Predictive Elastoplastic Damage Constitutive Law: Establishment of Equivalence Relation between Intrinsic and Extrinsic Material Parameters

The purpose of the current work is the development and application of a new identification method of material parameters of elastoplastic damage constitutive model under large strains. A relationship relating the intrinsic and extrinsic parameters of a reference material is built and transformed in equivalence relation. Extrinsic parameters concern the shape of their experimental tensile force/elongation curve, however, intrinsic parameters deal with Swift hardening law coupled with an isotropic damage variable. The relationship is carried out from a statistical characterization of a material reference (standard-steel E24). It based on multiple linear regression of a data set obtained according to a full factor design of numerical simulations of mechanical tensile tests. All materials satisfying this equivalence relation belong to the same equivalence class. This is motivated by observing that gathered materials must behave somewhat like the reference material. The material parameters can be immediately identified by only one task by running the found relationship. The current method facilitates the identification procedure and offers a substantial savings in CPU time. However it just needs only one simulation for the identification of similar behavior instead of the few hundred required when using other methods.

Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients

One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".

COMBINED ALGORITHM FOR THE ESSENTIAL GRAPH OF BAYESIAN NETWORK STRUCTURES

Learning Bayesian network structure is one of the most important branches in Bayesian network. The most popular graphical representative of a Bayesian network structure is an essential graph. This paper shows a combined algorithm according to the three rules for finding the essential graph of a given directed acyclic graph. Moreover, the complexity and advantages of this combined algorithm over others are also discussed. The aim of this paper is to present the proof of the correctness of the combined algorithm.

The Homotopical Proof of Π₁(<i>S</i>, <i>x_o</i>) as a Fundamental Group in a General Interval

The aim of this study is to establish that, the equivalent class which is made up of homotopic loops is a group with respect to in the general interval [m,n]. The study proved from homotopical point of view that is associative, has an identity and inverse function. The study established with proof that is a fundamental group in [m,n] ,.