Analytical solutions to a network of standard linear solids

Analytical solutions to a network of standard linear solids Various viscoelastic models, such as the standard linear solid, Maxwell model, and Kelvin–Voigt model, are frequently used to describe the behavior of biological materials from single cells to tissues. These models are expressed mathematically as simple differential equations, called constitutive equations, which relate the applied force (stress) to the resulting deformation (strain) of the material. Networks of these models, representing materials with heterogeneous mechanical properties, are described by systems of constitutive equations. We prove that the eigenvalues associated with such systems are all nonpositive real numbers, find bounds for them, and indicate how they can be estimated quickly and accurately. We then give formulas for the analytical solutions of the system of equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Engineering Mathematics Springer Journals

Analytical solutions to a network of standard linear solids

Loading next page...
 
/lp/springer_journal/analytical-solutions-to-a-network-of-standard-linear-solids-BAYhP1MXGK
Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Physics; Classical Mechanics; Applications of Mathematics; Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
0022-0833
eISSN
1573-2703
D.O.I.
10.1007/s10665-016-9882-6
Publisher site
See Article on Publisher Site

Abstract

Various viscoelastic models, such as the standard linear solid, Maxwell model, and Kelvin–Voigt model, are frequently used to describe the behavior of biological materials from single cells to tissues. These models are expressed mathematically as simple differential equations, called constitutive equations, which relate the applied force (stress) to the resulting deformation (strain) of the material. Networks of these models, representing materials with heterogeneous mechanical properties, are described by systems of constitutive equations. We prove that the eigenvalues associated with such systems are all nonpositive real numbers, find bounds for them, and indicate how they can be estimated quickly and accurately. We then give formulas for the analytical solutions of the system of equations.

Journal

Journal of Engineering MathematicsSpringer Journals

Published: Feb 15, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off