Abstract

This work presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso–strain relation among the components in the fibre (or parallel) direction and an iso–stress relation in the remaining directions (serial directions). The proposed procedure also uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress–strain performance of this material.

With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial direction. This reduction provides a composite performance equivalent to what is found in a delaminated material.

To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.

Abstract

An improved Rigid Body-Spring model (RBSM) for in-plane analyses is here proposed. The approach has been developed starting from the model presented by Casolo [4], according to which a continuum plate is discretized in an assembly of rigid quadrilateral elements connected by elasticplastic springs. In the proposed model, not only the elements that share one edge are connected, as it usually happens in RBSMs, but also the elements that share only one node, that are the elements on the diagonals. These elements are connected through an axial spring fixed to their centers of gravity. The spring stiffnesses have been obtained through the equivalence of the stored strain energy for a plane stress state. These, for an isotropic material, results to be function of the Young's modulus (E) and of the Poisson's ratio (). Thanks to the addition of the diagonal springs, this quadrilateral RBSM is capable of modeling isotropic materials with a Poisson's ratio different from zero. The effectiveness of the proposed computational method was proved comparing the elastic solution with a Finite element code for an uniaxial tensile test. About the failure response, on one hand, the addition of the diagonal springs introduces a new direction in which the failure condition is verified, reducing the intrinsic anisotropy of the failure response, typical of the discrete approaches [5, 14]. On the other hand, the new springs increase the complexity of the model and the spring constitutive behavior is no longer directly related to the material uni-axial behavior. In this work, the spring post elastic response was defined considering the mode I fracture energy of the material. In the end, the model was applied to the study of a concrete notched beam in a three point bending test. The results have been compared with the experimental one find in the literature. The analyses were executed with a dynamic explicit solver and different tensile spring behaviors were compared to highlight the importance of considering a bi-linear softening law for modeling the failure response of quasi-brittle materials like concrete.