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Add Draft Adhesion Docs (#144)
* Add Adhesion in refs.bib * Add Draft of Adhesion in getting_started.rst * Remove Bad Code * Remove comments * Improve docs * Remove Adhesion tutorial from getting started * Create adhesion.rst * Remove velocity here * Change displacement variable for x and not y
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‎docs/source/refs.bib

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@@ -75,3 +75,14 @@ @inproceedings{Chen2024Stabler
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booktitle = {{ACM} {SIGGRAPH} 2024 Conference Proceedings},
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note = {\url{https://www.cs.columbia.edu/cg/abs-psd/}}
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}
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@article{Fang2023AugmentedStickyInteractions,
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title = {Augmented Incremental Potential Contact for Sticky Interactions},
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author = {Fang, Yu and Li, Minchen and Cao, Yadi and Li, Xuan and Wolper, Joshuah and Yang, Yin and Jiang, Chenfanfu},
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journal = {IEEE Transactions on Visualization and Computer Graphics},
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year = {2024},
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volume = {30},
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number = {8},
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pages = {5596-5608},
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keywords = {Adhesives;Friction;Computational modeling;Deformation;Solids;Force;Deformable models;Physically based animation;optimization time integration},
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doi = {10.1109/TVCG.2023.3295656}
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}

‎docs/source/tutorial/adhesion.rst

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Adhesion
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--------
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Adhesion simulates the sticking interaction between surfaces, such as glue bonding or material contact.
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Provides functionality to compute normal adhesion (perpendicular forces) and tangential adhesion (parallel forces).
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Normal Adhesion
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^^^^^^^^^^^^^^^
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For a given distance :math:`d`:
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- If :math:`d < \hat{d}_p`:
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.. math::
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A_n(d) = a_1 \cdot d^2 + c_1, \quad \text{where } a_1 = a_2 \left(1 - \frac{\hat{d}_a}{\hat{d}_p}\right)
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- If :math:`\hat{d}_p \leq d < \hat{d}_a`:
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.. math::
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A_n(d) = (a_2 \cdot d + b_2) \cdot d + c_2, \quad \text{where } b_2 = -2 a_2 \hat{d}_a, \, c_2 = a_2 \hat{d}_a^2
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- If :math:`d \geq \hat{d}_a`:
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.. math::
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A_n(d) = 0
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The normal adhesion potential models the attraction force based on the distance between two surfaces.
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Here dhat_p (:math:\hat{d}_p) is the threshold distance for adhesion (in units of distance) where the largest adhesion force is applied.
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Here dhat_a (:math:\hat{d}_a) is the adhesion activation distance (in units of distance), representing the maximum range where adhesion forces are active.
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Here Y (:math:Y) is the adhesion stiffness (in units of stress, such as Young's modulus), controlling the intensity of adhesion forces.
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Here eps_c (:math:\epsilon_c) is the adhesion coefficient (unitless) that defines the critical strain at which adhesion forces decrease.
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.. md-tab-set::
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.. md-tab-item:: C++
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.. code-block:: c++
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const double dhat_p = 1e-3;
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const double dhat_a = 2 * dhat_p;
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const double Y = 1e3;
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const double eps_c = 0.5;
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const NormalAdhesionPotential A(dhat_p, dhat_a, Y, eps_c)
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double adhesion_potential = A(normal_collisions, collision_mesh, displacement);
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.. md-tab-item:: Python
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.. code-block:: python
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dhat_p = 1e-3
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dhat_a = 2 * dhat_p
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Y = 1e3
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eps_c = 0.5
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A = NormalAdhesionPotential(dhat_p, dhat_a, Y, eps_c)
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adhesion_potential = A(normal_collisions, collision_mesh, displacement)
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Normal Derivatives
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^^^^^^^^^^^
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We can also compute the first and second derivatives of the normal adhesion potential with respect to the displacement.
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.. md-tab-set::
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.. md-tab-item:: C++
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.. code-block:: c++
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Eigen::VectorXd adhesion_potential_grad =
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A.gradient(normal_collisions, collision_mesh, displacement);
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Eigen::SparseMatrix<double> adhesion_potential_hess =
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A.hessian(normal_collisions, collision_mesh, displacement);
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.. md-tab-item:: Python
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.. code-block:: python
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adhesion_potential_grad = A.gradient(
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normal_collisions, collision_mesh, displacement)
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adhesion_potential_hess = A.hessian(
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normal_collisions, collision_mesh, displacement)
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Tangential Adhesion
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^^^^^^^^^^^^^^^
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The tangential adhesion potential models resistance to sliding (parallel to surfaces).
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For displacement :math:`x`:
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- If :math:`0 \leq x < 2 \varepsilon_a`:
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.. math::
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A_t(x) = \frac{x^2}{\varepsilon_a} \left(1 - \frac{y}{3 \varepsilon_a}\right)
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- If :math:`x \geq 2 \varepsilon_a`:
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.. math::
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A_t(x) = \frac{4 \varepsilon_a}{3}
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Here ``eps_a`` (:math:`\epsilon_a`) is the adhesion threshold (in units of displacement) used to smoothly transition.
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.. md-tab-set::
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.. md-tab-item:: C++
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.. code-block:: c++
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const double eps_a = 0.01;
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const TangentialAdhesionPotential A(eps_a);
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double adhesion_potential = A(tangential_collisions, collision_mesh, displacement);
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.. md-tab-item:: Python
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.. code-block:: python
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eps_a = 0.01
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A = TangentialAdhesionPotential(eps_a)
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adhesion_potential = A(tangential_collisions, collision_mesh, displacement);
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Derivatives
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^^^^^^^^^^^
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We can also compute the first and second derivatives of the tangential adhesion potential with respect to the displacement.
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.. md-tab-set::
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.. md-tab-item:: C++
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.. code-block:: c++
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Eigen::VectorXd adhesion_potential_grad =
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A.gradient(tangential_collisions, collision_mesh, displacement);
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Eigen::SparseMatrix<double> adhesion_potential_hess =
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A.hessian(tangential_collisions, collision_mesh, displacement);
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.. md-tab-item:: Python
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.. code-block:: python
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adhesion_potential_grad = A.gradient(
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tangential_collisions, collision_mesh, displacement)
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adhesion_potential_hess = A.hessian(
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tangential_collisions, collision_mesh, displacement)

‎docs/source/tutorial/getting_started.rst

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collision_free_vertices =
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(vertices_t1 - vertices_t0) * max_step_size + vertices_t0
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assert(ipctk.is_step_collision_free(
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mesh, vertices_t0, collision_free_vertices, min_distance=1e-4))
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mesh, vertices_t0, collision_free_vertices, min_distance=1e-4))

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