TY - JOUR
T1 - A circular inhomogeneity with interface slip and diffusion under in-plane deformation
AU - Wang, Xu
AU - Pan, Ernie
PY - 2010/12
Y1 - 2010/12
N2 - We consider the in-plane deformation of a circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to remote uniform stresses or uniform heat flow. The inhomogeneity and matrix have different material properties. The rate-dependent slip and mass transport by stress-driven diffusion concurrently occur on the inhomogeneity/matrix interface. For the remote uniform stress case, it is observed that the internal stresses within the inhomogeneity are quadratic functions of the coordinates x and y, and decay with two relaxation times. Interestingly the average mean stress within the circular inhomogeneity is in fact time-independent. As time approaches infinity, the internal stress field within the inhomogeneity becomes uniform and hydrostatic. In addition the change of strain energy due to the introduction of the circular elastic inhomogeneity is derived, containing various existing results as special cases. Furthermore, a simple condition leading to an internal uniform stress state within the inhomogeneity is found. This condition, which is independent of the elastic properties of the inhomogeneity and matrix, gives a simple relationship between the interface drag and diffusion parameters. For the remote heat flow case, the internal thermal stresses are linear functions of the coordinates x and y and decay only with a single relaxation time. Numerical results are presented to demonstrate the obtained solution and the corresponding physics.
AB - We consider the in-plane deformation of a circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to remote uniform stresses or uniform heat flow. The inhomogeneity and matrix have different material properties. The rate-dependent slip and mass transport by stress-driven diffusion concurrently occur on the inhomogeneity/matrix interface. For the remote uniform stress case, it is observed that the internal stresses within the inhomogeneity are quadratic functions of the coordinates x and y, and decay with two relaxation times. Interestingly the average mean stress within the circular inhomogeneity is in fact time-independent. As time approaches infinity, the internal stress field within the inhomogeneity becomes uniform and hydrostatic. In addition the change of strain energy due to the introduction of the circular elastic inhomogeneity is derived, containing various existing results as special cases. Furthermore, a simple condition leading to an internal uniform stress state within the inhomogeneity is found. This condition, which is independent of the elastic properties of the inhomogeneity and matrix, gives a simple relationship between the interface drag and diffusion parameters. For the remote heat flow case, the internal thermal stresses are linear functions of the coordinates x and y and decay only with a single relaxation time. Numerical results are presented to demonstrate the obtained solution and the corresponding physics.
KW - Circular inhomogeneity
KW - Complex variable method
KW - Interface slip and diffusion
KW - Plane elasticity
KW - Relaxation time
UR - http://www.scopus.com/inward/record.url?scp=78649629803&partnerID=8YFLogxK
U2 - 10.1016/j.ijengsci.2010.09.026
DO - 10.1016/j.ijengsci.2010.09.026
M3 - Article
AN - SCOPUS:78649629803
SN - 0020-7225
VL - 48
SP - 1733
EP - 1748
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
IS - 12
ER -