Rostislav Rypl

Using Python for scientific computing: Efficient and flexible evaluation of the statistical characteristics of functions with multivariate random inputs ✩

Abstract This paper examines the feasibility of high-level Python based utilities for numerically intensive applications via an example of a multidimensional integration for the evaluation of the statistical characteristics of a random variable. We discuss the approaches to the implementation of mathematically formulated incremental expressions using high-level scripting code and low-level compiled code. Due to the dynamic typing of the Python language, components of the algorithm can be easily coded in a generic way as algorithmic templates. Using the Enthought Development Suite they can be effectively assembled into a flexible computational framework that can be configured to execute the code for arbitrary combinations of integration schemes and versions of instantiated code. The paper describes the development cycle using a simple running example involving averaging of a random two-parametric function that includes discontinuity. This example is also used to compare the performance of the available algorithmic and executional features. The implemented package including further examples and the results of performance studies have been made available via the free repository [1] and CPCP library. Program summary Program title: spirrid Catalogue identifier: AENL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Special licence provided by the author No. of lines in distributed program, including test data, etc.: 10722 No. of bytes in distributed program, including test data, etc.: 157099 Distribution format: tar.gz Programming language: Python and C. Computer: PC. Operating system: LINUX, UNIX, Windows. Classification: 4.13, 6.2. External routines: NumPy ( http://numpy.scipy.org/ ), SciPy ( http://www.scipy.com ) Nature of problem: Evaluation of the statistical moments of a function of random variables. Solution method: Direct multidimensional integration. Running time: Depending on the number of random variables the time needed for the numerical estimation of the mean value of a function with a sufficiently low level of numerical error varies. For orientation, the time needed for two included examples: examples/fiber_tt_2p/fiber_tt_2p.py with 2 random variables: few milliseconds examples/fiber_po_8p/fiber_po_8p.py with 8 random variables: few seconds

A novel tensile test device for effective testing of high-modulus multi-filament yarns:

The paper introduces a novel clamp adapter with the goal to improve the quality of the tensile test setup for high-modulus multi-filament yarns. Common tensile test machines damage the yarns initially or prematurely due to non-uniform load introduction which causes stress concentrations. As a result, the theoretical yarn strength (perfectly clamped filaments at a unique length and no initial damage) is underestimated. With the new clamp adapter, higher strengths close to the theoretical values can be measured since the adapter largely eliminates the problems with non-uniform load introduction. A test series comparing yarns strengths tested with the clamp adapter and with commonly used test methods has been performed and the results are discussed in this paper. Furthermore, they are compared with theoretical values using the Daniels’ fibre-bundle model.

Identification of the effective bundle length in a multifilament yarn from the size effect response

The article proposes a method for characterizing the in situ interaction between filaments in a multifilament yarn. The stress transfer between neighboring filaments causes the reactivation of a broken filament at some distance from the break. The utilized statistical bundle models predict a change in the slope of the mean size effect curve once the specimen length becomes longer than the stress transfer length. This fact can be exploited in order to determine the stress transfer length indirectly using the yarn tensile test with appropriately chosen test lengths. The identification procedure is demonstrated using two test series of tensile tests with AR-glass and carbon yarns.

The role of fiber volume fraction in tensile strength of fibrous composites

It has been proved experimentally that a finer crack pattern in brittle matrix composites with heterogeneous fibrous reinforcement increases the reinforcement efficiency in terms of fiber strength by up to 100 %. In the present paper, we simulate this phenomenon by a semi-analytical model of a composite crack bridge based on probabilistic fiber bundle models. The model is able to quantify the reinforcement efficiency increase with finer crack spacing given the information on the reinforcement heterogeneity. Possible sources of heterogeneity are variabilities in fiber diameter, modulus of elasticity or bond quality. With finer crack spacing, the heterogeneous stress state of the reinforcement is homogenized which leads to a more efficient load bearing behavior. Since the crack spacing is (within the practical range of values) a monotonic function of the fiber volume fraction and fiber diameter, these quantities should be taken into account in structural analysis and design of composites with heterogeneous reinforcement.