MES is capable of three analysis formulations:
- Linear or Material Nonlinear Only Analysis: Element displacements are assumed to be negligibly small and the strains are infinitesimal. For a linear analysis, the material is isotropic or orthotropic linear elastic. For a material nonlinear only analysis, the material stress-strain description is nonlinear.
- Total Lagrangian Formulation: This formulation is effective for elastic-plastic analysis involving large displacement, large rotation, or small strain. For more information on Total Lagrangian formulation, refer to Finite Element Procedures in Engineering Analysis (Bathe) or NAFEMS Introduction to Nonlinear Finite Element Analysis (Hinton)
- Updated Lagrangian Formulation: This formulation is effective for elastic-plastic analysis involving large displacement, large rotation, or small and large strain. For more information on updated Lagrangian formulation, refer to Finite Element Procedures in Engineering Analysis (Bathe) or NAFEMS Introduction to Nonlinear Finite Element Analysis (Hinton).
Linear analysis does not allow for any nonlinearities, while the materially nonlinear only analysis includes material nonlinearities, but no geometric nonlinearities. The total Lagrangian and updated Lagrangian formulations can include all nonlinearities, and the formulation you should use depends essentially on the material model you used.
Total versus Updated Lagrangian
- Both types support large displacements, rotations and strains.
- Total Lagrangian is formulated in terms of 2nd Piola-Kirchhoff stresses and Green-Lagrangian strains.
- Updated Lagrangian is formulated in terms of Cauchy stresses and Almansi strains.
- Total Lagrangian is most effective for large displacement, large rotation but small-strain analysis.
- If geometric stiffness changes are expected, then you should select the Updated Lagrangian method. The Updated Lagrangian method is more effective in large strain analysis.