A three-dimensional transient explicit finite-element method is applied to simulate the coupled and highly-nonlinear thermo-mechanical phenomena that occur during steel solidification in continuous casting of thin slabs in a funnel mold. Variable mass scaling is used to efficiently model the phenomena in their natural time scale using a Lagrangian formulation. The model features an efficient and robust local-global viscoplastic integration scheme to solve the elasticviscoplastic constitutive equations of solidifying steel [1], using a VUMAT subroutine in ABAQUS/Explicit [2], which varies greatly with temperature, strain rate, steel phase, and composition. The model is applied to simulate temperature and stress development in typical repeating segment of the solidifying shell in a continuous casting funnel mold using realistic temperature-dependent properties and including the effects of ferrostatic pressure, narrow face taper, and mechanical contact, and thermal-mechanical coupling through the size of the interfacial gap. Explicit temperature and stress results as well as computational efficiency are compared with the results of an implicit formulation. The explicit formulation shows significant advantages for these large contact-solidification problems on parallel computers.

Direct methods for solving sparse systems of linear equations have a high asymptotic computational and memory requirements relative to iterative methods. However, systems arising in some applications, such as structural analysis, can often be too ill-conditioned for iterative solvers to be effective. We cite real applications where this is indeed the case, and using matrices extracted from these applications to conduct experiments on three different massively parallel architectures, show that a well designed sparse factorization algorithm can attain very high levels of performance and scalability. We present strong scalability results for test data from real applications on up to 8,192 cores, along with both analytical and experimental weak scalability results for a model problem on up to 16,384 cores---an unprecedented number for sparse factorization. For the model problem, we also compare experimental results with multiple analytical scaling metrics and distinguish between some commonly used weak scaling methods.

Computational models of the mold and steel shell have been developed to investigate mold taper, gap formation, crack formation, and the effects of mold distortion and oscillation during beam blank casting. The models have been validated with plant measurements.

The explicit finite element method is applied in this work to simulate the coupled and highly non‐linear thermo‐mechanical phenomena that occur during steel solidification in continuous casting processes. Variable mass scaling is used to efficiently model these processes in their natural time scale using a Lagrangian formulation. An efficient and robust local–global viscoplastic integration scheme (Int. J. Numer. Meth. Engng 2006; 66:1955–1989) to solve the highly temperature‐ and rate‐dependent elastic–viscoplastic constitutive equations of solidifying steel has been implemented into the commercial software ABAQUS/Explicit (ABAQUS User Manuals v6.7. Simulia Inc., 2007) using a VUMAT subroutine. The model is first verified with a known semi‐analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145–154). It is then applied to simulate temperature and stress development in solidifying shell sections in continuous casting molds using realistic temperature‐dependent properties and including the effects of ferrostatic pressure, narrow face taper, and mechanical contact. Example simulations include a fully coupled thermo‐mechanical analysis of a billet‐casting and thin‐slab casting in a funnel mold. Explicit temperature and stress results are compared with the results of an implicit formulation and computing times are benchmarked for different problem sizes and different numbers of processor cores. The explicit formulation exhibits significant advantages for this class of contact‐solidification problems, especially with large domains on the latest parallel computing platforms. Copyright © 2008 John Wiley & Sons, Ltd.

