GMatNonLinearElastic

Non-linear elastic material model. An overview of the theory can be found in docs/theory/readme.tex conveniently compiled to this PDF.

Disclaimer

This library is free to use under the MIT license. Any additions are very much appreciated, in terms of suggested functionality, code, documentation, testimonials, word-of-mouth advertisement, etc. Bug reports or feature requests can be filed on GitHub. As always, the code comes with no guarantee. None of the developers can be held responsible for possible mistakes.

Download: .zip file | .tar.gz file.

(c - MIT) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GMatNonLinearElastic

Python implementation

Partial example

import GMatNonLinearElastic.Cartesian3d as GMat

shape = [...]
kappa = np.empty(shape)
sig0 = np.empty(shape)
eps0 = np.empty(shape)
m = np.empty(shape)
...

GMat.NonLinearElasticXd model(kappa, sig0, eps0, m);
...

Eps = np.empty(shape + [3, 3])
...

model.Eps = Eps
print(model.Sig)

Installation

Using conda

conda install -c conda-forge python-gmatnonlinearelastic

Note that xsimd and hardware optimisations are not enabled. To enable them you have to compile on your system, as is discussed next.

From source

You need xtensor, xtensor-python and optionally xsimd as prerequisites. The easiest is to use conda to get the prerequisites:

conda install -c conda-forge xtensor xsimd xtensor-python

If you then compile and install with the same environment you should be good to go. Otherwise, a bit of manual labour might be needed to treat the dependencies.

git checkout https://github.com/tdegeus/GMatNonLinearElastic.git
cd GMatNonLinearElastic

# Only if you want to use hardware optimisation:
export SKBUILD_CONFIGURE_OPTIONS="-DUSE_SIMD=1"

python -m pip install . -v

C++ implementation

Partial example

#include <GMatNonLinearElastic/Cartesian3d.h>

namespace GMat = GMatNonLinearElastic::Cartesian3d;

int main()
{
    static const size_t rank = ...;

    xt::xtensor<double, rank> kappa = ...;
    xt::xtensor<double, rank> sig0 = ...;
    xt::xtensor<double, rank> eps0 = ...;
    xt::xtensor<double, rank> m = ...;

    GMat::NonLinearElasticXd model(kappa, sig0, eps0, m);
    ...

    xt::xtensor<double, rank + 2> Eps;
    ...

    // all necessary computation are done at this point
    model.set_Eps(Eps);
    ...

    // get reference to stress
    auto Sig = model.Sig();

    return 0;
}

Installation

Using conda

conda install -c conda-forge gmatnonlinearelastic

From source

git checkout https://github.com/tdegeus/GMatNonLinearElastic.git
cd GMatNonLinearElastic

cmake -Bbuild
cd build
cmake --install .

Compiling

Using CMake

Example

Your CMakeLists.txt can be as follows

cmake_minimum_required(VERSION 3.1)
project(example)
find_package(GMatNonLinearElastic REQUIRED)
add_executable(example example.cpp)
target_link_libraries(example PRIVATE GMatNonLinearElastic)

Targets

The following targets are available:

• GMatNonLinearElastic Includes the library and its dependencies.

• GMatNonLinearElastic::assert Enables IO-assertions by defining GMATNONLINEARELASTIC_ENABLE_ASSERT.

• GMatNonLinearElastic::debug Enables assertions of all dependencies.

• GMatNonLinearElastic::compiler_warings Enables compiler warnings (generic).

Optimisation

It is advised to think about compiler optimisation and enabling xsimd. Using CMake this can be done using the xtensor::optimize and xtensor::use_xsimd targets. The above example then becomes:

cmake_minimum_required(VERSION 3.1)
project(example)
find_package(GMatNonLinearElastic REQUIRED)
find_package(xtensor REQUIRED)
find_package(xsimd REQUIRED)
add_executable(example example.cpp)
target_link_libraries(example PRIVATE
    GMatNonLinearElastic
    xtensor::optimize
    xtensor::use_xsimd)

See the documentation of xtensor.

By hand

Presuming that the compiler is c++, compile using:

c++ -I/path/to/GMatNonLinearElastic/include ...

Note that you have to take care of the xtensor dependency, the C++ version, optimisation, enabling xsimd, ...

Using pkg-config

Presuming that the compiler is c++, compile using:

c++ `pkg-config --cflags GMatNonLinearElastic` ...

Note that you have to take care of the xtensor dependency, the C++ version, optimization, enabling xsimd, ...

Upgrading instructions

Upgrading to >v0.3.*

The individual material point and the array of material points was fully integrated. In addition, the number of copies was reduced.

C++

There is only a single class NonLinearElastic. It's functions where renamed:

• .setStrain(...) -> .set_Eps(...)
• .Stress() -> .Sig() (now returns a reference).
• .stress(...): deprecated.
• .Tangent() -> .C() (now returns a reference).
• .tangent(...): deprecated.

Python

There is only a single class NonLinearElastic. It's functions are converted to properties:

• .setStrain(...) -> .Eps = ...
• .Stress() -> .Sig (now returns a reference).
• .stress(...): deprecated.
• .Tangent() -> .C (now returns a reference).
• .tangent(...): deprecated.

Upgrading to >v0.2.*

xtensor_fixed was completely deprecated in v0.2.0, as were the type aliases Tensor2 and Tensor4. Please update your code as follows:

• Tensor2 -> xt::xtensor<double, 2>.
• Tensor4 -> xt::xtensor<double, 4>.

Tip: Used auto as return type as much as possible. This simplifies implementation, and renders is less subjective to library return type changes.

Compared to v0.1.0, v0.2.0 has some generalisations and efficiency updates. This requires the following changes:

• Matrix has been generalised to Array<rank>. Practically this requires changing:

  • Matrix to Array<2> in C++.
  • Matrix to Array2d in Python. Note that Array1d, Array3d, are also available.

• Array<rank>.check ->

  if (xt::any(xt::equal(array.type(), Type::Unset))) {
      throw std::runtime_error("Please set all points");
  }

  Note however that it is no longer required to set all points, unset points are filled-up with zeros.

• Strain is now stored as a member. Functions like stress now return the state based on the last specified strain, specified using setStrain(Esp). This leads to the following changes:

  • stress: no argument.
  • tangent: no argument, single return value (no longer returns stress).

Change-log

v0.3.0

Complete API overhaul.

v0.2.1

• Using scikit-build, setuptools_scm, xtensor-python (#21)
• CMake clean-up (#21)

v0.2.0

Compared to v0.1.0, v0.2.0 has some generalisations and efficiency updates. This requires the following changes:

• Matrix has been generalised to Array<rank>. Practically this requires changing:

  • Matrix to Array<2> in C++.
  • Matrix to Array2d in Python. Note that Array1d, Array3d, are also available.

• Array now sets zeros for all Type::Unset points. The function check is deprecated accordingly.

• Strain is now stored as a member. Functions like stress now return the state based on the last specified strain, specified using setStrain(Esp). This leads to the following changes:

  • stress: no argument.
  • tangent: no argument, single return value (no longer returns stress).

• Tensor operations are now provided centrally in the GMat eco-system, by GMatTensor