Elasto-Plastic Analysis of Thick/Thin Shells with Damage due to Microvoids

The problem of damage mechanics in thick/thin shells and plates in Solid Mechanics has been a very complex problem due to the various boundary conditions.  Voyiadjis and his group addressed the non-linear finite element analysis for the elasto-plastic behavior of thick/thin shells and plates with large rotations and damage effects. The refined shell theory given by Voyiadjis and his group provides a set of shell constitutive equations. Numerical implementation of the shell theory leading to the development of the C0 quadrilateral shell element is used as an effective tool for a linear elastic analysis of shells. The large rotation elasto-plastic model for shells presented is enhanced to account for the damage effects due to microvoids, formulated within the framework of a micromechanical damage model. The evolution equation of the scalar porosity parameter is used to describe the most relevant damage effects for isotropic plates and shells, i.e. the growth of voids as a function of the plastic flow. The contributions in this area include:

  • the damage modeled through the evolution of porosity is incorporated directly into the yield function, giving a generalized and convenient loading surface expressed in terms of stress resultants and stress couples,
  • a plastic node method is used to derive the large rotation, elasto-plastic-damage tangent stiffness matrix,
  • some of the important features of this work are that the elastic stiffness matrix is derived explicitly, with all the integrals calculated analytically,
  • in addition, a non-layered model is adopted in which integration through the thickness is not necessary, consequently, the elasto-plastic-damage stiffness matrix is also given explicitly and numerical integration is not performed,
  • the model is consistent mathematically, accurate for a variety of applications, and very inexpensive from the point of view of computer power and time,
  • a simple and efficient method of finite element analysis of shear flexible composite laminates is also obtained, where the effect of transverse shear deformation is especially important in the consideration of delamination of composite plates and shells,
  • accurate distribution of transverse shear stresses across the thickness of the laminate is given special attention, and the formulation is a generalization of the effective section method, commonly applied in composite beams.

A book is published in this area at the special invitation of a publishing company:

Voyiadjis, G. Z., and Woelke, P., Elasto-Plastic and Damage Analysis of Plates and Shells, 200 p., Springer-Verlag GmbH & Co.KG, Heidelberg, 201 p., Springer-Verlag GmbH & Co.KG, ISBN-10: 354079350X, 2008.