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In this paper, an unconditionally stable algorithm for the numerical integration and finite-element implementation of a class of pressure dependent plasticity models with nonlinear isotropic and kinematic hardening is presented. Existing algorithms are improved in the sense that the number of equations to be solved iteratively is significantly reduced. This is achieved by exploitation of the structure of Armstrong-Frederik-type kinematic hardening laws. The consistent material tangent is derived analytically and compared to the numerically computed tangent in order to validate the implementation. The performance of the new algorithm is compared to an existing one that does not consider the possibility of reducing the number of unknowns to be iterated. The algorithm is used to implement a time and temperature dependent cast iron plasticity model, which is based on the pressure dependent Gurson model, in the finite-element program ABAQUS. The implementation is applied to compute stresses and strains in a large-scale finite-element model of a three cylinder engine block. This computation proofs the applicability of the algorithm in industrial practice that is of interest in applied sciences.
Der vorliegende Beitrag beschreibt erste Untersuchungsergebnisse an Wellenabsätzen mit im Kerbgrund überlagerter Schrägbohrung, mit Hilfe der Finite-Elemente-Methode (FEM). Als Beispiel hierfür können Walzen mit Heizkanälen in Walzwerken, Turbinen- und Kurbelwellen genannt werden. Es ist nicht bekannt, welche Spannungserhöhung die Schrägbohrung im Wellenabsatz hervorruft. In den Normen oder Richtlinien sind keine Angaben über Formzahlen für diese Kerbkombination vorhanden. Deshalb werden die Formzahlen für unterschiedliche schräggebohrte Wellenabsätze je Belastungsart ermittelt, ausgewertet und entsprechende Formzahldiagramme und Gestaltungshinweise angegeben.
In this paper, the correlation of the cyclic J-integral, ΔJ, and the cyclic crack-tip opening displacement, ΔCTOD, is studied in the presence of crack closure to assess the question if ΔJ describes the crack-tip opening displacement in this case. To this end, a method is developed to evaluate ΔJ numerically within finite-element calculations. The method is validated for an elastic–plastic material that exhibits Masing behavior. Different strain ranges and strain ratios are considered under fully plastic cyclic conditions including crack closure. It is shown that the cyclic J-integral is the parameter to determine the cyclic crack-tip opening displacement even in cases where crack closure is present.
The aim of this study was to develop a biomechanically validated finite element model to predict the biomechanical behaviour of the human lumbar spine in compression.
For validation of the finite element model, an in vitro study was performed: Twelve human lumbar cadaveric spinal segments (six segments L2/3 and six segments L4/5) were loaded in axial compression using 600 N in the intact state and following surgical treatment using two different internal stabilisation devices. Range of motion was measured and used to calculate stiffness.
A finite element model of a human spinal segment L3/4 was loaded with the same force in intact and surgically altered state, corresponding to the situation of biomechanical in vitro study.
The results of the cadaver biomechanical and finite element analysis were compared. As they were close together, the finite element model was used to predict: (1) load-sharing within human lumbar spine in compression, (2) load-sharing within osteoporotic human lumbar spine in compression and (3) the stabilising potential of the different spinal implants with respect to bone mineral density.
A finite element model as described here may be used to predict the biomechanical behaviour of the spine. Moreover, the influence of different spinal stabilisation systems may be predicted.