Traction Condition¶

The traction boundary condition prescribes a surface load (force per unit area) on the boundary \(\Gamma\):

where \(\bar{\mathbf{t}}\) [Pa] is the user-supplied traction vector and \(\mathbf{n}\) is the outward unit normal. This is the natural (Neumann) boundary condition of the elasticity equation: untreated boundaries inherit \(\bar{\mathbf{t}} = \mathbf{0}\) (traction-free).

When to use this¶

• Distributed mechanical loads — pressure on a vessel wall, wind load on a panel, snow load on a roof.
• Point / patch forces approximated as a uniform traction on a small marker.
• Maxwell-stress coupling — surface tractions exported from an electromagnetic model (motor air gap, magnetic bearing, MRI gradient coil) applied as a structural load.
• Calibration / benchmarks with analytic traction profiles (cantilever tip load, pressure-loaded plate).

Usage¶

A constant traction tuple:

from mufem.structural import TractionBoundaryCondition

load_bc = TractionBoundaryCondition(
    name="Load",
    marker="Beam::Loaded" @ Bnd,
    traction=(0.0, -1000.0, 0.0),  # [Pa], pointing in -y
)

structural_model.add_condition(load_bc)

A vector coefficient for spatially- or time-dependent loads:

import mufem

cff_traction = mufem.CffExpressionVector(
    "[0, -1e5 * (1 - x()/L), 0]"
)

ramped_load = TractionBoundaryCondition(
    name="Ramped Load",
    marker="Beam::Top" @ Bnd,
    traction=cff_traction,
)