The influence of elastic constants on the shape of an inclusion

A continuum mechanics model is proposed to investigate coherent misfitting precipitates in a matrix material. This elasticity based method takes arbitrary anisotropic materials, eigenstrains and interface energies into account. The equilibrium shape of the precipitate is described in terms of Eshelby’s driving forces acting on the precipitate interface. According to this force, an efficient shape optimization technique is formulated to investigate the influence of various parameters such as particle size, elastic constants and inhomogeneity on the equilibrium morphology. Using stable equilibrium shapes, the macroscopical response of the composite is calculated and compared with some common approximation techniques. The numerical treatment is realised with the finite element method.