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 Netherlands
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 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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