J. Reinoso

A consistent interface element formulation for geometrical and material nonlinearities

Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to an operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.

Revisiting the problem of a crack impinging on an interface: a modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model

Abstract The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In the current investigation, this problem is revisited in view of the recent progresses on the phase field approach of brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and of the characteristic fracture-length scales of the dissipative models is analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk. The obtained computational trends are in very good agreement with previous experimental observations and the theoretical considerations on the competition and interplay between both fracture mechanics models open new research perspectives for the simulation and understanding of complex fracture patterns.

Mixed-mode failure of interfaces studied by the 2D Linear Elastic-Brittle Interface Model: macro- and micro-mechanical finite element applications in composites

ABSTRACT Macro-scale delamination and micro-scale fiber–matrix debonding events may notably affect the mechanical performance of fibrous composite elements. This article presents a two-dimensional finite-element (FE)-based formulation of interface of a small but finite thickness relying on the so-called linear elastic-brittle interface model (LEBIM) to be applied for simulation of an adhesive interface debonding and fiber–matrix decohesion failures. This modeling strategy is implemented in the commercial FE package ABAQUS by means of the user-defined subroutine UMAT. The practicability of the developed interface model is assessed through the comparison of the computational results with experimental data and with previous boundary element method (BEM) analyses using the LEBIM formulation. Specifically, LEBIM results for the interlaminar fracture toughness test showed an excellent agreement with experimental results (adhesive saw-tooth post-peak response was captured). Besides, studies of several micro-mechanical fiber–matrix configurations showed that fiber–matrix debonding events are the predominant failure mechanisms for moderate transverse loading values. The developed tool will certainly contribute to elucidate several open aspects regarding the interface crack behavior in fiber-reinforced composite materials.

A thermodynamically consistent framework to couple damage and plasticity microplane-based formulations for fracture modeling: development and algorithmic treatment

For a wide variety of quasi-brittle materials, the constitutive microplane models of damage are capable of describing the anisotropic development and growth of microcracks when materials exhibit inelastic response. Damage development in solids leads to the degradation of the macroscopic material stiffness and results in different response in loading and unloading. On the other hand, the constitutive microplane models of plasticity describe the anisotropic plastic sliding that originates macroscopic permanent deformation and remains upon unloading. For realistic modeling of these materials, in which both damage and plasticity mechanisms can evolve simultaneously, the microplane damage and plasticity models can be coupled in a systematic and robust manner. This work presents a theoretical formulation of a consistent framework to couple both microplane damage and plasticity models for triggering inelastic behavior (damage and plastic effects) in engineering materials. Throughout the derivation, it is specifically shown that the proposed derivation complies with the thermodynamical restrictions with regard to the assessment of the local energy dissipation based on the Clausius–Duhem inequality. Finally, the algorithmic treatment of the developed constitutive framework is outlined for its incorporation into incremental-iterative solution procedures using Newton–Raphson schemes and examined by means of simple benchmark examples.

Adhesive behaviour of bonded paper layers: Mechanical testing and statistical modelling

In this study, an experimental methodology based on micromechanical testing inside a scanning electron microscope is proposed to characterise bonding of paper layers connected by wet pressing. The peeling force–displacement evolution law that characterises the delamination of micromechanical double cantilever beam specimens of paper tissue have been extracted from such peeling tests. It is observed that the force–displacement evolution curve achieves a steady-state value related to the effective adhesive energy of the interface. This behaviour is explained by examining the complex load transfer mechanism between the layers exerted by cellulose fibrils. A statistical approach is used for the computation of the effective adhesive energy. It is argued that the observed force–displacement evolution law may be satisfactory described by a stochastic model that depends on the distribution function of the fibrils strength, and on two geometrical distribution functions related to the in-plane and out-of-plane fibrils angles with respect to the undeformed interface configuration. Some applications of the proposed model are demonstrated on examples.

