We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant J3. The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors A obtained as second\ud
derivatives of isotropic scalar functions of a symmetric tensor argument A. The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy\ud
between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity
SUMMARYWe present an algorithmic procedure for the ÿnite element solution of structural problems for no-tension materials. The approach is based upon a suitable modiÿcation of the tangent strategy which is shown to be computationally superior to conventional procedures for non-linear material models, namely the tangent strategy enhanced with line searches and the tangent-secant approach. The solution of the constitutive problem for no-tension materials is derived by an original path of reasoning and its formulation in a strain-driven format, directly amenable to a computer implementation, is presented. For completeness the existing expressions of the tangent and secant operators for the no-tension model are brie y recalled and an original formula for the secant operator derived. The robustness of the proposed strategy is exempliÿed by the numerical results obtained for a masonry panel with openings. Remarkably, the solution is achieved by assigning a single load step and an asymptotically quadratic convergence rate is attained. Further, the numerical properties of the proposed solution strategy are practically una ected by the adopted discretization.
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