A stabilized mixed finite element formulation for finite strain deformation

When improving the current state of technology in the finite element method, element formulation is a very important area of investigation. The objective of this dissertation is to develop a robust low-order tetrahedral element that is capable of meshing complicated geometries which cannot be meshed with standard brick elements. This element will be applicable to a large class of nonlinear materials that include nearly incompressible and incompressible materials and capable of analyzing small and large deformation as well as large rotations. Development of such an element will particularly benefit large strain metal-forming applications.; Linear tetrahedral elements are very practical for several reasons including their simplicity and efficiency. Despite their advantages, these elements have known shortcomings in their performance when applied to incompressible or nearly incompressible materials because of their tendency to lock. To overcome this problem a stabilized mixed formulation is proposed for tetrahedral elements that can be utilized in solid mechanics and large deformation problems.; An enhanced strain derived from a bubble function is added to the element to provide the necessary stabilization. The uniqueness of the proposed formulation lies within the fact that it does not require any geometric or material dependent parameters and no specific material model so that the formulation is completely general.; The element was implemented through a user-programmable element into the commercial finite element software, ANSYS. Using the ANSYS platform, the performance of the element was evaluated by different numerical investigations encompassing both small and large deformation, linear and nonlinear materials as well as near and fully incompressible conditions.; The element formulation was tested with several standard metal forming problems such as metal extrusion and punch forging that are known to experience difficulties during large deformations. The results were compared with analytical results or other available finite element results in the literature.; Finally, conclusions are drawn and possible future investigations are discussed such as the application of the new element in 3D rezoning, dynamic problems and anisotropic materials.