The Monte Carlo method is a well-known method for calculating uncertainty, but it has the disadvantage of high computational cost because it usually requires 10,000 sampling points. In this paper, a practical sampling algorithm named Stepwise Limited Sampling (SLS) is proposed to obtain both accurate expected values and very accurate tail probability values in the Monte Carlo simulation. This method was then applied to a biomechanics problem concerning the risk prediction of pressure ulcers. It is known that the initial damage that leads to a fatal stage of pressure ulcer occurs in deep muscle, but its location has not been clarified. By modeling assumed damage at the bone-muscle interface in the human buttock as a cutout, and by judging whether the damage propagates or not, sets of material properties of muscle and fat in the tail probability that result in high interface shear strain were obtained as a function of body positioning during nursing.
Stress intensity factor have been used as a parameter of crack growth evaluation such as fatigue or stress-corrosion cracking. Especially, welds and heat affected zones have two distributions: residual stress and yield strength. Those distributions might affect the crack growth evaluation. In other words, the potential exists to deviate from the applicable range of the stress intensity factor in those regions. In this study, the applicability of stress intensity factor was analytically investigated by comparing an elasticity solution with an elastoplastic solution of the stress state in front of a crack when the stress distribution and yield strength distribution were simultaneously present along the crack propagation path. As a result, the stress intensity factor tended to be inapplicable when the steep distributions were present in front of the crack. Additionally, the modified method of stress intensity factor for incorporating the influence of those distributions was proposed and the applicability of that was investigated.
This paper presents a novel methodology for implementing an Ogden-type hyperelastic material model with numerically computed consistent tangent moduli using complex-step derivative approximation (CSDA). In this formulation, numerical calculations of exact eigenvalues and eigenvectors of complex symmetric matrices are required to obtain the accurate consistent tangent moduli . For the request, the numerical calculations have convergence criteria which are defined in each of real and imaginary part independently. Finite element analyses using Ogden material model implemented with the present methodology are presented to show that the consistent tangent moduli are in good agreement with the analytic ones.