cases/fig9/case.py

"""Native AgentFEM FE reproduction of Ye et al. (2026), Figure 9.

The paper's homogenized orientational potential is added to a finite-thickness
Saint-Venant--Kirchhoff solid. AgentFEM owns the mesh, P2 displacement field,
material, boundary conditions, Newton solve, DG0 projections, ParaView series,
result manifest and run provenance. The paper equations are used only as an
independent reference and as the Newton initial guess.
"""

from __future__ import annotations

from pathlib import Path
import sys
sys.path.insert(0, str(Path(__file__).resolve().parent))

import matplotlib.pyplot as plt
import numpy as np
import h5py
import copy
import xml.etree.ElementTree as ET
import ufl
from dolfinx import fem

from agentfem import (
    constitutive,
    fields,
    io,
    mesh,
    models,
    problems,
    project,
    results,
    solvers,
    studies,
)
from agentfem.constitutive import geometric_elasticity, hyperelasticity

from paper_reference import (
    CHI,
    DELTA,
    H,
    LOADS,
    critical_load_continuum,
    critical_load_discrete,
    solve_continuum,
    solve_discrete,
)


def build_native_model(*, nx=100, ny=4):
    thickness = float(np.sqrt(12.0 * CHI))
    young = 1.0 / thickness
    domain = mesh.rectangle(
        (0.0, -0.5 * thickness),
        (1.0, 0.5 * thickness),
        (nx, ny),
        cell_type="quadrilateral",
    )
    model = models.create(
        study=studies.static_solid(
            dimension=2,
            assumption="plane_stress",
            nonlinear=True,
        ),
        mesh=domain,
        name="homogenized_microforce_rod",
    )
    displacement = model.field(fields.displacement(domain, degree=2))
    displacement.value.name = "U"
    material = model.material(
        constitutive.saint_venant_kirchhoff(
            young=young,
            poisson=0.0,
            plane_stress=True,
            name="EA=1_EI=chi",
        )
    )
    left = mesh.boundary(domain, lambda x: np.isclose(x[0], 0.0), name="clamp")
    right = mesh.boundary(domain, lambda x: np.isclose(x[0], 1.0), name="loaded_end")
    model.clamp(displacement, on=left)

    u = displacement.value
    F = ufl.Identity(2) + ufl.grad(u)
    axial_vector = ufl.dot(F, ufl.as_vector((1.0, 0.0)))
    axial_stretch = ufl.sqrt(ufl.dot(axial_vector, axial_vector))
    cosine = axial_vector[0] / axial_stretch
    load_p = fem.Constant(domain, 0.0)
    elastic_density = geometric_elasticity.energy(F, material)
    microforce_density = -4.0 * H * DELTA / thickness * (1.0 - cosine)
    effective_force = load_p + 2.0 * H
    potential = (
        (elastic_density + microforce_density) * ufl.dx
        - (effective_force / thickness) * u[0] * right.measure
    )
    residual = ufl.derivative(potential, u, displacement.test)
    jacobian = ufl.derivative(residual, u, displacement.trial)
    nonlinear = problems.nonlinear(
        residual,
        u,
        jacobian=jacobian,
        constraints=model.constraints,
        solver_options=solvers.NewtonSolverOptions(
            absolute_tolerance=1.0e-9,
            relative_tolerance=1.0e-9,
            maximum_iterations=80,
            line_search="basic",
        ),
        name="ye_2026_model_i_native_fe",
    )

    sigma = hyperelasticity.cauchy_stress(u, material)
    mises_expression = ufl.sqrt(
        sigma[0, 0] ** 2
        - sigma[0, 0] * sigma[1, 1]
        + sigma[1, 1] ** 2
        + 3.0 * sigma[0, 1] ** 2
    )
    mises = results.prepare_projection(
        mises_expression,
        domain=domain,
        family="DG",
        degree=0,
        name="MISES",
    )
    orientation_energy = results.prepare_projection(
        microforce_density,
        domain=domain,
        family="DG",
        degree=0,
        name="MICROFORCE_POTENTIAL",
    )
    return {
        "domain": domain,
        "model": model,
        "displacement": displacement,
        "material": material,
        "problem": nonlinear,
        "load_p": load_p,
        "mises": mises,
        "orientation_energy": orientation_energy,
        "thickness": thickness,
        "young": young,
        "nx": nx,
        "ny": ny,
    }


def seed_from_reference(displacement, p):
    sample, theta, center_x, center_y = solve_continuum(float(p))

