Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation

Research on automatic grinding platform for rare earth ingot casting

Aiming at the problems of low grinding efficiency and difficulty in ensuring grinding uniformity of rare earth metal ingots, a rare earth metal ingot grinding system was designed. Based on Creo software and ANSYS/Workbench software, the kinematics analysis, modal analysis and transient dynamics analysis were carried out on the walking mechanism and flipping mechanism of automatic displacement platform of grinding system. The results show that the rare earth metal ingot grinding system has good stability and is beneficial to improving the grinding quality

Research on automatic grinding platform for rare earth ingot casting

Aiming at the problems of low grinding efficiency and difficulty in ensuring grinding uniformity of rare earth metal ingots, a rare earth metal ingot grinding system was designed. Based on Creo software and ANSYS/Workbench software, the kinematics analysis, modal analysis and transient dynamics analysis were carried out on the walking mechanism and flipping mechanism of automatic displacement platform of grinding system. The results show that the rare earth metal ingot grinding system has good stability and is beneficial to improving the grinding quality

Imbalanced Deep Learning by Minority Class Incremental Rectification

Model learning from class imbalanced training data is a long-standing and significant challenge for machine learning. In particular, existing deep learning methods consider mostly either class balanced data or moderately imbalanced data in model training, and ignore the challenge of learning from significantly imbalanced training data. To address this problem, we formulate a class imbalanced deep learning model based on batch-wise incremental minority (sparsely sampled) class rectification by hard sample mining in majority (frequently sampled) classes during model training. This model is designed to minimise the dominant effect of majority classes by discovering sparsely sampled boundaries of minority classes in an iterative batch-wise learning process. To that end, we introduce a Class Rectification Loss (CRL) function that can be deployed readily in deep network architectures. Extensive experimental evaluations are conducted on three imbalanced person attribute benchmark datasets (CelebA, X-Domain, DeepFashion) and one balanced object category benchmark dataset (CIFAR-100). These experimental results demonstrate the performance advantages and model scalability of the proposed batch-wise incremental minority class rectification model over the existing state-of-the-art models for addressing the problem of imbalanced data learning.Comment: Accepted for IEEE Trans. Pattern Analysis and Machine Intelligenc

Suppressing longitudinal double-layer oscillations by using elliptically polarized laser pulses in the hole-boring radiation pressure acceleration regime

It is shown that well collimated mono-energetic ion beams with a large particle number can be generated in the hole-boring radiation pressure acceleration regime by using an elliptically polarized laser pulse with appropriate theoretically determined laser polarization ratio. Due to the $\bm{J}\times\bm{B}$ effect, the double-layer charge separation region is imbued with hot electrons that prevent ion pileup, thus suppressing the double-layer oscillations. The proposed mechanism is well confirmed by Particle-in-Cell simulations, and after suppressing the longitudinal double-layer oscillations, the ion beams driven by the elliptically polarized lasers own much better energy spectrum than those by circularly polarized lasers.Comment: 6 pages, 5 figures, Phys. Plasmas (2013) accepte

Flexible constant force grinding of rare earth metal ingot

The rare earth metal ingots obtained by molten salt electrolysis method have oxide layers, salt layers, and other impurities on the surface, which require polishing processing. However, currently, manual polishing processing has problems such as low processing efficiency and resource waste. By designing a flexible end effector and adopting a parallel fuzzy Proportion Integration Differentiation (PID) control strategy for constant force control of the end effector, automation and high efficiency of rare earth metal ingot grinding are achieved

Flexible constant force grinding of rare earth metal ingot

The rare earth metal ingots obtained by molten salt electrolysis method have oxide layers, salt layers, and other impurities on the surface, which require polishing processing. However, currently, manual polishing processing has problems such as low processing efficiency and resource waste. By designing a flexible end effector and adopting a parallel fuzzy Proportion Integration Differentiation (PID) control strategy for constant force control of the end effector, automation and high efficiency of rare earth metal ingot grinding are achieved