scholarly journals The study of mathematical models of the linear theory of elasticity by presenting the fundamental solution in harmonic potentials

2020 ◽  
Vol 7 (2) ◽  
pp. 259-268
Author(s):  
V. V. Pabyrivskyi ◽  
◽  
N. V. Pabyrivska ◽  
P. Ya. Pukach ◽  
◽  
...  
Keyword(s):  
Fundamental Solution ◽  
Mathematical Models ◽  
Linear Theory ◽  
Theory Of Elasticity

Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent

Soft Matter ◽  
2020 ◽  
Vol 16 (5) ◽  
pp. 1179-1189 ◽  
Author(s):  
Timur R. Galimzyanov ◽  
Pavel V. Bashkirov ◽  
Paul S. Blank ◽  
Joshua Zimmerberg ◽  
Oleg V. Batishchev ◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Linear Theory ◽  
Linear Elasticity ◽  
Lipid Membranes ◽  
Bilayer Membrane ◽  
Theory Of Elasticity ◽  
Linear Elasticity Theory ◽  
Effect Of Solvent ◽  
Model Based ◽  
Membrane Deformations

The linear theory of elasticity can be expanded through the range from weak to strong bilayer membrane deformations using a generalized Helfrich model based on monolayer membrane additivity.

LINEAR ELASTICITY AND POTENTIAL THEORY: A COMMENT ON GURTIN (1972)

2008 ◽  
Vol 22 (28) ◽  
pp. 5035-5039 ◽  
Author(s):  
FALK H. KOENEMANN
Keyword(s):  
Potential Theory ◽  
Linear Theory ◽  
Elastic Deformation ◽  
Physical Process ◽  
Linear Elasticity ◽  
Short Note ◽  
Theory Of Elasticity ◽  
Divergence Free ◽  
Fundamental Physical

In an exhaustive presentation of the linear theory of elasticity by Gurtin [The Linear Theory of Elasticity (Springer-Verlag, 1972)], the author included a chapter on the relation of the theory of elasticity to the theory of potentials. Potential theory distinguishes two fundamental physical categories: divergence-free and divergence-involving problems. From the criteria given in the source quoted by the author, it is evident that elastic deformation of solids falls into the latter category. It is documented in this short note that the author presented volume-constant elastic deformation as a divergence-free physical process, systematically ignoring all the information that was available to him that this is not so.

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