The Solid Mechanics Interface

The interface (

), found under the branch (

) when adding a physics interface, is intended for general structural analysis of 3D, 2D, or axisymmetric bodies. In 2D, plane stress or plane strain assumptions can be used. The Solid Mechanics interface is based on solving the equations of motion together with a constitutive model for a solid material. Results such as displacements, stresses, and strains are computed.

The functionality provided by the Solid Mechanics interface depends on the products you are using. The Acoustics Module, MEMS Module, and Structural Mechanics Module add several features, for example geometric nonlinearity and advanced boundary conditions such as contact, follower loads, and nonreflecting boundaries.

The default material is a Linear Elastic Material. With either the Nonlinear Structural Materials Module or the Geomechanics Module, the physics interface is extended with more materials, for example, material models for plasticity, hyperelasticity, creep, and concrete. You can also add your own material models using an External Stress-Strain Relation


	For a detailed overview of the functionality available in each product, visit http://www.comsol.com/products/specifications/

When this physics interface is added, these default nodes are also added to the — , (a boundary condition where boundaries are free, with no loads or constraints), and . Then, from the toolbar, you can add other nodes that implement, for example, solid mechanics material models, boundary conditions, and loads. You can also right-click to select physics features from the context menu.

Settings

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is solid.

2D Approximation


	From the 2D approximation list, select Plane strain (the default), Plane stress, or Generalized Plane Strain. Plane strain is relevant when the 2D model can be considered as a cut through an object that is infinitely long in the out-of-plane direction or as a soft object confined between rigid walls. The strain in the out-of-plane direction is assumed to be zero. Plane stress is relevant for structures that are thin in the out-of-plane direction, such as a thin plate. When using plane stress, the Solid Mechanics interface solves for the out-of-plane strain displacement derivative, , in addition to the displacement field u, in order to fulfill the zero stress criterion. The generalized plane strain condition is similar to plane strain but allows for a nonzero out-of-plane strain. It is representative for the central parts of a long object, which is stress free at the ends. For more information see the theory section. When combining Solid Mechanics with other types of physics, there is often an assumption that the out-of-plane extension is infinitely long. This is the case in, for example, Acoustic-Structure interaction problems. In these cases, Plane strain is usually the correct choice. Select Out-of-plane mode extension (time-harmonic) to prescribe an out-of-plane wave number to be used in mode analysis, eigenfrequency, and frequency domain studies. When selected, enter the Out-of-plane wave number kz. Note that the input value will only be taken into account in eigenfrequency and frequency domain studies. For mode analysis, the out-of-plane wave number is computed as an eigenvalue. For more information, see Out-of-plane and Circumferential Modes in the Structural Mechanics Theory chapter.

Axial Symmetry Approximation


	Select Circumferential mode extension (time-harmonic) to prescribe a circumferential wave number to be used in eigenfrequency or frequency domain studies. When selected, enter the Circumferential mode number m. For more information, see Out-of-plane and Circumferential Modes in the Structural Mechanics Theory chapter.


	Eigenfrequency Analysis of a Free Cylinder: Application Library path Structural_Mechanics_Module/Verification_Examples/free_cylinder.

Thickness


	For 2D components, enter a value or expression for the Thickness d. The default value of 1 m is suitable for plane strain models, where it represents a unit-depth slice, for example. For plane stress models, enter the actual thickness, which should be small compared to the size of the plate for the plane stress assumption to be valid. When manually combining Solid Mechanics with other physics interfaces, you must make sure that the same thickness assumption is used everywhere. In most cases, the default settings will be correct since interfaces which do not have an explicit thickness property will implicitly assume unit thickness. Use a Change Thickness node to change thickness in parts of the geometry if necessary.

Structural Transient Behavior

From the list, select (the default) or . Use to treat the dynamic behavior as quasi-static (with no mass effects; that is, no second-order time derivatives). Selecting this option gives a more efficient solution for problems where the variation in time is slow when compared to the natural frequencies of the system. The default solver for the time stepping is changed from Generalized alpha to BDF when is selected.

For problems with creep, and sometimes viscoelasticity, the problem can be considered as quasi-static. This is also the case when the time dependence exists only in some other physics, like a transient heat transfer problem causing thermal strains.

Reference Point for Moment Computation

Enter the coordinates for the xref (variable refpnt). The resulting moments (applied or as reactions) are then computed relative to this reference point. During the results and analysis stage, the coordinates can be changed in the section in the result nodes.

Typical Wave Speed

The typical wave speed cref is a parameter for the perfectly matched layers (PMLs) if used in a solid wave propagation model. The default value is solid.cp, the pressure-wave speed. To use another wave speed, enter a value or expression in the field.

Note: This section is only available with COMSOL products that include PMLs (see http://www.comsol.com/products/specifications/)

Discretization

In the Solid Mechanics interface you can choose not only the order of the discretization, but also the type of shape functions: Lagrange or serendipity. For highly distorted elements, Lagrange shape functions provide better accuracy than serendipity shape functions of the same order. The serendipity shape functions will however give significant reductions of the model size for a given mesh containing hexahedral, prism, or quadrilateral elements.

The default is to use shape functions for the . Using shape functions will give what is sometimes called constant stress elements. Such a formulation will for many problems make the model overly stiff, and many elements may be needed for an accurate resolution of the stresses.

Dependent Variables

The physics interface uses the global spatial components of the u as dependent variables. The default names for the components are (u, v, w) in 3D. In 2D the component names are (u, v), and in 2D axisymmetry they are (u, w). You can however not use the “missing” component name in the 2D cases as a parameter or variable name, since it is still used internally.

You can change both the field name and the individual component names. If a new field name coincides with the name of another displacement field, the two fields (and the interfaces which define them) share degrees of freedom and dependent variable component names. You can use this behavior to connect a Solid Mechanics interface to a Shell directly attached to the boundaries of the solid domain, or to another Solid Mechanics interface sharing a common boundary.

A new field name must not coincide with the name of a field of another type (that is, it must contain a displacement field), or with a component name belonging to some other field. Component names must be unique within a model except when two interfaces share a common field name.


	In the COMSOL Multiphysics Reference Manual see Table 2-3 for links to common sections and Table 2-4 to common feature nodes. You can also search for information: press F1 to open the Help window or Ctrl+F1 to open the Documentation window.

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Domain, Boundary, Edge, Point, and Pair Nodes for Solid Mechanics

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Solid Mechanics Theory

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Selecting Discretization

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Stresses in a Pulley: Application Library path

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Eigenvalue Analysis of a Crankshaft: Application Library path