Russell Tensor - Tensor analysis, calculus, and functions for continuum mechanics

This crate is part of Russell - Rust Scientific Library

Contents

• Introduction
  • Documentation
• Installation
  • Setting Cargo.toml
  • Optional features
• 🌟 Examples
  • Allocating Second Order Tensors
• For developers

Introduction

This library implements structures and functions for tensor analysis and calculus. The library focuses on applications in engineering and Continuum Mechanics. The essential functionality for the targeted applications includes second-order and fourth-order tensors, scalar "invariants," and derivatives.

This library implements derivatives for scalar functions with respect to tensors, tensor functions with respect to tensors, and others. A convenient basis representation known as Mandel basis (similar to Voigt notation) is considered by this library internally. The user may also use the Mandel basis to perform simpler matrix-vector operations directly.

Documentation

• — russell_tensor documentation

Installation

This crate depends on some non-rust high-performance libraries. See the main README file for the steps to install these dependencies.

Setting Cargo.toml

👆 Check the crate version and update your Cargo.toml accordingly:

[dependencies]
russell_tensor = "*"

Optional features

The following (Rust) features are available:

• intel_mkl: Use Intel MKL instead of OpenBLAS

Note that the main README file presents the steps to compile the required libraries according to each feature.

🌟 Examples

This section illustrates how to use russell_tensor. See also:

• More examples on the documentation
• Examples directory

Allocating Second Order Tensors

use russell_tensor::{Mandel, StrError, Tensor2, SQRT_2};

fn main() -> Result<(), StrError> {
    // general
    let a = Tensor2::from_matrix(
        &[
            [1.0, SQRT_2 * 2.0, SQRT_2 * 3.0],
            [SQRT_2 * 4.0, 5.0, SQRT_2 * 6.0],
            [SQRT_2 * 7.0, SQRT_2 * 8.0, 9.0],
        ],
        Mandel::General,
    )?;
    assert_eq!(
        format!("{:.1}", a.vector()),
        "┌      ┐\n\
         │  1.0 │\n\
         │  5.0 │\n\
         │  9.0 │\n\
         │  6.0 │\n\
         │ 14.0 │\n\
         │ 10.0 │\n\
         │ -2.0 │\n\
         │ -2.0 │\n\
         │ -4.0 │\n\
         └      ┘"
    );

    // symmetric-3D
    let b = Tensor2::from_matrix(
        &[
            [1.0, 4.0 / SQRT_2, 6.0 / SQRT_2],
            [4.0 / SQRT_2, 2.0, 5.0 / SQRT_2],
            [6.0 / SQRT_2, 5.0 / SQRT_2, 3.0],
        ],
        Mandel::Symmetric,
    )?;
    assert_eq!(
        format!("{:.1}", b.vector()),
        "┌     ┐\n\
         │ 1.0 │\n\
         │ 2.0 │\n\
         │ 3.0 │\n\
         │ 4.0 │\n\
         │ 5.0 │\n\
         │ 6.0 │\n\
         └     ┘"
    );

    // symmetric-2D
    let c = Tensor2::from_matrix(
        &[[1.0, 4.0 / SQRT_2, 0.0], [4.0 / SQRT_2, 2.0, 0.0], [0.0, 0.0, 3.0]],
        Mandel::Symmetric2D,
    )?;
    assert_eq!(
        format!("{:.1}", c.vector()),
        "┌     ┐\n\
         │ 1.0 │\n\
         │ 2.0 │\n\
         │ 3.0 │\n\
         │ 4.0 │\n\
         └     ┘"
    );
    Ok(())
}

For developers

• This crate is pure Rust with no C dependencies
• Run the examples with cargo run --example <name>