EFFECTIVE COMPLIANCE OF AN ELASTIC INHOMOGENEITY WITH NON-UNIFORM STRAIN

摘要

A method is proposed to estimate contribution of an elastic inhomogeneity into the overall strain of the material for the case when strain inside the inhomogeneity is not uniform. Uniform strain is a common situation when the inhomogeneity has an ellipsoidal shape and placed into the uniform stress field. However, the assumption of uniformity is inadequate in many applications when geometrical irregularities of the inhomogeneity, surface effects as well as interactions with other inhomogeneities cause local strain variations in the medium. The proposed method may have far reaching implications when impact of local strain variations on the material overall elastic response is of interest. For example, it may bring insight on how to account for strong interactions between inhomogeneities when predicting material properties and how to mobilize these interactions to achieve better properties. It is well known that interactions may produce stiffening and toughening effects depending on the material microstructure. The compliance contribution tensor is found to be dependent on the boundary displacements of the inhomogeneity and material properties. To illustrate the method we calculated elastic compliances of (1) a circular inclusion with perfectly bonded interface (test problem), (2) a circular inclusion with partially debonded interface, and (3) two strongly interacting cracks in parallel setting.