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Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space 总被引:2,自引:0,他引:2
The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space. 相似文献
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