Probabilistic inference of fatigue damage propagation with limited and partial information

A general method of probabilistic fatigue damage prognostics using limited and partial information is developed.Limited and partial information refers to measurable data that are not enough or cannot directly be used to statistically identify model parameter using traditional regression analysis.In the proposed method, the prior probability distribution of model parameters is derived based on the principle of maximum entropy（Max Ent） using the limited and partial information as constraints.The posterior distribution is formulated using the principle of maximum relative entropy（MRE） to perform probability updating when new information is available and reduces uncertainty in prognosis results.It is shown that the posterior distribution is equivalent to a Bayesian posterior when the new information used for updating is point measurements.A numerical quadrature interpolating method is used to calculate the asymptotic approximation for the prior distribution.Once the prior is obtained, subsequent measurement data are used to perform updating using Markov chain Monte Carlo（MCMC） simulations.Fatigue crack prognosis problems with experimental data are presented for demonstration and validation.

Damage evolution and crack propagation in rocks with dual elliptic flaws in compression

To give an insight into the understanding of damage evolution and crack propagation in rocks,a series of uniaxial and biaxial compression numerical tests are carried out.The investigations show that damage evolution occurs firstly in the weak rock,the area around the flaw and the area between the flaw and the neighboring rock layer.Cracks mostly generate as tensile cracks under uniaxial compression and shear cracks under biaxial compression.Crack patterns are classified and divided.The relationship between the accumulated lateral displacement and the short radius（b）is fitted,and the equation of crack path is also established.

Multiscale analysis of composite material reinforced by randomly-dispersed particles

A multiscale analysis method is presented in which detailed information on the microscopic level is incorporated into macroscopic models capable of simulating damage evolution and ultimate failure.The composite considered is reinforced by randomly-dispersed particles,which reflects the statistical characteristics of real materials,such as cement-based materials.Specifically,a three-dimensional material body is decomposed into many unit cells.Each unit cell is reinforced by a cylindrical particle,the orientation of which is characterized by three Euler angles generated by the random number generator.Based on a detailed finite element analysis,the material properties of the representative volume element are obtained.As verification,the properties of the cylindrical particles are set equal to those of the matrix and the computed‘composite’properties reduce exactly to those of the‘isotropic’material,as expected.Through coordinate transformation,the effective material properties of each unit cell are calculated.The assembly of stiffness matrices of all unit cells leads to the stiffness matrix of the whole specimen.Under the simple tension loading condition,the initial damaged unit cell can be identified according to the vonMises yield criterion.The stiffness of the damaged unit cell will then be reduced to zero and it will cause stress redistribution and trigger further damage.It was found that the reinforcement is effective to mitigate and arrest the damage propagation,and therefore prolongs the material’s lifetime.These results suggest that the hierarchical coupling approaches used here may be useful for material design and failure protection in composites.