******************** Pseudo-Solid Lame MU ******************** :: Pseudo-Solid Lame MU = {model_name} {float_list} [M/Lt2] ----------------------- **Description / Usage** ----------------------- This card is required only for *TOTAL_ALE* mesh motion types (see *Mesh Motion* card) and is used to specify the model for the Lame coefficient :math:`\mu` for the mesh motion solid constitutive equation (see Sackinger et al. 1995, and *Solid Constitutive Equation* card); this coefficient is equivalent to the shear modulus G. The model list here is abbreviated as compared to the *Lame MU* card as these properties are just used to aid in the elastic mesh motion, independent of the material. Definitions of the input parameters are as follows: +-----------------+------------------------------------------------------------------------------------------+ |{model_name} |Name of the Lame’ Mu coefficient model. This parameter can have one of the following | | |values: **CONSTANT** or **CONTACT_LINE**. | +-----------------+------------------------------------------------------------------------------------------+ |{float_list} |One or more floating point numbers ( through ) whose values are | | |determined by the selection for {model_name}. These are identified in the | | |discussion of each model below. | +-----------------+------------------------------------------------------------------------------------------+ The details of each model option are: +----------------------------------------------------+------------------------------------------------------------------------------------------+ |**CONSTANT** |For the **CONSTANT** model, {float_list} is a single value: | | | * - Standard value of the μ (or the shear modulus G for the mesh). See | | | *Pseudo Solid Constitutive Equation* card. | +----------------------------------------------------+------------------------------------------------------------------------------------------+ |**CONTACT_LINE** |The CONTACT_LINE model is a convenient way to control mesh deformation near a fixed point | | | | | |and is normally used ONLY for *TOTAL_ALE* or *ARBITRARY Mesh Motion* types. This model | | |enables the user to make the shear modulus much larger near the contact line (fixed point)| | |than far away from the contact line, so that elements near the contact line are forced to | | |retain their shape. The shear modulus in this model varies inversely with distance from | | |the contact line: | | | | | |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. | | | | | |.. figure:: /figures/375_goma_physics.png | | | :align: center | | | :width: 90% | | | | | |*r* is the distance from the fixed point, :math:`r_0` is a decay length, :math:`G_0` is | | |the modulus far from the contact line, and :math:`G_0`+`r_0` is the modulus at the contact| | |line. | | | | | |The {float_list} contains four values for this model, where: | | | | | | * - Node set number of the fixed point (converted to an integer by *Goma*) | | | * - :math:`G_0` (or :math:`\mu_0`) | | | * - :math:`G_1` | | | * - :math:`r_0` | +----------------------------------------------------+------------------------------------------------------------------------------------------+ ------------ **Examples** ------------ :: Pseudo-Solid Lame MU = CONSTANT 0.5 This card specifies that the current material have a constant shear modulus of 0.5 for the mesh elasticity. Note that the real-solid mesh Lame MU is set with the *Lame MU* card. ------------------------- **Technical Discussion** ------------------------- It is best to consult the TALE tutorial (Schunk, 1999) for details of this card. -------------- **References** -------------- 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 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.