Paolo Lonetti

Continuum Damage-healing Mechanics with Application to Self-healing Composites

The general behavior of self-healing materials is modeled including both irreversible and healing processes. A constitutive model, based on a continuum thermodynamic framework, is proposed to predict the general response of self-healing materials. The self-healing materials’ response produces a reduction in size of microcracks and voids, opposite to damage. The constitutive model, developed in the mesoscale, is based on the proposed Continuum Damage-Healing Mechanics (CDHM) cast in a consistent thermodynamic framework that automatically satisfies the thermodynamic restrictions. The degradation and healing evolution variables are obtained introducing proper dissipation potentials, which are motivated by physically based assumptions. An efficient three-step operator slip algorithm, including healing variables, is discussed in order to accurately integrate the coupled elastoplastic-damage-healing constitutive equations. Material parameters are identified by means of simple and effective analytical procedures. Results are shown in order to demonstrate the numerical modeling of healing behavior for damaged polymer-matrix composites. Healed and not healed cases are discussed in order to show the model capability and to describe the main governing characteristics concerning the evolution of healed systems.

An Inelastic Damage Model for Fiber Reinforced Laminates

A new modelfor damage behavior of polymer matrix composite laminates is presented. The model is developed for an individual lamina, and then assembled to describe the nonlinear behavior of the laminate. The model predicts the inelastic effects as reduction of stiffness and increments of damage and unrecoverable deformation. The modelis defined using Continuous Damage Mechanics coupled with Classical Thermodynamic Theory. Unrecoverable deformations and Damage are coupled by the concept of effective stress. New expressions of damage and unrecoverable deformation domains are presented so that the number of model parameters is small. Furthermore, model parameters are obtained from existing test data for unidirectional laminae, supplemented by cyclic shear stress strain data. Comparison with lamina and laminate test data are presented to demonstrate the ability of the model to predict the observed behavior.

INTERLAMINAR DAMAGE MODEL FOR POLYMER MATRIX COMPOSITES

A constitutive model for fiber-reinforced composite materials with damage and unrecoverable deformation, which for the first time accounts for interlaminar damage, is presented. The formulation is based on Continuous Damage Mechanics coupled with Classical Plasticity Theory in a consistent thermodynamic framework using internal state variables. In-plane damage and novel formulation of interlaminar damage are included in order to describe the main failure modes of laminates structures. A novel implementation of the constitutive model into a finite element formulation incorporating geometric nonlinearity is presented. The model uses a small number of adjustable parameters, which are identified from available experimental data. Comparisons with experimental data for composite laminates under torsion loading are shown to validate the model for interlaminar damage. Coupled material and geometrical nonlinear analysis with simultaneous in-plane and interlaminar damage is demonstrated. The effect of warping on interlaminar damage is shown to be significant.

Damage Model for Composites Defined in Terms of Available Data

A model to predict stiffness reduction and stress redistribution due to damage of laminated polymer composites is presented. The material properties required by the model are limited to those already available for unidirectional composites. Classical lamination theory is generalized for the case of a continuously damaging material using concepts from continuous damage mechanics. The Tsai-Wu failure criteria can be recovered as a limiting case. The damage model is validated with experimental results for various laminates built with aramid/epoxy, T300/5208, and T300/914 carbon/epoxy.

Influence of micro-cracking and contact on the effective properties of composite materials

Abstract In the present work a novel micro-mechanical approach to analyze the influence of micro-crack evolution and contact on the effective properties of elastic composite materials is proposed, based on homogenization techniques, interface models and fracture mechanics concepts. By means of the finite element method, enhanced non-linear macroscopic constitutive laws are developed by taking into account changes in micro-structural configuration associated with the growth of micro-cracks and with contact between crack faces. Numerical simulations are carried out for the cases of a porous composite with edge cracks and of a debonded fibre reinforced composite, loaded along extension/compression uniaxial macro-strain paths. Micro-crack propagation is modelled by using an original methodology based on the J-integral technique in conjunction with an interface model taking into account the unilateral contact of crack faces. In the context of a micro-to-macro transition obtained by controlling the macro-deformation of the micro-structure, the effects of adopting three types of boundary conditions on the macroscopic constitutive law, namely linear deformation, uniform tractions and periodic deformations and anti-periodic tractions, are studied. As a consequence, the proposed method can be applied to a large class of problems including periodic, locally periodic and irregular composite materials. Micro-crack and contact evolution result in a progressive loss of stiffness and can lead to failure for homogeneous macro-deformations associated with unstable crack propagation.

An analytical delamination model for laminated plates including bridging effects

A penalised interface model, whose strain energy is the penalty functional related to interface adhesion constraint, is introduced in conjunction with a damageable interface whose local constitutive law, in turn, represents bridging stress effects, in order to analyse delamination and bridging phenomena in laminated plates. The laminate is modelled by means of first-order shear deformable layer-wise kinematics and the governing equations are formulated in the form of a non-linear differential system with moving intermediate boundary conditions related to opportune delamination and bridging growth conditions. The problem is solved through an analytical approach. The model leads to an accurate and self-consistent evaluation of the energy release rate and its mode components due to the inclusion of significant contributions arising from coupling between in-plane and transverse shear stresses, and to an asymptotic estimate of interlaminar stresses. The salient features of the proposed model are investigated in the context of an energy balance approach and of a J-integral formulation, thus providing simple results useful to model delamination growth and bridging behaviour when mixed mode loading is involved. The accuracy of the proposed model is substantiated through comparisons with results from continuum analysis obtained by a finite element (FE) procedure. The effectiveness of the proposed model is highlighted by showing the solution of a two-layered plate scheme subjected to pure and mixed mode loading conditions and to fibre bridging stresses. The results point out that the present model, despite its low computational cost in comparison with more complex FE analyses, is an efficient tool to predict delamination and bridging evolution.

