The energy variational formulation of finite strain problems is an effective way to derive the incremental equilibrium equations of motion of elastic and hypoelastic structures. It provides important insights in large deformation analysis and structural stability. The variational approach is used to identify work-conjugate pairs of incremental finite strain tensor and objective stress rate tensor which are related by incremental elastic moduli. A unique stress dependent transformation relates the moduli for one work-conjugate pair with the corresponding moduli for another work-conjugate pair. The commercial softwares such as ABAQUS, ANSYS, LS-DYNA use the Jaumann rate of Cauchy stress(JC) and the Hencky (logarithmic) strain measure (H) while the softwares OOFEM and ATENA use the Truesdell rate (T) with Green Lagrangian Strain measure (GL), which give different force and displacement responses.
The first part of this dissertation implements a stress dependent transformation of incremental elastic moduli to show the work conjugate equivalence of these two groups of software. The second part of dissertation presents numerical demonstrations showing that the FEM codes using the JC stress rate can give solutions with large errors, caused by the fact that the JC rate is not conjugate to any finite strain tensor except if the material is incompressible. A simple correction to the incremental stiffness tensor is used in the user's material subroutine to restore work-conjugacy. Examples of indentation of a naval-type sandwich plate with a polymeric foam core, in which the error can reach 28.8% in the load and 15.3% in the work of load, is demonstrated.
For stability problems, accurate calculation of the second-order work terms is necessary. In the case of structures such as sandwich panels or highly orthotropic columns, which are very stiff in the longitudinal loading direction and soft in the transverse direction, the assumption of constant values of the elastic moduli corresponding to the work conjugate pair of T & GL can match the experimental results and also agrees with the energy variational analysis. This result is used in the third part of the dissertation to develop analytical and numerical solutions for global buckling analysis of sandwich panels to be employed in prospective naval ship hulls. An analysis treating as constant the elastic moduli corresponding to the Jaumann rate of Kirchhoff stress and the Hencky strain measure is shown to result in a 40% over-estimation of the critical buckling loads, in comparison to treating as constant the elastic moduli for the correct work-cojugate pair, which is T & GL.
Another aspect of failure of materials with damage is the size effect in prestressed beams. The energy release caused by propagation of shear bands in axial compression fracture has been shown to lead to size-dependence of the nominal strength of concrete columns. This motivates the question of size dependence of nominal strength in flexural compression failure of prestressed concrete beams. Numerical simulations conducted in the final part of the dissertation reveals that the size effect on compressive strength in the investigated size range exists, but is only mild . This size effect is linked to an increase of the descending slope of post-peak response of concrete in compression.
|Advisor:||Bazant, Zdenek Pavel|
|Commitee:||Cusatis, Gianluca, Huang, Yonggang, Rudnicki, John W., Vorel, Jan|
|Department:||Civil and Environmental Engineering|
|School Location:||United States -- Illinois|
|Source:||DAI-B 74/05(E), Dissertation Abstracts International|
|Subjects:||Engineering, Mechanical engineering|
|Keywords:||Compression damage, Compression softening, Finite strain, Incremental analysis, Objective stress rate, Orthotropic, Sandwich skin-foam composites, Structural stability, Work conjugacy|
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