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math.NA2026

An implicit octree-based adaptive Material Point Method

Robert E. Bird, William M. Coombs, Charles E. Augarde +2

The Material Point Method provides an effective approach for modelling the large deformations that often arise from contact interactions between rigid structures and surrounding co…

math.NA2026

Caveats on formulating finite elasto-plasticity in curvilinear coordinates

Giuliano Pretti, Robert E. Bird, William M. Coombs +1

Tensor analysis provides a frame-invariant foundation for continuum mechanics, yet numerical implementations rely on matrix representations expressed in user-selected bases. When t…

math.NA2025

Three-dimensional modelling of drag anchor penetration using the material point method

Robert E. Bird, William M. Coombs, Michael J. Brown +6

Drag embedment anchors are a key threat to buried subsea linear infrastructure, such as power/data cables and pipelines. For cables, selecting a burial depth is a compromise betwee…

math.NA2024

A dynamic implicit 3D material point-to-rigid body contact approach for large deformation analysis

Robert E. Bird, Giuliano Pretti, William M. Coombs +6

Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechan…

math.NA2024

A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation

Giuliano Pretti, Robert E. Bird, Nathan D. Gavin +2

The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formul…