scholarly journals On an Implicit Model Linear in Both Stress and Strain to Describe the Response of Porous Solids

2021 ◽  
Author(s):  
Hiromichi Itou ◽  
Victor A. Kovtunenko ◽  
Kumbakonam R. Rajagopal
Keyword(s):  
Elastic Response ◽  
Porous Solids ◽  
Stress And Strain ◽  
Well Posedness ◽  
Porous Metals ◽  
Mathematical Properties ◽  
Implicit Model ◽  
Linearized Strain ◽  
The One ◽  
Linear Elliptic Problem

AbstractWe study some mathematical properties of a novel implicit constitutive relation wherein the stress and the linearized strain appear linearly that has been recently put into place to describe elastic response of porous metals as well as materials such as rocks and concrete. In the corresponding mixed variational formulation the displacement, the deviatoric and spherical stress are three independent fields. To treat well-posedness of the quasi-linear elliptic problem, we rely on the one-parameter dependence, regularization of the linear-fractional singularity by thresholding, and applying the Browder–Minty existence theorem for the regularized problem. An analytical solution to the nonlinear problem under constant compression/extension is presented.

scholarly journals On a model for internal waves in rotating fluids

2018 ◽  
Vol 3 (2) ◽  
pp. 627-648 ◽  
Author(s):  
A. Durán
Keyword(s):  
Internal Waves ◽  
Fluid Model ◽  
Well Posedness ◽  
Solitary Wave Solutions ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
Mathematical Properties ◽  
Gravity Effects ◽  
Two Fluid Model ◽  
Two Fluid

AbstractIn this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the dispersion balance. The physical regime of validation is discussed and mathematical properties of the new system, concerning well-posedness, conservation laws and existence of solitary-wave solutions, are analyzed.

scholarly journals Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

2019 ◽  
Vol 23 (5) ◽  
pp. 2339-2350 ◽  
Author(s):  
Vazken Andréassian ◽  
Tewfik Sari
Keyword(s):  
Water Balance ◽  
Mathematical Reasoning ◽  
Technical Note ◽  
The Other ◽  
Partial Differential ◽  
Mathematical Properties ◽  
The Difference ◽  
The One

Abstract. This Technical Note documents and analyzes the puzzling similarity of two widely used water balance formulas: Turc–Mezentsev and Tixeront–Fu. It details their history and their hydrological and mathematical properties, and discusses the mathematical reasoning behind their slight differences. Apart from the difference in their partial differential expressions, both formulas share the same hydrological properties, and it seems impossible to recommend one over the other as more “hydrologically founded”: hydrologists should feel free to choose the one they feel more comfortable with.

scholarly journals Surface Roughness and Porosity of Hydrated Cement Pastes

10.14311/1374 ◽  
2011 ◽  
Vol 51 (3) ◽  
Author(s):  
T. Ficker ◽  
D. Martišek ◽  
H. M. Jennings
Keyword(s):  
The Other ◽  
Porous Solids ◽  
Surface Irregularity ◽  
Hydrated Cement ◽  
Cement Pastes ◽  
Cement Ratio ◽  
Fracture Surfaces ◽  
Water To Cement Ratio ◽  
The One ◽  
Highly Porous

. Seventy-eight graphs were plotted to describe and analyze the dependences of the height and roughness irregularities on the water-to-cement ratio and on the porosity of the cement hydrates. The results showed unambiguously that the water-to-cement ratio or equivalently the porosity of the specimens has a decisive influence on the irregularities of the fracture surfaces of this material. The experimental results indicated the possibility that the porosity or the value of the water-to-cement ratio might be inferred from the height irregularities of the fracture surfaces. It was hypothesized that there may be a similarly strong correlation between porosity and surface irregularity, on the one hand, and some other highly porous solids, on the other, and thus the same possibility to infer porosity from the surfaces of their fracture remnants.

scholarly journals Well-posedness of the linear heat equation with a second order memory term

2020 ◽  
Vol 34 ◽  
pp. 03011
Author(s):  
Constantin Niţă ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Unique Solution ◽  
Source Term ◽  
Memory Term ◽  
Well Posedness ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Linear Heat ◽  
The One

In this article we prove that the heat equation with a memory term on the one-dimensional torus has a unique solution and we study the smoothness properties of this solution. These properties are related with some smoothness assumptions imposed to the initial data of the problem and to the source term.

