TY - JOUR
T1 - Wave propagation in nonlinear and hysteretic media - A numerical study
AU - Meurer, T.
AU - Qu, J.
AU - Jacobs, L. J.
PY - 2002/10/23
Y1 - 2002/10/23
N2 - This paper considers the problem of one dimensional wave propagation in nonlinear, hysteretic media. The constitutive law in the media is prescribed by an integral relationship based on the Duhem model of hysteresis. It is found that the well known nonlinear elastic stress-strain relationship is a special case of this integral relationship. It is also shown that the stress-strain relationship from the McCall and Guyer model of hyesteretic materials can also be derived from this integral stress-strain relationship. The first part of this paper focuses on a material with a quadratic stress-strain relationship, where the initial value problem is formulated into a system of conservation laws. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by Kurganov and Tadmor. The second part of this research is devoted to wave propagation in hysteretic media. Several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis. The results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials.
AB - This paper considers the problem of one dimensional wave propagation in nonlinear, hysteretic media. The constitutive law in the media is prescribed by an integral relationship based on the Duhem model of hysteresis. It is found that the well known nonlinear elastic stress-strain relationship is a special case of this integral relationship. It is also shown that the stress-strain relationship from the McCall and Guyer model of hyesteretic materials can also be derived from this integral stress-strain relationship. The first part of this paper focuses on a material with a quadratic stress-strain relationship, where the initial value problem is formulated into a system of conservation laws. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by Kurganov and Tadmor. The second part of this research is devoted to wave propagation in hysteretic media. Several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis. The results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials.
KW - Conservation law
KW - High-resolution scheme
KW - Hysteretic media
KW - Integro-differential equations
KW - Nonlinear media
KW - Wave propagation
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U2 - 10.1016/S0020-7683(02)00366-9
DO - 10.1016/S0020-7683(02)00366-9
M3 - Article
AN - SCOPUS:0037164194
SN - 0020-7683
VL - 39
SP - 5585
EP - 5614
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 21-22
ER -