda Rossi
Keyword(s):  
Solid Mechanics ◽  
Correction Term ◽  
Solution Concept ◽  
Adhesive Contact ◽  
Continuous Limit ◽  
Energetic Solutions ◽  
Fixed Parameter ◽  
Limit Passage ◽  
Incremental Scheme ◽  
Weak Solvability

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic ([Formula: see text]) and Balanced Viscosity ([Formula: see text]) solutions. Visco-Energetic ([Formula: see text]) solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for [Formula: see text] solutions, but perturbed by a “viscous” correction term, as in the case of [Formula: see text] solutions. However, for VE solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion turns out to describe a kind of evolution in between Energetic and BV evolution. In this paper we aim to investigate the application of [Formula: see text] solutions to nonsmooth rate-independent processes in solid mechanics such as damage and plasticity at finite strains. We also address the limit passage, in the [Formula: see text] formulation, from an adhesive contact to a brittle delamination system. The analysis of these applications reveals the wide applicability of this solution concept, in particular to processes for which [Formula: see text] solutions are not available, and confirms its intermediate character between the [Formula: see text] and [Formula: see text] notions.

scholarly journals Local-solution approach to quasistatic rate-independent mixed-mode delamination

2015 ◽  
Vol 25 (07) ◽  
pp. 1337-1364 ◽  
Author(s):  
Tomáš Roubíček ◽  
Christos G. Panagiotopoulos ◽  
Vladislav Mantič
Keyword(s):  
Mixed Mode ◽  
Solution Concept ◽  
Adhesive Contact ◽  
Mathematical Methods ◽  
Solution Approach ◽  
Homogeneous Potential ◽  
Internal Parameters ◽  
Contact Models ◽  
Local Solutions ◽  
The One

The model of quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e. distinguishing opening (Mode I) from shearing (Mode II), devised in [Delamination and adhesive contact models and their mathematical analysis and numerical treatment, Chap. 9, in Mathematical Methods and Models in Composites, ed. V. Mantič (Imperial College Press, 2014), pp. 349–400; and in Quasistatic mixed-mode delamination model, Discrete Contin. Dynam. Syst. Ser. S 6 (2013) 591–610], is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the one-homogeneous potential of dissipative forces driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretization in time is shown to converge to (specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretization, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial two-dimensional example.

scholarly journals Multi-Physics and Multi-Scale Meshless Simulation System for Direct-Chill Casting of Aluminium Alloys

2019 ◽  
Vol 65 (11-12) ◽  
pp. 658-670 ◽  
Author(s):  
Božidar Šarler ◽  
Tadej Dobravec ◽  
Gašper Glavan ◽  
Vanja Hatić ◽  
Boštjan Mavrič ◽  
...  
Keyword(s):  
Aluminium Alloys ◽  
Solid Mechanics ◽  
Weighted Least Squares ◽  
Solution Concept ◽  
Direct Chill ◽  
Solution Procedure ◽  
Simulation System ◽  
Multi Scale ◽  
Chill Cast ◽  
Direct Chill Cast

This paper represents an overview of the elements of the user-friendly simulation system, developed for computational analysis and optimization of the quality and productivity of the electromagnetically direct-chill cast semi-products from aluminium alloys. The system also allows the computational estimation of the design changes of the casting equipment. To achieve this goal, the electromagnetic and the thermofluid process parameters are coupled to the evolution of Lorentz force, temperature, velocity, concentration, strain and stress fields as well as microstructure evolution. This forms a multi-physics and multi-scale problem of great complexity, which has not been demonstrated before. The macroscopic fluid mechanics, solid mechanics, and electromagnetic solution framework is based on local strong-form meshless formulation, involving the radial basis functions and monomials as trial functions, and local collocation or weighted least squares approximation. It is coupled to the micro-scale by incorporating the point automata solution concept. The entire macro-micro solution concept does not require meshing and space integration. The solution procedure can be easily and efficiently automatically adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with fields exhibiting sharp gradients, which occur in the phase-change problems. The simulation system is coded from scratch in modern Fortran. The elements of the experimental validation of the system and the demonstration of its use for round billet casting in IMPOL Aluminium Industry are shown.

