Polymer Viscosity#

Pseudo-Solid Constitutive Equation = {model_name}

Description / Usage#

This card specifies the constitutive equation used to control mesh motion for arbitrary Lagrangian Eulerian solid mechanics and is required for use with the TOTAL_ALE mesh motion type (see Mesh Motion card). Details are discussed in references provided below.

The single input parameter is the type of model for the constitutive equation:


The name of the constitutive equation; {model_name} can be one of the following:

  • LINEAR - the mesh deformations are assumed to be small and thus simplifies the analysis of strain and stress.

  • NONLINEAR - a nonlinear neo-Hookean elastic model for which the deformations can be large without loss of frame invariance. This is the recommended model (and all materials currently default to NONLINEAR if the mesh is arbitrary).

The following models are allowed but not recommended.

  • HOOKEAN_PSTRAIN - a nonlinear neo-Hookean model with plane strain assumption 2D only).

  • INCOMP_PSTRAIN - an incompressible nonlinear neo-Hookean model with plane strain and a Lagrangian pressure constraint on the volume.

  • INCOMP_3D - Incompressible version of the neo-Hookean solid in a special Segalman formulation that removes the volume-change from the strain tensor (like the INCOMP_PSTRAIN model above), and is specifically designed for 3D applications (not a widely used option).

Note again the requirement that the Mesh Motion type for the material in which this constitutive equation applies must be TOTAL_ALE.


Pseudo-Solid Constitutive Equation = NONLINEAR

This card specifies the mesh motion in the ALE solid region is to conform to the nonlinear elastic model, as described on the Solid Constitutive Equation card. This card is required together with Pseudo-Solid Lame Mu and Pseudo-Solid Lame Lambda cards.

Technical Discussion#

The Pseudo-Solid mesh motion, like the ARBITRARY mesh motion, is governed by the equations of elasticity. These cards, together with the other cards required by the real solid constitutive behavior, are required for ALE solid mechanics. The theory is explained in detail in the provided references. Throughout the boundary condition options, the user will notice an appended _RS. This signifies that the boundary conditions apply to the real-solid elasticity in TOTAL_ALE problems. All other boundary conditions on force and displacement, viz. those without the _RS, are applied to the mesh motion.


GT-005.3: THE NEW TOTAL-ARBITRARY-LAGRANGIAN-EULERIAN (TALE) CAPABILITY and its applicability to coating with/on deformable media, August 6, 1999, P. R. Schunk

SAND2000-0807: TALE: An Arbitrary Lagrangian-Eulerian Approach to Fluid- Structure Interaction Problems, P. R. Schunk (May 2000)

Sackinger, P. A., Schunk, P. R. and Rao, R. R. 1995. “A Newton-Raphson Pseudo-Solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation”, J. Comp. Phys., 125 (1996) 83-103.