Simulating submarine landslides combining the material point method with a spatially adaptive scheme to improve numerical accuracy

Resumo

Particles, in the material point method (MPM), are the representation of the material domain, which
moves through a background mesh. As deformation occurs, particles positions are updated accordingly and may
generate regions with suboptimal particle density. In cases with excessive tractions, increased deformations can
make distance between particles to be greater than the background mesh element size, causing fractures to occur in

materials where no fracture law was applied. Moreover, this numerical fracture undermines computational accu-
racy and stability of the simulations. Therefore, a spatially adaptive method is a suitable alternative to prevent the

formation of numerical fractures in problems with large deformations. Furthermore, spatial adaptivity, a technique
that tunes the spatial discretization of the problem dynamically, has already been used to simulate engineering
problems with large deformations and complex soil-structure interactions. However, such simulations are unstable
depending on the material constitutive model and the computational cost is quite expensive. This study proposes
a spatially adaptive algorithm based on the accumulated deformation of each particle. The algorithm divides each
particle into four new ones that inherit the quantities of interest from old particles, maintaining the continuity of
state variables. The algorithm showed to be efficient in problems with analytical solutions, such as the vibration
of an elastic bar. In addition, as submarine landslides involve large deformations, numerical fractures are bound to
happen and often imposes constraints to the scale of the mesh discretization. In this regard, our algorithm handled,

successfully, submarine landslides simulations, introducing new particles to regions that presented a poor distribu-
tion of particles during the sliding process, enhancing the visual aspect and allowing a correct computation of state

variables. Lastly, the spatial adaptivity scheme was coupled into the software E-Sub, a numerical analysis software
developed by the Laboratory of Scientific Computing and Visualization (LCCV).