Nonlinear Geometry Model Reference

For linear geometry phenomena (infinitesimal strain) and linear materials, the equilibrium equations are linear and can be satisfied in the undeformed configuration. For nonlinear geometry phenomena (large strain) and nonlinear materials, the equilibrium equations are nonlinear and must be satisfied in the deformed configuration. To solve the nonlinear equations, Simcenter STAR-CCM+ updates the stiffness matrix using Newton iteration methods. At each iteration step, the direct solver solves the linearized system of equations.

Theory

See Finite Element Discretization.

Provided by

[physics continuum] > Models > Optional Models

Example Node Path

Continua > [Solid Physics Continuum] > Models > Nonlinear Geometry

Requires

Physics Models:

Solid Stress
Linear Isotropic Elastic

注	For nonlinear geometry, the linear isotropic elastic approximation becomes inaccurate for strains grater than 20%.

Activates

Solver Controls

Solid Stress Solver > Stiffness Matrix Update

See Solid Stress Solver Controls.

Physics Conditions

Surface Load Linearization

See Physics Conditions.

Treatment of Loads in Nonlinear Geometry

Linear geometry applications assume that the loads magnitude and orientation do not change during the simulation. Nonlinear geometry applications require updates of the load orientation, as the surfaces where the loads are applied can significantly change their orientation due to the large deformations. Nonlinear geometry uses follower forces, which are loads that adjust as the structure deforms, so that their orientation relative to the structure geometry remains unchanged.

Simcenter STAR-CCM+ treats the Force, Traction, and Pressure loads according to the rules described in the table below. The rules are independent of the motion model, that can be either Stationary or Solid Displacement:

Force—the force vector (direction and magnitude) is preserved, the corresponding traction changes with deformation when Nonlinear Geometry is active.
Traction—the traction vector (direction and magnitude) is preserved, the force resultant of the segment changes with deformation when Nonlinear Geometry is active.
Pressure—the pressure magnitude is preserved. The direction of the pressure is normal to the surface and changes with the deformation when Nonlinear Geometry is active.


Load	Linear Geometry	Nonlinear Geometry
Force $F$	$t_{0} = F / A_{0}$ where $F$ is preserved for all combinations and $A_{0}$ is the undeformed area.	$t = F / A$ where $F$ is preserved for all combinations and $A$ is the deformed area.
Traction $t$	$F_{0} = t \cdot A_{0}$ where $t$ is preserved for all combinations.	$F = t \cdot A$ where $t$ is non follower.
Pressure $p$	$F_{0} = p \cdot n_{0} \cdot A_{0}$ where $p$ is preserved for all combinations and $n_{0}$ is the normal to the undeformed area.	$F = p \cdot n \cdot A$ where $p$ is follower and $n$ is the normal to the deformed area.

Physics Conditions

Surface Load Linearization

In nonlinear simulations, pressure and traction loads generally depend on the deformation of the surface they are applied to, and therefore on the solution. When you activate this option, Simcenter STAR-CCM+ includes the linearization of the surface area (and, if required, the linearization of the surface normal) in the linearization process underlying the Newton-Raphson scheme (see 位移场求解), improving overall convergence.

This physics condition is available for:

FSI interface solid boundaries, in order to linearize the applied fluid loads and, if required, the effects of dynamic stabilization (see Solid Region > Interface Boundary > Physics Conditions).
surface segments that define either pressure or traction loads (see Segment Conditions and Values).