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Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.

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Exact closed-form expressions have been derived for the stresses and the electric fields induced in piezoelectric multilayers deposited on a substrate with lattice misfit and thermal expansion coefficient mismatch. The derived formulations can model any number of layers using recursive relations that minimize the computation time. A proper rotation matrix has been utilized to generalize the expressions so that they can be used for various growth orientations with each layer having hexagonal crystal symmetry. As an example, the influence of lattice misfit and thermal expansion coefficient mismatch on the state of electroelastic fields in different layers of GaN multi quantum wells has been examined. A comparison with the finite element analysis results showed very close agreement. The analytical expressions developed herein will be useful in designing optoelectronic devices as well as in predicting defect density in multi quantum wells.