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math.NA2026
Automatic differentiation in finite element stress updating
Mao Ouyang, Alexandros Petalas, William M. Coombs +1
Computational solid mechanics relies on the discretisation of differential equations, requiring numerical differentiation and integration, often via quadrature. Recently, automatic…
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…