Coupled thermo-mechanical models based on highly nonlinear elastic visco-plastic constitutive laws are applied to simulate simultaneous development of temperature and stress that occurs during steel solidification in continuous casting processes. The efficient and robust local visco-plastic integration scheme [Koric 2006] is implemented into both implicit and explicit FE commercial software ABAQUS/Standard and ABAQUS/Explicit via user defined subroutines VUMAT and UMAT. The models are first verified with a semi-analytical solution [Weiner 1963], and later they are applied to simulate 2D and 3D transverse sections of a thin slab caster under realistic operating conditions as they move down the mold. The execution times of the implicit and explicit parallel solvers performing some of these highly computationally demanding analyses are benchmarked on the latest high performance computing platforms. INTRODUCTION: Continuous casting is the process by which over 90% of steel is produced today. The harsh environment and extreme temperatures make experimenting and taking measurements difficult, and so many numerical models have been developed over the years, mostly using implicit finite element methods. The few seconds the steel spends in the mold are often the most critical, given the large number of possible defects related to initial solidification. The quality of continuously cast products is constantly improving, but there is still a significant amount of modeling work needed to minimize the amount of defects and to maximize the productivity. Numerical modeling of the thermo-mechanical behavior of the shell presents a large number of computational difficulties, such as the integration of the highly nonlinear visco-plastic constitutive laws, treatment of liquid/mushy zone, treatment of latent heat, accounting for the temperature dependence of material properties, contact between the solidified shell and mold surfaces, and coupling between the heat transfer and stress analysis. A new approach is proposed here to link a cost-effective explicit time integration solution method on the global level with an efficient and robust implicit integration scheme to integrate the highly-nonlinear viscoplastic equations at the local level. The explicit and traditionally-favored implicit FE numerical methods for solidification problems are compared and the advantages that the explicit FE formulation exhibits for this class of difficult, coupled contact problems are demonstrated. PROCEDURES, RESULTS AND DISCUSSION: Inertial effects are negligible in solidification problems, so using the static mechanical equilibrium as the governing Plasticity ’09 Conference, St. Thomas, Jan. 3-8, 2009.

A computational thermo-mechanical model has been developed to simulate the continuous casting of shaped sections, such as used for thin steel slabs. A general form of the transient heat equation including latent-heat from phase transformations such as solidification and other temperature-dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo-elastic-viscoplastic contitutive equations using a two-level method. The procedure has been implemented into Abaqus, (Abaqus Inc., 2005) using a user-defined subroutine (UMAT) to integrate the constitutive equations at the local level (Koric, 2006). The model is validated both with a semi-analytical solution from Weiner and Boley (Weiner, 1963) as well as with an in-house finite element code CON2D (Li, 2004, Zhu, 1993) specialized in thermo-mechanical modeling of continuous casting. The model is applied to simulate a 3D segment of the solidifying steel shell as it moves down through a thin slab caster with a funnel mold, known for its complex geometry, using realistic operating conditions and temperature-dependant properties. It has provided valuable new insights into the complex dynamic 3D mechanical state of stress experienced by the solidifying shell due to the funnel geometry.

A new, computationally efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent‐heat from phase transformations such as solidification and other temperature‐dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo‐elastic‐viscoplastic constitutive equations using a two‐level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton–Raphson (NR) iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full NR iteration. The procedure has been implemented into the commercial package Abaqus (Abaqus Standard Users Manuals, v6.4, Abaqus Inc., 2004) using a user‐defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. The model is validated both with a semi‐analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145–154) as well as with an in‐house finite element code CON2D (Metal. Mater. Trans. B 2004; 35B(6):1151–1172; Continuous Casting Consortium Website. http://ccc.me.uiuc.edu [30 October 2005]; Ph.D. Thesis, University of Illinois, 1993; Proceedings of the 76th Steelmaking Conference, ISS, vol. 76, 1993) specialized in thermo‐mechanical modelling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature‐dependent properties. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared. Copyright © 2006 John Wiley & Sons, Ltd.

A new, computationally-efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent-heat from phase transformations such as solidification and other temperature-dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermoelastic-viscoplastic constitutive equations using a two-level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton-Raphson iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full Newton-Raphson iteration. The procedure has been implemented into the commercial package Abaqus [1] using a user-defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared. The model is validated both with a semi-analytical solution from Weiner and Boley [2] as well as with an in-house finite element code CON2D [3,4,7,8] specialized in thermomechanical modeling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell

Analytical and numerical solutions are presented for viscoelastic lifting surfaces with piezoelectric control devices. Computational protocols in terms of spatial finite elements and temporal finite differences are formulated. ANSYS is used for mesh generation and numerical solutions are carried out in ABAQUS. Because of lack of provisions in ABAQUS for displacement dependent forces (lift), additional iterative subroutines were written and incorporated.