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

This crate is part of Russell - Rust Scientific Library

Contents

• Introduction
  • Documentation
• Installation
  • TL;DR (Debian/Ubuntu/Linux)
• Details
  • Setting Cargo.toml
• Examples
  • Allocating Second Order Tensors

Introduction

This library implements structures and functions for tensor analysis and calculus. The library focuses on applications in engineering and [Continuum Mechanics](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

Installation

At this moment, Russell works on Linux (Debian/Ubuntu; and maybe Arch). It has some limited functionality on macOS too. In the future, we plan to enable Russell on Windows; however, this will take time because some essential libraries are not easily available on Windows.

TL;DR (Debian/Ubuntu/Linux)

First:

sudo apt-get install -y --no-install-recommends \
    g++ \
    gdb \
    gfortran \
    liblapacke-dev \
    libmumps-seq-dev \
    libopenblas-dev \
    libsuitesparse-dev

Then:

cargo add russell_tensor

Details

This crate depends on russell_lab, which, in turn, depends on an efficient BLAS library such as OpenBLAS and Intel MKL.

The root README file presents the steps to install the required dependencies.

Setting Cargo.toml

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

[dependencies]
russell_tensor = "*"

Or, considering the optional features (see more about these here):

[dependencies]
russell_tensor = { version = "*", features = ["intel_mkl"] }

Examples

• russell_tensor/examples

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.vec),
        "┌      ┐\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.vec),
        "┌     ┐\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.vec),
        "┌     ┐\n\
         │ 1.0 │\n\
         │ 2.0 │\n\
         │ 3.0 │\n\
         │ 4.0 │\n\
         └     ┘"
    );
    Ok(())
}