Constitutive Modelling in Thermomechanical Processes, Using The Control Volume Method on Staggered Grid

The objective of this thesis has been to improve and further develop the existing staggered grid control volume formulation of the thermomechanical equations. During the last ten years the method has proven to be efficient and accurate even for calculation on large structures. The application of the method has been focused on high temperature processes such as casting and welding and the interest of using nonlinear constitutive stress-strain relations has grown to extend the applicability of the method. The work of implementing classical plasticity into the control volume formulation has been based on the $J_2$ flow theory describing an isotropic hardening material with a temperature dependent yield stress. This work has successfully been verified by comparing results to analytical solutions. Due to the comprehensive implementation in the staggered grid an alternative constitutive stress-strain relation has been suggested. The intention of this method is to provide fast numerical results with reasonable accuracy in relation to the first order effects of the presented classical plasticity model. Application of the $J_2$ flow theory and the alternative method have shown some agreement in the results and the expected reduction in calculation time is obtained. Further application and verification of the method will be addressed in the future and hopefully the method can be used to give preliminary results for process optimization. It is important to emphasize that the main thrust of the work, however, is constituted by the implementation of the $J_2$ flow theory in the control volume method. To apply the control volume formulation on the process of hardening concrete viscoelastic stress-strain models has been examined in terms of various rheological models. The generalized 3D models are based on two different suggestions in the literature, that is compressible or incompressible behaviour of the viscos response in the dashpot element. Numerical implementation of the models has shown very good agreement with corresponding analytical solutions. The viscoelastic solid mechanical model is used in connection with the thermal model to describe the general process of hardening concrete, i.e release of energy during hardening, creep in early age concrete and maturity dependent material properties. Generally the work presented in this thesis is motivated by the intention of using numerical modelling to analyse the thermal and mechanical conditions in various components and structures. This will hopefully lead to a useful tool during the process optimization phase.