    def initial(x):
        s = np.clip(x[0], 0.0, 1.0)
        xc = np.interp(s, sample, center_x)
        yc = np.interp(s, sample, center_y)
        angle = np.interp(s, sample, theta)
        transverse = x[1]
        return np.vstack(
            (
                xc - s - transverse * np.sin(angle),
                yc + transverse * np.cos(angle) - transverse,
            )
        )

    displacement.value.interpolate(initial)
    return sample, center_x, center_y


def sample_centerline(displacement, count=301):
    s = np.linspace(0.0, 1.0, count)
    values = np.asarray(
        [results.probe(displacement, at=(float(x), 0.0)) for x in s],
        dtype=float,
    )
    return s, s + values[:, 0], values[:, 1]


def comparison_plot(path: Path, cases):
    figure, axes = plt.subplots(1, 3, figsize=(13.4, 4.7), constrained_layout=True)
    for axis, case in zip(axes, cases):
        axis.plot(
            case["reference_x"],
            case["reference_y"],
            color="#e31a1c",
            lw=3.2,
            label="Paper Model (i)",
        )
        axis.plot(
            case["fe_x"],
            case["fe_y"],
            color="#00a6a6",
            lw=2.0,
            ls="--",
            label="AgentFEM P2 solid",
        )
        axis.plot(
            case["discrete_x"],
            case["discrete_y"],
            "o-",
            color="#111827",
            markerfacecolor="#facc15",
            markeredgecolor="#1d4ed8",
            lw=1.1,
            ms=3.0,
            label="Paper discrete n=15",
        )
        axis.set_aspect("equal", adjustable="box")
        axis.grid(alpha=0.18)
        axis.set_xlabel(r"$x/L$")
        axis.set_ylabel(r"$y/L$")
        axis.set_title(
            rf"$p={case['p']:.6f}$" + "\n" + rf"AgentFEM vs Model (i): {100*case['fe_nrmse']:.3f}%",
            fontsize=11,
        )
    handles, labels = axes[0].get_legend_handles_labels()
    figure.legend(handles, labels, loc="lower center", ncol=3, frameon=False)
    figure.suptitle(
        "Native AgentFEM finite-element reproduction of Ye et al. (2026), Figure 9\n"
        + rf"P2 StVK solid; $\chi=10^{{-4}},\;\delta=0.1,\;h=0.01$",
        fontsize=14,
    )
    figure.savefig(path, dpi=220, bbox_inches="tight", facecolor="white")
    plt.close(figure)


def main():
    run = project.current_run()
    native = build_native_model(nx=100, ny=4)
    cases = []
    pvd = run.artifact("paraview/native_agentfem_fig9.pvd")
    xdmf = run.artifact("xdmf/native_agentfem_fig9.xdmf")
    exact = run.artifact("scientific/p2_coefficients.h5")
    exact.parent.mkdir(parents=True, exist_ok=True)
    with io.ParaViewTimeSeries(pvd, native["domain"]) as writer, io.XDMFTimeSeries(xdmf, native["domain"]) as xwriter, h5py.File(exact, "w") as h5:
        h5.attrs["note"] = "Independent load cases, not physical time. Exact P2 coefficients; XDMF U is interpolated to P1."
        h5.create_dataset("dof_coordinates", data=native["displacement"].value.function_space.tabulate_dof_coordinates())
        h5.create_dataset("cell_dofs", data=native["displacement"].value.function_space.dofmap.list)
        h5.attrs["element"] = "Q2 vector, block size 2, serial coefficients"
        for frame, p in enumerate(LOADS):
            sample, reference_x, reference_y = seed_from_reference(
                native["displacement"], float(p)
            )
            native["load_p"].value = float(p)
            native["problem"].solve()
            group = h5.create_group(f"case_{frame}")
            group.attrs["p"] = float(p)
            group.create_dataset("U_P2", data=native["displacement"].value.x.array)
            mises = native["mises"].solve()
            orientation = native["orientation_energy"].solve()
            xwriter.write_fields(float(frame), io.interpolate_for_xdmf(native["displacement"], name="U"), mises, orientation)
            writer.write_fields(
                float(frame),
                native["displacement"],
                mises,
                orientation,
            )

