Mathematical Modeling in Continuum Mechanics

2001 ◽  
Vol 54 (4) ◽  
pp. B57-B57 ◽  
Author(s):  
R Temam, ◽  
A Miranville, ◽  
P Gremaud,
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics

scholarly journals Experimental and theoretical researches of high-speed interaction of thin obstacles with a metal fragment

2019 ◽  
Vol 221 ◽  
pp. 01043
Author(s):  
Svetlana Afanasyeva ◽  
Viktor Burkin ◽  
Aleksey Dyachkovsky ◽  
Alexandr Ishchenko ◽  
Konstantin Rogaev ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Titanium Alloy ◽  
Continuum Mechanics ◽  
High Speed ◽  
Interaction Process ◽  
Actual Problem ◽  
Cost Weight ◽  
Ballistic Resistance ◽  
Protective Structures ◽  
Metal Fragment

The development of lightweight protective structures of increased ballistic resistance is not an easy task, since often there are conflicting requirements in terms of cost, weight, thickness, materials availability, processability, etc. To assess the effectiveness of protective structures one should use methods that allow to research the obstacles destruction when collided with high-speed particles. The paper is devoted to the actual problem of studying the ballistic stability of thin barriers made of various protective materials (steel, titanium alloy, ceramics, metal ceramics) when interacting with a metal fragment simulator a spherical steel drummer in the range of interaction speeds of about 2500 m/s. An experimental technique has been developed to study the most important indicators: the depth of a crater in an obstacle, a fragment’s velocity drop when interacting with protection, the obstacle’s and splinter’s fragments scattering in overgraded space. Mathematical modeling was carried out within the framework of continuum mechanics, which adequately describes the interaction process of the drummer and the obstacle under various impact conditions.

scholarly journals Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

2020 ◽  
Vol 66 (5) ◽  
pp. 1131-1152 ◽  
Author(s):  
Alex Viguerie ◽  
Alessandro Veneziani ◽  
Guillermo Lorenzo ◽  
Davide Baroli ◽  
Nicole Aretz-Nellesen ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Mathematical Analysis ◽  
Numerical Study ◽  
Interdisciplinary Collaboration ◽  
Compartmental Models ◽  
Diffusion Reaction ◽  
Pde Model ◽  
Fundamental Equations ◽  
Detailed Derivation

Abstract The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

scholarly journals Application Of More Complex Rheological Models In Continuum Mechanics

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Mária Minárová ◽  
Jozef Sumec
Keyword(s):  
Mathematical Modeling ◽  
Relaxation Process ◽  
Rheological Properties ◽  
Continuum Mechanics ◽  
Rheological Behavior ◽  
Constitutive Equations ◽  
Structural Materials ◽  
Rheological Models ◽  
Complex Models ◽  
Maxwell Models

Abstract The paper deals with mathematical modeling of the structural materials representing their rheological properties. The materials are modeled by more complex models (enhancement of Voigt and Maxwell models). The constitutive equations are derived; the relationships within the creep and relaxation process are developed. The rheological behavior of the materials is introduced.

Mathematical Modeling in Continuum Mechanics

2005 ◽  
Author(s):  
Roger Temam ◽  
Alain Miranville
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics

scholarly journals The Scientific and Life Path of Academician O.M. Belotserkovsky

2021 ◽  
Vol 1 (2) ◽  
pp. 51-60
Keyword(s):  
Mathematical Modeling ◽  
Numerical Methods ◽  
Continuum Mechanics ◽  
Physical Processes ◽  
Full Member ◽  
Outstanding Scientist ◽  
Russian Academy Of Sciences ◽  
The World ◽  
Life Path ◽  
Academy Of Sciences

Oleg Mikhailovich Belotserkovsky is an outstanding scientist and teacher, a full member of the world-famous Russian Academy of Sciences, a mathematician and mechanic, the founder of a number of scientific areas in numerical methods for solving problems of continuum mechanics, mathematical modeling of physical processes, rector of the Moscow Institute of Physics and Technology, director of the Institute of Automation Design of the Russian Academy of Sciences Oleg Mikhailovich Belotserkovsky.

Mathematical Modeling of Bio-Macromolecule Dynamics in Living Cells: A Continuum Mechanics Approach

2007 ◽  
Author(s):  
Kouroush Sadegh Zadeh ◽  
Hubert J Montas ◽  
Adel Shirmohammadi
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Living Cells
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