Details

Autor(en) / Beteiligte

• Coombs, William M.
• Augarde, Charles E.
• Brennan, Andrew J.
• Brown, Michael J.
• Charlton, Tim J.
• Knappett, Jonathan A.
• Ghaffari Motlagh, Yousef
• Wang, Lei

Titel

On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity

Ist Teil von

• Computer methods in applied mechanics and engineering, 2020-01, Vol.358, p.112622, Article 112622

Ort / Verlag

Amsterdam: Elsevier B.V

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms of formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being defined on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satisfies equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specific focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, different domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation fields. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former. •New Lagrangian mechanics formulation focused on the material point method.•Equilibrium satisfied on the undeformed mesh at the start of the load step.•New formulation applicable to all existing implicit and explicit material point methods.•Deficiencies in domain updating methods highlighted and new procedure provided.