Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body
Part of book or chapter of book
- Publisher: Tech Science Press
Elasticity | Damage | Inhomogeneous material | Variable coefficients | Direct formulation | Integro-differential equation | Localization | Mesh-based discretization | Mesh-less discretization
Copyright @ 2006 Tech Science Press
A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Using a cut-off function approach, the corresponding localized parametrix of the auxiliary problem is constructed to reduce the problem to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations for the displacement increments.