Failure of Porous Metals Based on Strain Energy Density Criterion

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
A. Y. Elruby ◽  
Sam Nakhla
Keyword(s):  
Strain Energy ◽  
Elastic Response ◽  
Micromechanical Modeling ◽  
Plastic Behavior ◽  
Extensive Literature ◽  
Loading Capacity ◽  
Porous Metals ◽  
Elastoplastic Behavior ◽  
Damage Process ◽  
Extensive Literature Search

Abstract Porosity in metals is well known to influence the mechanical behavior, namely, the elastic response, the plastic behavior, and the material loading capacity. The main focus of the current work is to investigate the failure of porous metals. Extensive literature search was conducted to identify failure mechanisms associated with the increase of porosity for up to 15% by volume. Consequently, micromechanical modeling is utilized to investigate the damage process at microlengths. Finally, a complete macromechanical modeling approach is proposed for specimen-sized models. The approach utilizes the extended Ramberg–Osgood relationship for the elastoplastic behavior, while the failure is predicted using a strain energy-based failure criterion capturing the effect of porosity. The proposed approach is validated against several testing results for different metals at various porosity levels.

scholarly journals On the global well-posedness of the one-dimensional Schrödinger map flow

2009 ◽  
Vol 2 (2) ◽  
pp. 187-209 ◽  
Author(s):  
Igor Rodnianski ◽  
Yanir Rubinstein ◽  
Gigliola Staffilani
Keyword(s):  
Well Posedness ◽  
One Dimensional ◽  
The One ◽  
Schrödinger Map

Two-Dimensional Numerical Modelling of Hydrogen Diffusion in Metals Assisted by Both Stress and Strain

2010 ◽  
Vol 138 ◽  
pp. 117-126 ◽  
Author(s):  
Jesús Toribio ◽  
Viktor Kharin ◽  
Diego Vergara ◽  
Miguel Lorenzo
Keyword(s):  
Concentration Distribution ◽  
Hydrogen Diffusion ◽  
Numerical Approach ◽  
Stress And Strain ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Weighted Residual Method ◽  
One Dimensional ◽  
Triangular Elements ◽  
The One

The present work is based on previous research on the one-dimensional (1D) analysis of the hydrogen diffusion process, and proposes a numerical approach of the same phenomenon in two-dimensional (2D) situations, e.g. notches. The weighted residual method was used to solve numerically the differential equations set out when the geometry was discretized through the application of the finite element method. Three-node triangular elements were used in the discretization, due to its simplicity, and a numerical algorithm was numerically implemented to obtain the hydrogen concentration distribution in the material at different time increments. The model is a powerful tool to analyze hydrogen embrittlement phenomena in structural materials.

Mathematical Approach to N-Centered DFT and Associated Methods for the Study of Open Systems

2021 ◽  
Author(s):  
Guillaume Grente
Keyword(s):  
Density Functional ◽  
Optimal Transport ◽  
Open Systems ◽  
Fundamental Aspect ◽  
Electronic Systems ◽  
Electronic Density ◽  
Mathematical Properties ◽  
Seminal Article ◽  
The One ◽  
Definition Of

Abstract A fundamental aspect of the study of N−electronic systems (systems containing N electrons) is to obtain information on the states in which these systems have minimal energy. In practice a numerical search of such states is impossible to carry out, so that alternative approaches have been developped, the one around which this work revolves being to consider electronic systems through their electronic density rather than their state. This approach, known today as Density Functional Theory (DFT), was formalised in Kohn and Sham’s seminal article [1] and its mathematical aspects were studied a few years later by Lieb [2]. Since then, the ideas leading to the construction of DFT have been adapted to the context of electronic systems with a fractionnal number of electrons (open systems), first through PPLB DFT[3] and more recently through the definition of N−centered DFT[4, 5]. In both cases it is unclear wherether the mathematical properties established for classical DFT can be expected to hold true. This question is the main problematic of our work, in which we shall study the analogy between N−centered and classical DFT, from their construction to the methods that are derived from them. This will lead us to construct a Kohn-Sham scheme for N−centered DFT, investigate the links between this theory and optimal transport and present the Hubbard Dimer in this particular situation.

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