Applied Solid Mechanics

2001 ◽  
Author(s):  
Peter Howell ◽  
Gregory Kozyreff ◽  
John Ockendon
Keyword(s):  
Solid Mechanics

Interstitial vs. Substitutional Metal Insertion in V2O5 as Post-Lithium Ion Battery Cathode: A Comparative GGA/GGA+U Study with Localized Bases

2020 ◽  
Author(s):  
Daniel Koch ◽  
Sergei Manzhos
Keyword(s):  
Electronic Structure ◽  
Plane Wave ◽  
Transition Metal Oxides ◽  
Reasonable Agreement ◽  
Correction Term ◽  
Lithium Ion ◽  
Generalized Gradient ◽  
Main Group Metals ◽  
Generalized Gradient Approximation ◽  
Metal Insertion

<p></p><p>The generalized gradient approximation (GGA) often fails to correctly describe the electronic structure and thermochemistry of transition metal oxides and is commonly improved using an inexpensive correction term with a scaling parameter <i>U</i>. We tune <i>U</i> to reproduce experimental vanadium oxide redox energetics with a localized basis and a GGA functional. We find the value for <i>U</i> to be significantly lower than what is generally reported with plane-wave bases, with the uncorrected GGA results being in reasonable agreement with experiments. We use this computational setup to calculate interstitial and substitutional <a>insertion energies of main group metals in vanadium pentoxide</a> and find <a>interstitial doping to be thermodynamically favored</a>.</p><p></p>

The Limit Situation And The Narrative Of War (On The Material Of The Novel “My Lieutenant” By Daniil Granin)

2020 ◽  
Vol 6 (1) ◽  
pp. 90-104
Author(s):  
Anatoly S. Kuprin ◽  
Galina I. Danilina
Keyword(s):  
20Th Century ◽  
Scientific Work ◽  
Point Of View ◽  
Continuous Limit ◽  
The Novel ◽  
Term Limit ◽  
Abstract Author ◽  
The Third ◽  
Definition Of

The purpose of this study is the analysis of limit situation in the narrative of war. The material of the study is the novel of Daniil Granin “My Lieutenant” and related texts. In the first part of the paper, the authors explore existing approaches to the term “limit situation” and similar concepts into scientific and philosophical traditions; limits of its applicability in literary studies and its relation to the categories of “narrative instances” and “event”. Proposed a literary-theoretical definition of the limit situation, which can be used in the analysis of fiction texts. Existing approaches to the examination of the situation of war are analyzed: philosophical-existential, psychoanalytic, sociological, literary. In the second part of the paper, the authors propose their method for analyzing limit situations in texts about war, which basis on existing approaches and preserves the text-centric principle of studying the structure of the story. Two interrelated areas of research have been identified: the study of war as a continuous limit situation in the intertextual aspect (the discourse of war); the study of limit situations (death, suffering, guilt, accident) in the narrative of war as part of a specific text. In the third part of the scientific work,the analysis of war as a continuous limit situation results in the study of the concept of “limit” (border) in a fiction text. The role of “limit” (border) concept in the texts about the war is studied, the possible types of limits in the discourse of war are examined. Limit situations in the narrative of war are analyzed on the basis of the novel “My Lieutenant” by Daniil Granin. A review of journalistic and scientific works about the novel revealed both the continuity and the differences between the novel and the “lieutenant” prose of the 20th century. An analysis of the limit situations in the novel revealed their key position in the narrative. These situations are independent of the fiction time, of the fluctuation of the point of view’; the function of the abstract author is to build the narrative as a “directive” immersion of the hero and narrator in these situations.

Lattice Thermal Conductivity Modelling of a Diatomic Nanoscale Material

2020 ◽  
Vol 10 (5) ◽  
pp. 602-609
Author(s):  
Adil H. Awad
Keyword(s):  
Thermal Conductivity ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Correction Term ◽  
Nanoscale Material ◽  
New Approach ◽  
Two Samples ◽  
Conductivity Modelling ◽  
Callaway Model

Introduction: A new approach for expressing the lattice thermal conductivity of diatomic nanoscale materials is developed. Methods: The lattice thermal conductivity of two samples of GaAs nanobeam at 4-100K is calculated on the basis of monatomic dispersion relation. Phonons are scattered by nanobeam boundaries, point defects and other phonons via normal and Umklapp processes. Methods: A comparative study of the results of the present analysis and those obtained using Callaway formula is performed. We clearly demonstrate the importance of the utilised scattering mechanisms in lattice thermal conductivity by addressing the separate role of the phonon scattering relaxation rate. The formulas derived from the correction term are also presented, and their difference from Callaway model is evident. Furthermore their percentage contribution is sufficiently small to be neglected in calculating lattice thermal conductivity. Conclusion: Our model is successfully used to correlate the predicted lattice thermal conductivity with that of the experimental observation.

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