Failure criteria play a vital role in the numerical analysis of reinforced concrete structures. The current failure criteria can be classified into two types, namely the empirical and theoretical failure criteria. Empirical failure criteria normally lack reasonable theoretical backgrounds, while theoretical ones either involve too many parameters or ignore the effects of intermediate principal stress on the concrete strength. Based on the octahedral shear stress model and the concrete tensile strength under the state of triaxial and uniaxial stress, a new failure criterion, that is, the simplified unified strength theory (UST), is developed by simplifiing the five-parameter UST for the analysis of reinforced concrete structures. According to the simplified UST failure criterion, the concrete strength is influenced by the maximum and intermediate principal shear stresses together with the corresponding normal stresses. Moreover, the effect of hydrostatic pressure on the concrete strength is also taken into account. The failure criterion involves three concrete strengths, namely the uniaxial tensile and compressive strengths and the equal biaxial compressive strength. In the numerical analysis, a degenerated shell element with the layered approach is adopted for the simulation of concrete structures. In the layered approach, concrete is divided into several layers over the thickness of the elements and reinforcing steel is smeared into the corresponding number of layers of equivalent thickness. In each concrete layer, three-dimensional stresses are calculated at the integration points. For the material modelling, concrete is treated as isotropic material until cracking occurs. Cracked concrete is treated as an orthotropic material incorporating tension stiffening and the reduction of cracked shear stiffness. Meanwhile, the smeared craclc model is employed. The bending reinforcements and the stirrups are simulated using a trilinear material model. To verify the correctness of the simplified UST failure criterion, comparisons are made with concrete triaxial empirical results as well as with the Kupfer and the Ottosen failure criteria. Finally, the proposed failure criterion is used for the flexural analysis of simply supported reinforced concrete beams. Also conducted are the punching shear analyses of single- and multi-column-slab connections and of half-scale flat plate models. In view of its accuracy and capabilities, the simplified UST failure criterion may be used to analyse beam- and slab-type reinforced concrete structures.

Longitudinal growth of long bone occurs at growth plates by a process called endochondral ossification. Endochondral ossification is affected by both biological and mechanical factors. This thesis focuses on the mechanical modulation of femoral bone growth occurring at the proximal growth plate, using mechanobiological theories reported in the literature. Finite element analysis was used to simulate bone growth. The first study analyzed the effect of subject-specific growth plate geometry over simplified growth plate geometry in numerical prediction of bone growth tendency. Subject-specific femur finite element model was constructed from magnetic resonance images of one able- bodied child. Gait kinematics and kinetics were acquired from motion analysis and analyzed further in musculoskeletal modelling to determine muscle and joint contact forces. These were used to determine loading on the femur in finite element analysis. The growth rate was computed based on a mechanobiological theory proposed by Carter and Wong, and a growth model in the principal stress direction was introduced. Our findings support the use of subject- specific geometry and of the principal stress growth direction in prediction of bone growth. The second study aimed to illustrate how different muscle groups’ activation during gait affects proximal femoral growth tendency in able-bodied children. Subject-specific femur models were used. Gait kinematics and kinetics were acquired for 3 able-bodied children, and muscle and joint contact forces were determined, similar to the first study. The contribution of different muscle groups to hip contact force was also determined. Finite element analysis was performed to compute the specific growth rate and growth direction due to individual muscle groups. The simulated growth model indicated that gait loading tends to reduce neck shaft angle and femoral anteversion during growth. The muscle groups that contributes most and least to growth rate were hip abductors and hip adductors, respectively. All muscle groups’ activation tended to reduce the neck shaft and femoral anteversion angles, except hip extensors and adductors which showed a tendency to increase the femoral anteversion. The third study’s aim was to understand the influence of different physical activities on proximal femoral growth tendency. Hip contact force orientation was varied to represent reported forces from a number of physical activities. The findings of this study showed that all studied physical activities tend to reduce the neck shaft angle and anteversion, which corresponds to the femur’s natural course during normal growth. The aim of the fourth study was to study the hypothesis that loading in the absence of physical activity, i.e. static loading, can have an adverse effect on bone growth. A subject-specific model was used and growth plate was modeled as a poroelastic material in finite element analysis. Prendergast’s indicators for bone growth was used to analyse the bone growth behavior. The results showed that tendency of bone growth rate decreases over a long duration of static loading. The study also showed that static sitting is less detrimental than static standing for predicted cartilage-to-bone differentiation likelihood, due to the lower magnitude of hip contact force. The prediction of growth using finite element analysis on experimental gait data and person- specific femur geometry, based on mechanobiological theories of bone growth, offers a biomechanical foundation for better understanding and prediction of bone growth-related deformity problems in growing children. It can ultimately help in treatment planning or physical activity guidelines in children at risk at developing a femur or hip deformity. / <p>QC 20170616</p>