Giulio Alfano

An interface-element formulation for the simulation of delamination with buckling

The paper describes a simple corotational formulation applied to one-dimensional interface elements which embed a fracturing procedure for mixed-mode delaminations. Having thereby introduced geometric non-linearity, the technique can be applied to situations involving a combination of buckling and delamination. Detailed comparisons are made with experimental results for such a problem.

MITC finite elements for laminated composite plates

Within the framework of the first-order shear deformation theory, 4- and 9-node elements for the analysis of laminated composite plates are derived from the MITC family developed by Bathe and coworkers. To this end the bases of the MITC formulation are illustrated and suitably extended to incorporate the laminate theory. The proposed elements are locking-free, they do not have zero-energy modes and provide accurate in-plane deformations. Two consecutive regularizations of the extensional and flexural strain fields and the correction of the resulting out-of-plane stress profiles necessary to enforce exact fulfillment of the boundary conditions are shown to yield very satisfactory results in terms of transverse and normal stresses. The features of the proposed elements are assessed through several numerical examples, either for regular and highly distorted meshes. Comparisons with analytical solutions are also shown. Copyright

General solution procedures in elasto/viscoplasticity

Constitutive relations and numerical integration algorithms for elasto/viscoplastic problems are investigated. A fully implicit integration scheme is adopted and the relevant expression of the consistent tangent operator for yield criteria and flow functions of arbitrary type is derived by suitably generalizing the approach exploited for rate-independent plasticity. This is achieved by replacing the consistency condition of plasticity with a relation between the viscoplastic consistency parameter and the flow function of the constitutive model in use. The methodology adopted simplifies alternative procedures for the evaluation of consistent tangent operators which necessitate the inversion of a viscoplastic compliance operator. The general expression of the consistent tangent operator is then specialized to the von Mises yield criterion endowed with commonly adopted viscoplastic constitutive models. Numerical examples are finally presented.

A Finite Element Analysis for Unbonded Flexible Risers Under Torsion

This paper presents a detailed finite-element analysis of unbonded flexible risers. The numerical results are compared to the analytical solutions for various load cases. In the finite-element model, all layers are modeled separately with contact interfaces between each layer. The finite-element model includes the main features of the riser geometry with very little simplifying assumptions made. The numerical model was solved using a fully explicit time-integration scheme implemented in a parallel environment on a 16-processor cluster. The very good agreement found from numerical and analytical comparisons validates the use of our numerical model to provide benchmark solutions against which further detailed investigation will be made.

A general approach to the evaluation of consistent tangent operators for rate-independent elastoplasticity

Abstract We present a general approach to the derivation of the explicit expression of tangent operators, consistent with the finite-step integration schemes of the flow rule, for rate-independent elastoplastic models with mixed hardening. By exploiting the model of generalized standard material, we show that the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix. Use of the Sherman-Morrison-Woodbury formula allows us to reduce to a half the burden associated with such inversion and to derive an expression of the consistent tangent operator prone to computer implementation. The application of the proposed approach to the von Mises yield criterion with linear kinematic and isotropic hardening shows that the closed-form expression of the operator can be obtained by a straightforward procedure.

Numerical and Analytical Modeling of Unbonded Flexible Risers

This paper presents an analytical formulation and a finite element analysis of the behavior of multilayer unbonded flexible risers. The finite element model accurately incorporates all the fine details of the riser that were previously considered to be important but too difficult to simulate due to the significant associated computational cost. All layers of the riser are separately modeled, and contact interaction between layers has been accounted for. The model includes geometric nonlinearity as well as frictional effects. The analysis considers the main modes of flexible riser loading, which include internal and external pressures, axial tension, torsion, and bending. Computations were performed by employing a fully explicit time integration scheme on a parallel 16-processor cluster of computers. Consistency of simulation results was demonstrated by comparison with those of the analytical model of an identical structure. The close agreement gives confidence in both approaches.

A tangent–secant approach to rate-independent elastoplasticity: formulations and computational issues

A general and robust solution procedure for nonlinear finite element equations in small strain elastoplastic structural problems is presented. Its peculiar feature lies in the choice of the most suitable constitutive operator to be adopted at each iteration of a generic load step in order to ensure the utmost stability and convergence rate. Namely, the consistent tangent operator is replaced by a secant one, or vice versa, whether the adopted norm of the residual does not, or does, conveniently decrease at the current iteration. The secant operator is defined as to recover the finite-step increment of the plastically admissible stress from the total, not iterative, strain increment. The original formulation of the solution procedure, consisting of alternate tangent and secant iterations, is then extended to achieve an effective coupling with line searches. The excellent performances of the two procedures are illustrated by numerical examples carried out for typical benchmark problems in plane strain and three-dimensional cases.

A displacement-like finite element model for J2 elastoplasticity: Variational formulation and finite-step solution

The displacement-like finite element formulation for finite-step J2 elastoplasticity is revisited in this paper. The classical computational strategy, according to which, plastic loading is tested at the Gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements, is consistently derived from a suitably discretized version of a min-max variational principle. The sequence of solution phases to be performed within each load step adopting a full Newtons method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized. It is further shown that, in order to increase the rate of convergence and the stability properties of the Newtons method, the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model. This is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step. The effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems.

Automatic analysis of multicell thin-walled sections

An automatic procedure is outlined for the determination of the shear centre and the evaluation of the overall state of stress in multicell thin-walled sections subject to axial force, bending moment, shearing force and torque. Graph theory is shown to be the rationale to establish a topological model of the section which is preliminary to a computer implementation of the shear stress analysis. Specifically, we exploit the main features of the Depth-First-Search graph algorithm in order to automatically determine a number of independent circuits equal to the degree of connection m of the section. The algorithm also localize the m slits which make the section open, a preliminary step for the analysis of multicell sections subject to a shearing force. Further, the evaluation of the first elastic area moment at any point of the open section is addressed by means of the Open-Section-Cut algorithm elaborated in this paper. The outlined procedure entails a considerable simplification of the analysis, since the geometrical data which need to be assigned are only the strictly necessary ones, namely the coordinates of the vertices, the branches connecting them and their thickness. A numerical example, carried out for a ships hull by means of a computer program written in Mathematica, shows the effectiveness of the proposed approach.

Intermediate Debonding Failure of RC Beams Retrofitted in Flexure with FRP: Experimental Results versus Prediction of Codes of Practice

An experimental investigation has been conducted with the aim to investigate on the midspan debonding failure of reinforced concrete (RC) beams retrofitted in flexure by means of the application of a fiber-reinforced polymer (FRP) lamina externally applied to concrete substratum. Experimental tests on a series of RC beams with different geometries and type of internal steel reinforcing bars have been carried out in four-point bending up to failure to evaluate the influence of flexural/shear cracks on the debonding of FRP reinforcement from concrete substratum. It is widely known that the overall performance of a standard RC element is primarily influenced by the interaction between FRP and concrete substratum rather than by the strength of the FRP. The failure of such innovative retrofitting techniques may be attributed to an inadequate anchorage length; in other cases, when the FRP is correctly applied at the ends of beam, debonding starts in the vicinity of cracks and propagates toward the supports. The results of the experimental tests are used to investigate on the effectiveness of design procedures currently recommended for such debonding failure mode by the codes of practice. The results of the analytical calculations based on such models are presented in this paper and will provide an element of comparison and discussion with the experimental results. The codes of practice propose different analytical models based on the extensive research done in the last two decades, which involve different types of approximation and often yield quite different results.