Configurational forces in the theory of two-phase plates

Within the framework of the direct approach to the theory of plates the configurational forces are introduced taking into account the transverse shear stiffness. Their applications to plates made of non-homogeneous materials such as laminates, functionally graded materials, two-phase materials, etc., are discussed. The basic items of the applied theory of plates are related to the formulation of all balances for a deformable directed surface and to the specification of the constitutive equations. The variational principle of the total energy is established for plates assuming the presence of a variable surface singular curve. The surface singular curve separates the parts of the plate with different material properties. The continuity conditions at the singular curve are obtained. The energy-momentum tensor is constructed. Equilibrium and quasistatic motion of the surface singular curve are investigated on the base of the proposed kinetic equation. As an example of application of configurational forces we present the model of the deformation of a plate made of a material undergoing phase transitions (e.g., a shape memory alloy). © Springer Science+Business Media B.V. 2009