TY - JOUR

T1 - Application of Post–Widder inversion formula to the calculation of relaxation spectrum from relaxation modulus

AU - Cho, Gyuhyeon

AU - Choi, Jehyeok

AU - Lee, Junghaeng

AU - Cho, Kwang Soo

N1 - Publisher Copyright:
© Korean Society of Rheology 2024.

PY - 2024/2

Y1 - 2024/2

N2 - There have been developed a number of algorithms for the determination of relaxation spectrum from viscoelastic data. When viscoelastic data are given by stress relaxation test, the relation between relaxation spectrum and relaxation modulus can be transformed to that of Laplace transform. Hence, calculation of relaxation spectrum from relaxation modulus is a problem of inverting Laplace transform. Among various mathematical methods for inverse Laplace transform, the Post–Widder formula has been chosen by a number of researchers. However, they did not solve the problem by use of advance numerical technic but used low-order approximations. We suggest a new numerical algorithm which can calculate higher order solutions. In principle, the order of the Post–Widder formula is not limited in our algorithm.

AB - There have been developed a number of algorithms for the determination of relaxation spectrum from viscoelastic data. When viscoelastic data are given by stress relaxation test, the relation between relaxation spectrum and relaxation modulus can be transformed to that of Laplace transform. Hence, calculation of relaxation spectrum from relaxation modulus is a problem of inverting Laplace transform. Among various mathematical methods for inverse Laplace transform, the Post–Widder formula has been chosen by a number of researchers. However, they did not solve the problem by use of advance numerical technic but used low-order approximations. We suggest a new numerical algorithm which can calculate higher order solutions. In principle, the order of the Post–Widder formula is not limited in our algorithm.

KW - B-spline regression

KW - Linear viscoelasticity

KW - Post–Widder inversion formula

KW - Relaxation time spectrum

KW - Stirling number of first kind

UR - http://www.scopus.com/inward/record.url?scp=85184204295&partnerID=8YFLogxK

U2 - 10.1007/s13367-023-00086-7

DO - 10.1007/s13367-023-00086-7

M3 - Article

AN - SCOPUS:85184204295

SN - 1226-119X

VL - 36

SP - 79

EP - 88

JO - Korea Australia Rheology Journal

JF - Korea Australia Rheology Journal

IS - 1

ER -