Snap-Through of Bistable Configurations Generated from Variable Stiffness Composites

Structures made of variable stiffness (VS) composites possess a rich design space for bistable configurations that demonstrate different values of curvatures and out-of-plane displacements. In this study, several VS composites are investigated which can yield cylindrical bistable shapes similar to those generated from unsymmetrical cross-plies. Such configurations have been found favorable as a component for certain morphing applications. A semi-analytical model based on the Rayleigh-Ritz approach is presented to calculate the thermally induced multistable shapes as well as the snap-through forces particularly taking into account the curvilinear paths of VS composites. A nonlinear finite element analysis is performed to check the accuracy of the semi-analytical method. Cylindrical shapes generated from VS laminates and the corresponding straight fiber cross-ply laminates are analyzed and compared. The snap-through forces are subsequently calculated and compared for different VS laminates and the straight fiber cross-ply. It is observed that certain VS composites have a significant reduction of snap-through forces but with a marginal difference in out-of-plane displacement as compared to the corresponding straight fiber cross-ply laminate.

Invariant-Based Finite Strain Anisotropic Material Model for Fiber-Reinforced Composites

Short fibre reinforced plastic (SFRP) materials are intensively used in several engineering sectors due to their excellent mechanical properties and production rates. In this investigation, an invariant-based transversely isotropic elasto-plastic model for finite strain applications and its corresponding numerical treatment are presented. The current model is based on the multiplicative decomposition of the deformation gradient. The main characteristic of the formulation is the mathematical realization of the incompressibility assumption with regard to the plastic behaviour in anisotropic finite strain setting. The proposed model is complying with thermodynamic restrictions and allows robust reliable numerical simulations. The accuracy of the model is verified by comparison against experimental data, showing a very satisfactory level of agreement.

Surface-based and solid shell formulations of the 7-parameter shell model for layered CFRP and functionally graded power-based composite structures

ABSTRACT In this study, we present the extension of the so-called 7-parameter shell formulation to layered CFRP and functionally graded power-based composite structures using two different parametrizations: (i) the three-dimensional shell formulation, and (ii) the solid shell approach. Both numerical strategies incorporate the use of the Enhanced Assumed Strain (EAS) and the Assumed Natural Strain (ANS) methods to alleviate locking pathologies and are implemented into the FE code ABAQUS. The applicability of the current developments is demonstrated by means of several benchmark examples, whose results are compared with reference solutions using shell elements of ABAQUS, exhibiting an excellent level of accuracy

Recent advancements on the phase field approach to brittle fracture for heterogeneous materials and structures

Recent advancements on the variational approach to fracture for the prediction of complex crack patterns in heterogeneous materials and composite structures is herein proposed, as a result of the frontier research activities undertaken in the FP7 ERC Starting Grant project CA2PVM which focuses on the development of computational methods for the durability and the reliability assessment of photovoltaic laminates. From the methodological viewpoint, the phase field approach to describe the propagation of brittle fracture in the bulk has been coupled for the very first time with the cohesive zone model to depict interface crack growth events, for 2D isotropic and anisotropic constitutive laws, and also for 3D finite elasticity. After a summary of the key aspects underlying the theoretical formulation and the finite element implementation using a monolithic fully implicit solution scheme, an overview of the main technological applications involving layered shells, interface mechanical problems and polycrystalline materials is provided. The examples are selected to show the capability of the proposed approach to investigate complex phenomena such as crack deflection vs. crack penetration at an interface, intergranular vs. transgranular crack growth in polycrystals, and interlayer vs. translayer failure in laminates.

Damage simulations in composite structures in the presence of stress gradients

Different strategies for modeling damage in composite structures involving stress gradients, typically used in the aeronautical industry, are presented in this chapter. Stress gradients are in most cases associated with changes in the geometry, which in turn frequently appear to be associated with the bonding of subcomponents in the whole structure. These joints have the presence of interlaminar stresses in common, which, in many cases, are at the root of the failure of the composite structures. Interlaminar failure is considered through damage based on interface element formulations, using (1) standard cohesive zone models and (2) an enhanced linear elastic brittle interface model. Two different typologies of composite stiffened panels used for aeronautical applications are studied: (1) a series of runout specimens subjected to uniaxial tensile loading and (2) a multi-stringer panel under uniaxial compressive loading. Both panel types are analyzed up to the collapsing point. With reference to the first panel typology, the analysis is focused on evaluating the structural response in terms of damage tolerance for different runout concepts. The second type of panel is loaded onto the postbuckling region, undergoing significant structural instabilities prior to failure. Two methodologies based on a global/local approach for predicting interlaminar failure events are considered. Computational damage predictions are compared with experimental data, showing the applicability for complex structures of the analysis tools presented.