Continuum damage mechanics applied to numerical analysis of ship collisions

Over the last 20 years, the study of accidents involving ship collisions and strandings has led to the development of different methodologies, and to simulate numerically the material's ductile fracture, several failure criteria have been applied. Most of the failure criteria used in these problems are based on a critical value of the equivalent plastic strain, where it is admitted that fracture initiates when this value is reached. In the literature, there is still a great diversification of failure criteria alternatives, but the idea of considering the accumulated damage in the material has been more and more gaining ground. With this perspective, this article considers a new approach for the application of numerical analysis to ship collision and stranding, based on the Continuum Damage Mechanics (CDM), where new internal variables are inserted in the material constitutive equations, related to the damage produced by the stress field. The objective of the present paper is to propose and assess a modification in Lemaitre's damage model, which is the substitution of the constant denominator of damage by a function, called Model with Denominator of Damage Function (MDDF), for the prediction of the location and time instant of the material fracture initiation. This paper also describes the implementation of the proposed model, using the UMATs subroutines integrated to the LS-DYNA program. To validate the proposed fracture criterion, comparisons are conducted with the experimental results, present in the literature, of two stiffened panels subject to indentation, and also with the Rice-Tracey-Cockroft-Latham (RTCL) and Bressan-Williams-Hill (BWH) criteria applied to these panels. In such comparisons, the results in terms of the fracture location and the force versus displacement curve are excellent. Finally, a methodology is developed to simulate ship collisions using the proposed model as material failure criterion. The methodology is applied to a case study of a ship collision scenario and compared to RTCL and BWH failure criteria, resulting in a larger collision internal energy.