Governing Equations and Weak Form
Finite element discretizations for Lagrangian meshes are described. The notes are based on reference 1 and more details can be found on this book. In Lagrangian meshes, the nodes and elements move with the material. Boundaries and interfaces remain coincident with element edges, so that their treatment is simplified. Quadrature points also move with the material, so constitutive equations are always evaluated at the same material points, which is advantageous for history dependent materials. For these reasons, Lagrangian meshes are widely used for solid mechanics.
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