A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Influence of secondary void damage in the matrix material around voids

The mechanism of ductile damage caused by secondary void damage in the matrix around primary voids is studied by large strain, finite element analysis. A cylinder embedding an initially spherical void, a plane stress cell with a circular void and plane strain cell with a cylindrical or a flat void are analysed under different loading conditions. Secondary voids of smaller scale size nucleate in the strain hardening matrix, according to the requirements of some stress/strain criteria. Their growth and coalescence, handled by the empty element technique, demonstrate distinct mechanisms of damage as circumstances change. The macroscopic stress-strain curves are decomposed and illustrated in the form of the deviatoric and the volumetric parts. Concerning the stress response and the void growth prediction, comparisons are made between the present numerical results and those of previous authors. It is shown that loading condition, void growth history and void shape effect incorporated with the interaction between two generations of voids should be accounted for besides the void volume fraction.

The effect of strain softening in the matrix material during void growth

Furthermore, the compressed flow driven by the piston is discussed. The consistent solution of gasdynamical equations including solar gravity is obtained for the unsteady and two-dimensional configuration, which is applied to the region between the piston and shock wave. This solution may satisfy the jump conditions of shock wave, which separates the region of compressed flow and quiet corona.

Endogenous fisheries management in a stochastic model: Why do fishery agencies use TAC

The aim of this paper is to explain under which circumstances using TACs as instrument to manage a fishery along with fishing periods may be interesting from a regulatory point of view. In order to do this, the deterministic analysis of Homans and Wilen (1997)and Anderson (2000) is extended to a stochastic scenario where the resource cannot be measured accurately. The resulting endogenous stochastic model is numerically solved for finding the optimal control rules in the Iberian sardine stock. Three relevant conclusions can be highligted from simulations. First, the higher the uncertainty about the state of the stock is, the lower the probability of closing the fishery is. Second, the use of TACs as management instrument in fisheries already regulated with fishing periods leads to: i) An increase of the optimal season length and harvests, especially for medium and high number of licences, ii) An improvement of the biological and economic variables when the size of the fleet is large; and iii) Eliminate the extinction risk for the resource. And third, the regulator would rather select the number of licences and do not restrict the season length.

Reference Points and Optimal Management in Stochastic Age-Structured Fisheries Models

The purpose of this article is to characterize dynamic optimal harvesting trajectories that maximize discounted utility assuming an age-structured population model, in the same line as Tahvonen (2009). The main novelty of our study is that uses as an age-structured population model the standard stochastic cohort framework applied in Virtual Population Analysis for fish stock assessment. This allows us to compare optimal harvesting in a discounted economic context with standard reference points used by fisheries agencies for long term management plans (e.g. Fmsy). Our main findings are the following. First, optimal steady state is characterized and sufficient conditions that guarantees its existence and uniqueness for the general case of n cohorts are shown. It is also proved that the optimal steady state coincides with the traditional target Fmsy when the utility function to be maximized is the yield and the discount rate is zero. Second, an algorithm to calculate the optimal path that easily drives the resource to the steady state is developed. And third, the algorithm is applied to the Northern Stock of hake. Results show that management plans based exclusively on traditional reference targets as Fmsy may drive fishery economic results far from the optimal.