A component-free Lagrangian finite element formulation for large strain elastodynamics

Abstract Standard finite element formulation and implementation in solid dynamics at large strains usually relies upon indicial-tensor Voigt notation to factorized the weighting functions take advantage of symmetric structure algebraic objects involved. In present work, a novel component-free approach, where no reference basis, axes or components is made, implied required, adopted for formulation. Under this factorisation function also increment displacement field, can be performed by means operations avoiding both use any index subsequent reorganisation matrix form. This new approach leads straightforward only vectors second order tensors $${\mathbb {R}}^3$$ R 3 are required. The proposed as accurate standard based method however more efficient, concise, transparent easy implement.