Introduction

‘tmech’ is a C++ library for the numerical study of the physics of continuous materials using higher-order tensors.

tmech provides

• an extensible expression system enabling lazy evaluation.

• tmech is a high quality tensor algebra library for the C++ language, aiming towards a good balance between speed and ease of use.

• Integer and floating point numbers are fully supported, complex numbers are supported only for basic arithmetic operations.

• Provides high-level syntax and functionality for easy use.

• Can be used for solid mechanics, fluid mechanics, …

• isotropic tensor functions.

• compile-time differentiation of scalar and tensorial expressions

• many more…

tmech requires a modern C++ compiler supporting C++17. The following C++ compilers are supported:

• On Unix platforms, GCC 7+ or a recent version of Clang

• On Windows, MSVC (Visual Studio 2022); all three platforms are exercised in CI

Licensing

This software is licensed under the BSD 3-Clause License. See the LICENSE file for details.

INSTALLATION

• Install
  • From source with cmake
  • Including tmech in your project
• Changelog
  • 1.1.0
  • 1.0.0

USAGE

• Getting started
  • First example
  • Compiling the first example
  • Building with cmake
  • Second example: single contraction
  • Third example: index access
• Expressions and lazy evaluation
  • Expressions
  • Lazy evaluation
  • Aliasing: temporary evaluation
  • Accessing elements
  • Expression interface
• Tensors as arrays
  • Internal memory layout
  • Performance

QUICK REFERENCE TMECH

• Basic arithmetic
  • Addition
  • Subtraction
  • Single contraction
  • Scalar update
• Basis rearrangement
  • General basis rearrangement
  • Transposition
  • Left basis transposition
• Outer product
  • General outer product
  • Dyadic product
  • Lower dyadic product
  • Upper dyadic product
• Inner product
  • General inner product
  • Double contraction
  • Fourth contraction
• Invers of a tensor
  • Second order tensors and fourth order tensors with minior-symmetry
  • Fully anisotropic tensors
• Volumetric and deviatoric parts
  • Volumetric part
  • Deviatoric part
• Symmetric and skew-symmetric parts
  • Symmetric part
  • Skew-symmetric part
• Isotropic tensor functions
  • General function
  • Square root
  • Exponential map
  • Logarithmic map
• Positive-negative decomposition
  • General method
  • Only positive part
  • Only negative part
• Eigen-decomposition
  • eigen_decomposition()
• Sign decomposition
  • sign()
• Polar decomposition
  • polar_decomposition()
• Exponential map
  • exp()
• Isotropic tensor functions
• Tensor decompositions
  • Polar decomposition
  • Eigenvalue decomposition
• Numerical differentiation
  • Nonsymmetric input and result
  • Symmetric input and result
• Compare Operators
  • operator<()
  • operator<=()
  • operator>()
  • operator>=()
  • operator==()
  • operator!=()
• Adapting pointers of raw memory
  • Adapting raw pointers Voigt’s notation
  • Adapting raw pointers full representation
• Converting to Voigt’s notation

SYMBOLIC DIFFERENTIATION

• Symbolic differentiation
  • Minimal example
  • Tangent stiffness of a linear elastic model

API REFERENCE TMECH

• Tensors
  • Tensor
  • Adaptor
  • Identity
  • Zeros
  • Random normal
  • Random uniform
• Wrapper

API REFERENCE SYMDIFF

• Variable
• Wrappers

DESIGN

• Design and architecture
  • Expression templates with lazy evaluation
  • Storage model
  • Header layout (bones/meat)
  • Contraction kernels and SIMD
  • Testing
• Comparison with related libraries