Computation of Energy Release Rate and Mode Separation in Delaminated Composite Plates by Using Plate and Interface Variables

Abstract A model for analyzing mixed-mode delamination problems in laminated composite plates under general loading conditions is studied. The first-order shear deformable laminated plate theory and the interface methodology, which in turn is based on fracture mechanics, are adopted. The laminate is modeled as an assembly of laminated plate and interface layers in the thickness direction. When the limit case of interface stiffness coefficients approaching infinity is considered, a perfect adhesion between plate models is simulated. On the other hand, delamination between sublaminates is taken into account by assuming zero values for interface stiffnesses. Lagrange and penalty methods are adopted to simulate connections between plate elements. By using a variational approach and the virtual crack closure concept, expressions for total energy release rate and its mode components along the delamination front are obtained, in terms of both interface variables and plate stress resultant discontinuities. These formulas shed light on the effect of transverse shear in interface fracture analysis and establish the improvement and the accuracy of the proposed formulation compared to other plate-based delamination models existing in the literature. The method is implemented in a two-dimensional finite element analysis, which makes use of shear deformable plate elements and interface elements. To illustrate the present method, some typical delamination problems involving mode I, mode II, and mode III are examined and the numerical energy release rate distributions are compared to highly accurate three-dimensional (3D) finite element solutions. These results show that the procedure is accurate when a reasonable number of plate models are included in the analysis and more computationally efficient than 3D finite element models, for which determining fracture energies may lead to a remarkable increase in model complexity.

Dynamic Mode I and Mode II Crack Propagation in Fiber Reinforced Composites.

Dynamic crack phenomena in unidirectional composite laminates are investigated. The proposed formulation is based on the combination of beam and interface methodologies, which are utilized to predict crack behavior in the context of the steady state fracture mechanics. The relevant quantities related to delamination phenomena are discussed with reference to Lagrange and penalty methods utilized to simulate the connection between the sublaminates adjoining the delamination plane. Analytical solutions of the governing equations are proposed and closed form expressions for simple cases, involving pure mode I and mode II components, are provided. The accuracy of the proposed approach is validated through comparisons with results arising from continuum analysis obtained by finite element procedures. Some applications are developed to point out the influence of the crack front speed, the shear deformability and the inertial contributions on the energy release rate. The main features of the proposed model are investigated in the context of an energy balance approach based on the J-integral formulation and thus providing results useful to model delamination growth for simple cases involving pure mode I and mode II loading conditions. Special attention is devoted to analyzing the allowable speeds of the moving crack. In particular, a parametric study in terms of the main characteristic geometric parameters of the laminate is proposed to show the main features of the crack tip behavior.

Optimum design analysis of hybrid cable-stayed suspension bridges

Abstract A design methodology to predict optimum post-tensioning forces and dimensioning of the cable system for hybrid cable-stayed suspension (HCS) bridges is proposed. The structural model is based on the combination of an FE approach and an iterative optimization procedure. The former is able to provide a refined description of the bridge structure, which takes into account geometric nonlinearities involved in the bridge components. The latter is utilized to optimize the shape of post-tensioning forces as well as the geometry of the cable system to achieve minimum deflections, lowest steel quantity involved in the cable system and maximum performance of the cables under live load configurations. Results are proposed in terms of comparisons with existing formulations to validate the proposed methodology. Moreover, parametric studies on more complex long span structures are also developed to verify existing cable-dimensioning rules and to analyze between HCS bridges and conventional cable-stayed or suspension systems.

A Parametric Study on the Dynamic Behavior of Combined Cable-Stayed and Suspension Bridges under Moving Loads

A parametric study to investigate dynamic behavior of long-span combined cable bridges under moving loads is proposed. The bridge typology is based on the combination of both cable-stayed and suspension systems. The theoretical formulation is based on a continuum approach, which has been utilized in the literature to analyze long-span bridges. The bridge formulation is developed for combined stayed-suspension cable schemes, which can be easily specialized to analyze perfect cable-stayed and suspension bridges. In order to investigate the dynamic response of cable-supported bridges under moving loads, comparisons in terms of main deformability and stress-bridge parameters are proposed. Dynamic equilibrium equations lead to a partial differential problem, which has been solved, numerically, by means of a finite difference scheme. The formulation is developed in a dimensionless context by means of proper variables strictly connected with moving loads and bridge properties. In order to quantify the amplification effects produced by the moving system on typical design bridge variables, a comparative study involving the behavior of cable-stayed, suspension, and combined cable system configurations is developed. The optimal ratios of cable steel quantity involved in both cable-stayed and suspension systems are discussed, providing specific rules that guarantee smaller material amounts in the cable systems and an improved structural behavior of the combined bridge scheme.