ESHELBY INTEGRAL FORMULAS IN SECOND GRADIENT ELASTICITY

摘要

In classical elasticity, the Eshelby integral formulas allow one to estimate the strain energy of the media containing inhomogeneities by using a particular type of surface integration. In the present paper, we derive the Eshelby integral formulas in the framework of Mindlin's second gradient elasticity theory. These formulas can be used in micromechanics applications, for example, they can be used for evaluating the effective elastic properties of composite materials in the generalized self-consistent method taking strain gradient effects into account. These effects become significant in the composites filled with small inclusions, whose size is of the order of characteristic length of matrix material.