            s, fe_x, fe_y = sample_centerline(native["displacement"])
            assert fe_y[-1] < 0.0, "FE must solve the downward branch, not flip it in plotting"
            group.create_dataset("centerline", data=np.column_stack([s, fe_x, fe_y]))
            target_x = np.interp(s, sample, reference_x)
            target_y = np.interp(s, sample, reference_y)
            fe_nrmse = float(
                np.sqrt(np.mean((fe_x - target_x) ** 2 + (fe_y - target_y) ** 2))
            )
            _, discrete_x, discrete_y = solve_discrete(float(p))
            cases.append(
                {
                    "p": float(p),
                    "reference_x": reference_x,
                    "reference_y": reference_y,
                    "fe_x": fe_x,
                    "fe_y": fe_y,
                    "discrete_x": discrete_x,
                    "discrete_y": discrete_y,
                    "fe_nrmse": fe_nrmse,
                    "fe_tip_error": float(
                        np.hypot(fe_x[-1] - reference_x[-1], fe_y[-1] - reference_y[-1])
                    ),
                    "newton_iterations": int(native["problem"].last_solve_info.iterations),
                    "residual_norm": float(native["problem"].last_solve_info.function_norm),
                }
            )

    # DOLFINx emits one temporal collection per field. Merge attributes onto
    # one geometry per case so readers do not display undeformed duplicates.
    original = ET.parse(xdmf).getroot().find("Domain")
    base = original.find("Grid")
    merged = ET.Element("Xdmf", Version="3.0")
    domain_xml = ET.SubElement(merged, "Domain")
    series = ET.SubElement(domain_xml, "Grid", Name="Independent_cases", GridType="Collection", CollectionType="Temporal")
    for frame in range(len(LOADS)):
        grid = ET.SubElement(series, "Grid", Name=f"case_{frame}", GridType="Uniform")
        grid.append(copy.deepcopy(base.find("Topology")))
        grid.append(copy.deepcopy(base.find("Geometry")))
        ET.SubElement(grid, "Time", Value=str(frame))
        for collection in original.findall("Grid[@CollectionType='Temporal']"):
            grid.append(copy.deepcopy(collection.findall("Grid")[frame].find("Attribute")))
    ET.indent(merged)
    ET.ElementTree(merged).write(xdmf, encoding="utf-8", xml_declaration=True)

    table = np.asarray(
        [
            [
                item["p"],
                item["fe_nrmse"],
                item["fe_tip_error"],
                item["newton_iterations"],
                item["residual_norm"],
            ]
            for item in cases
        ]
    )
    metrics_path = run.artifact("native_fe_metrics.csv")
    np.savetxt(
        metrics_path,
        table,
        delimiter=",",
        header="p,agentfem_centerline_nrmse_over_L,tip_error_over_L,newton_iterations,residual_norm",
        comments="",
    )
    figure_path = run.artifact("figures/native_agentfem_vs_paper.png")
    comparison_plot(figure_path, cases)

    result = results.SimulationResult(
        "ye_2026_fig9_native_fe",
        metadata={
            "paper": {
                "title": "Three Homogenization Models for a Nonlinear Heterogeneous Rod with Microscale Dead Loading",
                "doi": "10.1016/j.jmps.2026.106870",
                "target": "Figure 9 / homogenized Model (i)",
            },
            "formulation": {
                "mesh": f"{native['nx']} x {native['ny']} quadrilateral",
                "field": "P2 displacement",
                "material": "plane-stress Saint-Venant--Kirchhoff",
                "microforce_term": "Eq. (42) orientation potential",
                "solver": "AgentFEM Newton",
                "EA": 1.0,
                "EI": CHI,
                "thickness": native["thickness"],
                "young": native["young"],
            },
        },
    )
    result.add_history(
        "centerline_nrmse",
        LOADS,
        np.asarray([item["fe_nrmse"] for item in cases]),
        abscissa_name="dimensionless_load_p",
        abscissa_unit=None,
        description="RMS centerline distance normalized by L against paper Model (i).",
    )
    result.add_quantity("continuum_critical_load", critical_load_continuum())
    result.add_quantity("discrete_n15_critical_load", critical_load_discrete())
    result.add_field(
        "native_agentfem_fields",
        artifact=pvd,
        description="ParaView PVD series containing U, MISES and MICROFORCE_POTENTIAL.",
    )
    result.add_artifact("comparison_figure", figure_path)
    result.add_artifact("metrics", metrics_path)
    result.add_artifact("exact_p2_coefficients", exact)
    result.add_artifact("xdmf_p1_visualization", xdmf)
    run.publish(result)
    return result


if __name__ == "__main__":
    main()