Simulation of Constrained Mechanical Systems—Part II: Explicit Numerical Integration

This paper presents an explicit to integrate differential algebraic equations (DAEs) method for simulations of constrained mechanical systems modeled with holonomic and nonholonomic constraints. The proposed DAE integrator is based on the equation of constrained motion developed in Part I of this work, which is discretized here using explicit ordinary differential equation schemes and applied to solve two nontrivial examples. The obtained results show that this integrator allows one to precisely solve constrained mechanical systems through long time periods. Unlike many other implicit DAE solvers which utilize iterative constraint correction, the presented DAE integrator is explicit, and it does not use any iteration. As a direct consequence, the present formulation is simple to implement, and is also well suited for real-time applications.

Constraint-Correction of Cleavage Fracture Data From Miniature Specimens and Improved Estimates of Lower Bound Fracture Toughness

Current assessments of pressurised components use fracture data collected on conventional size, 25 mm and 10 mm thick fracture specimens. It would be advantageous to be able to measure fracture toughness on what has commonly been termed miniature specimens (i.e. smaller than 10mm) as this would allow a more economical use of available plant material. However, tests on miniature specimens generally produce values of fracture toughness which over-estimate the fracture toughness of the material (as evaluated from the 25 mm or 10 mm specimens). In particular, the measured scatter in the data exhibits lower-bound values that are higher than the values obtained with conventional size specimens. A study has thus been undertaken in order to examine a methodology to derive fracture toughness from miniature specimens and allow a better determination of the lower-bound values. When cleavage fracture toughness tests are carried out using miniature specimens, the values of critical J obtained do not directly determine the cleavage fracture toughness of the material. This is because a loss of crack-tip constraint will generally occur before fracture. In such cases, it is necessary to apply an appropriate constraint correction to map the measured values to their equivalent small-scale yielding values. This paper uses a method for carrying out constraint corrections in order to assess data obtained from a recent UK miniature fracture toughness specimen testing programme. The method is based on the notion of matching areas enclosed by a same-stress contour of maximum principal stress around the crack tip in the specimen and small-scale yielding geometries. In applying the method, two-dimensional, plane strain finite element models of the specimen geometries have been developed together with a boundary layer model of the reference small-scale yielding condition to determine the appropriate areas.