Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis

A numerical implementation of the eXtended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms have been implemented, within an Oriented Object framework in C++, in the home made explicit FEM code. The new module, called DynaCrack, included in the dynamic FEM code DynELA, evaluates the crack geometry, the propagation of the crack and allow the post-processing of the numerical results. The module solves the system of discrete equations using an explicit integration scheme. Some numerical examples illustrating the main features and the computational efficiency of the DynaCrack module for dynamic crack propagation are presented in the last section of the paper

A comparison between some fracture modelling approaches in 2D LEFM using finite elements

[EN] The finite element method has been widely used to solve different problems in the field of fracture mechanics. In the last two decades, new methods have been developed to improve the accuracy of the solution in 2D linear elastic fracture mechanics problems, such as the extended finite element method (XFEM) or the phantom node method (PNM). The goal of this work is to quantify the differences between some numerical approaches: standard finite element method (FEM), mechanical property degradation, interelemental crack method with multi-point constraints, XFEM and PNM. We explain the different techniques analysed together with their advantages and disadvantages. We compare these numerical techniques to model fracture using problems of reference with known solutions, evaluating their behaviour in terms of convergence with respect to the element size and accuracy of the stress intensity factor (SIF), stresses ahead the crack tip and crack propagation prediction. Some of the new techniques have shown a better accuracy in SIF calculation or stress fields ahead the crack tip and other lead to high errors in local results estimations. However, all methods reviewed here can predict crack propagation for the problems of reference of this work, showing good accuracy in crack orientation prediction.The authors gratefully acknowledge the funding support received from the Spanish Ministerio de Ciencia, Innovacion y Universidades and the FEDER operation program in the framework of the projects DPI2017-89197-C2-1-R and DPI2017-89197-C2-2-R and the FPI subprograms BES-2014-068473 and BES-2015-072070. The financial support of the Generalitat Valenciana through the Programme PROMETEO 2016/007 is also acknowledged.Marco, M.; Infante-García, D.; Belda, R.; Giner Maravilla, E. (2020). A comparison between some fracture modelling approaches in 2D LEFM using finite elements. 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An adaptive shell element for explicit dynamic analysis of failure in laminated composites Part 2: Progressive failure and model validation

To enable modelling of the progressive failure of large, laminated composite components under crash or impact loading, it is key to have a numerical methodology that is both efficient and numerically robust. A potential way is to adopt an adaptive method where the structure is initially represented by an equivalent single-layer shell model, which during the analysis is adaptively transformed to a high-resolution layer-wise model in areas where higher accuracy is required. Such a method was recently developed and implemented in the commercial finite element solver LS-DYNA, aiming at explicit crash analysis (Fr\ue4mby, Fagerstr\uf6m and Karlsson: An adaptive shell element for explicit dynamic analysis of failure in laminated composites - Part 1: Adaptive kinematics and numerical implementation, 2020). In the current work, the method is extended to the case of interacting inter- and intralaminar damage evolution. As a key part, we demonstrate the importance of properly regularising the intralaminar failure described by a smeared-crack model, and show that neglecting to account for the crack-versus-mesh orientation may lead to significant errors in the predicted energy dissipation. We also validate the adaptive approach against a four-point beam bending test with matrix-induced delamination growth, and simultaneously show the capability of the proposed method to – at lower computational expense – replicate the results from a refined, non-adaptive model

An extended finite element model for modelling localised fracture of reinforced concrete beams in fire

Open Access funded by Engineering and Physical Sciences Research Council under a Creative Commons license.A robust finite element procedure for modelling the localised fracture of reinforced concrete beams at elevated temperatures is developed. In this model a reinforced concrete beam is represented as an assembly of 4-node quadrilateral plain concrete, 3-node main reinforcing steel bar, and 2-node bond-link elements. The concrete element is subdivided into layers for considering the temperature distribution over the cross-section of a beam. An extended finite element method (XFEM) has been incorporated into the concrete elements in order to capture the localised cracks within the concrete. The model has been validated against previous fire test results on the concrete beams.The Engineering and Physical Sciences Research Council of Great Britain under Grant No. EP/I031553/1

Macro- and micro-modeling of crack propagation in encapsulation-based self-healing materials : application of XFEM and cohesive surface techniques

Encapsulation-based materials are produced introducing some small healing fluid-filled capsules in a matrix. These materials can self-heal when internal cracks intercept and break the capsules. If the healing agent is released, the crack can be sealed. However, this is not always the case. These capsules need to be designed with the adequate shape and material to be properly broken. This paper presents two application models based on the combination of eXtended Finite Element Method (XFEM) elements and Cohesive Surfaces technique (CS) to predict crack propagation. Two types of encapsulated systems are considered: a concrete beam in a three-point bending test, and a micro-scale model of a representative volume element of a polymer subjected to a uniaxial tensile test. Despite both systems rely on different capsule shapes and different constituent materials, the models predict a similar non-linear response of the overall material strength governed by the coupled effect of the interface strength and the capsule radii-to-thickness ratio. Furthermore, even if an inadequate material and geometry combination is used, it is found that the mere presence of capsules might achieve, under certain conditions, an interesting overall reinforcement effect. This effect is discussed in terms of clustering and volume fraction of capsules