The bulletin of mathematical biophysics

, Volume 22, Issue 1, pp 53–61 | Cite as

Dilation-producing stresses and strains obtained with the aid of density measurements

  • William H. Gutstein
  • Heinz Scharfstein


Stress systems in a deformed medium are in general of two kinds: (i) dilation-producing and (ii) nondilation-producing. Ordinarily the dilation is computed from a knowledge of the stresses, which in turn are obtained by solving the general elastostatic equations of equilibrium, under specified boundary conditions. If, however, interest is centered only in dilation-producing stresses, or in the event that only such stresses exist in the deformed system, and the density changes in the medium may be experimentally determined or postulateda priori as functions of the coordinates, these stresses may be directly obtained by a simplified procedure of solving for a particular integral of the Poisson equation without appeal to boundary conditions.** In irrotational systems in which conservative body forces exist, there is a direct relationship between the dilation and the distributed body forces. Reference to both purely physical and biophysical systems is made.


Body Force Poisson Equation Elastic Medium Stress System Biophysical System 
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  1. Folkow, Björn and Löfving Birger. 1956. “The Distensibility of the Systemic Resistance Blood Vessels.”Acta Physiol. Scand.,38 (Fasc. 1), 37–52.Google Scholar
  2. Morse, Philip M. and Herman Feshbach. 1953.Methods of Theoretical Physics, New York: McGraw-Hill, Part II, p. 1786.MATHGoogle Scholar
  3. Peirce, B. O. 1929.A Short Table of Integrals. New York: Ginn & Co., ##402, 403.MATHGoogle Scholar
  4. Sokolnikoff, I. S. 1956.The Mathematical Theory of Elasticity. Second Ed. New York: McGraw-Hill, p. 73.Google Scholar
  5. Sommerfeld, Arnold. 1950.Lectures on Theoretical Physics. New York: Academic Press, Vol. II, p. 6.Google Scholar
  6. Wang, Chi-Teh. 1953.Applied Elasticity. New York: McGraw-Hill, p. 76, Problem 2.MATHGoogle Scholar

Copyright information

© University of Chicago 1960

Authors and Affiliations

  • William H. Gutstein
    • 1
    • 2
  • Heinz Scharfstein
    • 1
    • 2
  1. 1.Department of PathologyNew York University Bellevue Medical Center and Harlem HospitalNew YorkUSA
  2. 2.Department of Physics, Washington SquareNew York UniversityNew YorkUSA

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