| The primary objective of this study is the simulation of transient manufacturing processes in thermo-plasticity and poro-plasticity. The processes are characterized by inherently non-linear material behavior, possibly finite deformations (usually so in metal forming applications), non-linear interfaces and frictional effects at the interfaces. These complexities demand significant sophistication from the numerical techniques.; Relevant constitutive models, which adequately represent the material non-linearity are implemented as part of this research. An updated Lagrangian finite deformation algorithm is extended for use in three dimensional situations, in conjunction with the transient thermo-plastic and poro-plastic algorithms. Non-linear interfaces formed a significant part of this investigation, and are dealt with in great depth. The contact problem is implemented in a sub-structured form, using the Lagrange Multiplier technique of classical optimization theory. The frictional contact problem is also considered, and is approximately symmetricized for use in conjunction with the transient algorithms. The contact interfaces are extended to permit finite relative movements at the interfaces, while imposing virtually no restrictions on the mesh layout in those regions. Sophisticated contact searching schemes are implemented to provide constant updating of the master-slave pairing so that the interface detection is automatic, through the course of the analysis. The temperature constraints are implemented with care, so as to not violate the Babuska-Brezzi conditions for a mixed finite element form.; A general purpose assembly scheme is devised to permit the implementation of very general interface types. The Lagrange Multiplier technique is central to the assembly process, and it enforces the constraints exactly, at the cost of introducing additional equations into the system. The substructured finite element implementation permits reuse of previous decomposed matrices for linear regions in the problem, and causes the contact iterations to be performed only over the defined interface equations, instead of the entire set of equations.; Several examples are solved using the developed finite element tools, which demonstrate the accuracy and versatility of the implementation. Important manufacturing processes in poro-plasticity and thermo-plasticity are studied using the sub-structured implementation. |
