Cohesive Model for the Simulation of Crack Initiation and Propagation in Mixed-Mode I/II in Composite Materials
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Cohesive Model for the Simulation of Crack Initiation and Propagation in Mixed-Mode I/II in Composite Materials Antonio Pantano 1 Received: 16 February 2019 / Accepted: 31 May 2019/ # Springer Nature B.V. 2019
Abstract A cohesive element able to connect and simulate crack growth between independently modeled finite element subdomains with non-matching meshes is proposed and validated. The approach is based on penalty constraints and has several advantages over conventional FE techniques in disconnecting two regions of a model during crack growth. The most important is the ability to release portion of the interface that are smaller than the local finite element length. Thus, the growth of delamination is not limited to advancing by releasing nodes of the FE model, which is a limitation common to the methods found in the literature. Furthermore, it is possible to vary the penalty parameter within the cohesive element, allowing to apply the damage model to a chosen fraction of the interface between the two meshes. A novel approach for modeling the crack growth in mixed mode I + II conditions has been developed. This formulation leads to a very efficient computational approach that is completely compatible with existing commercial software. In order to investigate the accuracy and to validate the proposed methodology, the growth of the delamination is simulated for the DCB, ENF and MMB tests and the results are compared with the experimental data. Keywords Finite element . Cohesive element . Penalty method . Composite materials . Delamination . Mixed-mode propagation
1 Introduction Unmatched interface problems are increasingly common because it is difficult to satisfy the connectivity of elements for complex domains and the transition between coarse and fine meshes often results in distorted elements that reduce the accuracy of the solution in transition regions. For example, there is a growing need to perform combined analyzes of complex
* Antonio Pantano [email protected]
1
Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy
Applied Composite Materials
structures, as an airplane or a ship, using sub-structural numerical models created independently by teams of engineers using different software and collaborating remotely. Frequently the meshes of these numerical models are incompatible at the interfaces, therefore all the substructural models must be joined to build the entire structure. Even within the same team, discretizing problems in regions, dividing them into sub-structural models, and then using a coupling technique to connect their mismatched interfaces, can be a winning strategy. Many different methodologies have proposed for non-matched interface problems [1–8]. Most of them use Lagrange multipliers with a negative result that the resulting system of equations is not definite positive. A possible fix is to enforce the interface constraints via a penalty method, the following advantages are obtained: a formulation that can be easily implem
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