PSI - Issue 33

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I.J. Sánchez-Arce et al. / Procedia Structural Integrity 33 (2021) 149–158 Sánchez-Arce et al. / Structural Integrity Procedia 00 (2019) 000–000

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Figure 5. Normal stress along the horizontal dimension,  xx . Comparison between NNRPIM solution and ABAQUS solution. Stress distributions in the plate: a) normal stresses in the horizontal direction,  xx ; b) normal stress in the vertical direction,  yy . Stresses in Pa.

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Figure 6. Shear stress (  xy ) comparison between solutions: a) NNRPIM solution, b) ABAQUS solution.

Although relatively simple, the proposed example allowed to validate the methodology and the correctness of the formulations; therefore, it can be used in analyses implying meshless methods and hyper-elastic materials. Moreover, the methodology and the scripts are written to consider multi-material domains, which is the next stage of this work. 6. Conclusions Although some ductile adhesives have a hyper-elastic behaviour, it is scarcely studied in the literature. In addition, applications of meshless methods to such extend is also limited. This work aimed to develop a methodology and to implement some of the available hyper-elastic models into the NNRPIM meshless method. Despite using a small strain approach, the solution based using the NNRPIM is close to that obtained using commercial software; it also agrees with the reported solutions in the literature. The implementation of the Ogden hyper-elastic model allows considering three different hyper-elastic models Ogden, Mooney-Rivlin, and Neo-Hookean, by means of choosing the parameters  i ,  i , and N ; consequently, extending the capabilities of this meshless implementation. The closeness between the solutions obtained with this