Explicit dynamics core: central differences, one-point hex8 with hourglass control, nodal-pressure tet4, solve.explicit (M10 X1) (#27)

* Model: explicit dynamic steps (end time, increment scale and cap, output intervals, initial velocities, rigid walls, hourglass and bulk viscosity controls); deck writers refuse them

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* fem: uniform-strain hex8 and tet4 kinematics, Flanagan–Belytschko hourglass shape vectors, element frequency bound

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Explicit solver crate (L2): central differences with lumped mass, one-point hex8 with Flanagan–Belytschko hourglass control, Bonet–Burton tet4, bulk viscosity, rigid walls, energy account; wave and impact verification

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Engine: solve.explicit and solve.history commands, explicit results in the session and solve.probe; cantilever period against the modal solver

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Docs: explicit solver in the architecture, roadmap (M10 started), parity and literature (Part H)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Simplify: Model::select_step shared by both solvers, Procedure::sets/is_dynamic, fused per-increment passes without allocation, shared element tail, generic command caps

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Catalogue: solve.explicit is ready; solve.history beside solve.probe

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Rebase onto the implicit couplings work: Procedure is no longer Copy

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

---------

Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

crates/explicit/src/lib.rs

@@ -0,0 +1,92 @@
+//! ModelCraft's explicit dynamics solver: transient response of a model's explicit dynamic step
+//! by central-difference time integration.
+//!
+//! The method is the explicit central-difference scheme of T. Belytschko, W. K. Liu, B. Moran,
+//! K. Elkhodary, *Nonlinear Finite Elements for Continua and Structures*, 2nd ed., Wiley 2014
+//! (ch. 6, the flowchart of Box 6.1): with a diagonal (lumped) mass M,
+//! a = M⁻¹(f_ext − f_int), v^{n+½} = v^{n−½} + Δt^n a^n, u^{n+1} = u^n + Δt^{n+½} v^{n+½},
+//! so a time increment is one pass over the elements and a division per degree of freedom.
+//!
+//! - **System** ([`system`]): the model is resolved; one-point hexahedra and nodal-pressure
+//!   tetrahedra with their materials, row-sum lumped masses, prescribed velocities, rigid walls,
+//!   initial velocities and the constant load vector of the step.
+//! - **Elements** ([`elements`]): the uniform-strain hexahedron with Flanagan–Belytschko
+//!   hourglass control (viscous or stiffness), the Bonet–Burton average nodal pressure
+//!   tetrahedron, von Neumann–Richtmyer/Wilkins bulk viscosity, and the element critical time
+//!   increments.
+//! - **Integration** ([`integrate`]): the time loop, kinematic constraints, energy accounting
+//!   with a balance check, history samples and field frames ([`result`]).
+//!
+//! This first version is geometrically linear (small displacements and strains; the elements'
+//! gradients are those of the undeformed mesh) with linear elastic materials, which is what the
+//! analytic verification problems need. Large deformation kinematics with objective stress rates
+//! and inelastic materials come next (docs/solvers/literature.md, Part F, X2).
+//!
+//! Everything is sequential, with elements in label order and no parallel reductions, so the
+//! same model gives the same numbers bit for bit; sizes, increments and output are capped by
+//! [`Limits`].
+#![deny(clippy::unwrap_used, clippy::expect_used, clippy::panic, clippy::unimplemented, clippy::todo, clippy::unreachable)]
+#![forbid(unsafe_code)]
+// Small fixed-size vector kernels read as the textbook formulas with index loops.
+#![allow(clippy::needless_range_loop)]
+
+pub mod elements;
+pub mod integrate;
+pub mod result;
+pub mod system;
+
+pub use integrate::solve_explicit;
+pub use result::{ControllingElement, Energies, ExplicitResult, Frame, History};
+
+#[derive(Debug, Clone, PartialEq, thiserror::Error)]
+pub enum Error {
+    #[error(transparent)]
+    Model(#[from] modelcraft_model::Error),
+    #[error("invalid input: {0}")]
+    Invalid(String),
+    #[error("not supported yet: {0}")]
+    NotSupported(String),
+    /// An element kernel failed (inverted geometry, …).
+    #[error("element {label}: {source}")]
+    Element { label: u32, source: modelcraft_fem::Error },
+    #[error("limit reached: {0}")]
+    Limit(String),
+    /// The solution stopped being finite.
+    #[error("the solution became unstable: {0}")]
+    Unstable(String),
+    /// A broken internal invariant (a bug), reported instead of a panic.
+    #[error("internal error: {0}")]
+    Internal(String),
+}
+
+pub type Result<T> = std::result::Result<T, Error>;
+
+impl Error {
+    /// A kernel error, naming the element.
+    pub fn element(label: u32, source: modelcraft_fem::Error) -> Error {
+        Error::Element { label, source }
+    }
+}
+
+/// Caps on the size and length of a run.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub struct Limits {
+    /// Degrees of freedom of the mesh.
+    pub max_dofs: usize,
+    /// Time increments; the step's own cap applies too, whichever is lower.
+    pub max_increments: u64,
+    /// Numbers kept in field frames and histories together (8 bytes each).
+    pub max_output_values: usize,
+}
+
+impl Limits {
+    pub const MAX_DOFS: usize = 6_000_000;
+    pub const MAX_INCREMENTS: u64 = modelcraft_model::steps::MAX_INCREMENTS;
+    pub const MAX_OUTPUT_VALUES: usize = 50_000_000;
+}
+
+impl Default for Limits {
+    fn default() -> Limits {
+        Limits { max_dofs: Limits::MAX_DOFS, max_increments: Limits::MAX_INCREMENTS, max_output_values: Limits::MAX_OUTPUT_VALUES }
+    }
+}