The Elastic Waves, Time Explicit Interface
The Elastic Wave, Time Explicit interface (), found under the Acoustics>Elastic Waves branch () when adding a physics interface, is used to model the transient propagation of elastic waves in linear elastic materials. It is used to compute the velocity and strain field in solids with propagating elastic waves. It is suited for time-dependent simulations with arbitrary time-dependent sources and fields. In general, the interface is suited for modeling the propagation of elastic waves over large distances relative to the wavelength, for example, ultrasound propagation for nondestructive testing (NDT), or seismic waves. The dedicated Fracture condition is useful for many of these applications. The interface includes absorbing layers that are used to set up effective nonreflecting like boundary conditions (sponge layers).The interface exists in 2D, 2D axisymmetric, and 3D.
The interface is based on the discontinuous Galerkin (dG or dG-FEM) method and uses a time explicit solver. The method is very memory efficient and can solve problems with many million degrees of freedom (DOFs). The method is also well suited for distributed computing on clusters.
The Elastic Waves, Time Explicit interface can be coupled to the The Pressure Acoustics, Transient Interface and The Nonlinear Pressure Acoustics, Time Explicit Interface, using either the Acoustic–Structure Boundary, Time Explicit or the Pair Acoustic–Structure Boundary, Time Explicit multiphysics couplings.
For modeling linear piezoelectric wave problems the Elastic Waves, Time Explicit interface can be coupled to the Electrostatics interface, see The Piezoelectric Waves, Time Explicit Interface.
The interface solves the equations of linear elasticity in the velocity-strain formulation. The dependent variables are the structural velocity v (SI unit: m/s) and the strain E (SI unit: 1). Structural damping can be introduced using a Rayleigh damping model. The displacement u (SI unit: m) can be computed by solving additional equations, see Computing the Displacement in the Elastic Waves, Time Explicit.
When the Elastic Wave, Time Explicit interface is added, these default nodes are also added to the Model Builder: Elastic Wave, Time Explicit Model, Free, and Initial Values.
Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and sources. You can also right-click Elastic Wave, Time Explicit to select physics features from the context menu.
Settings
The Label is the default physics interface name.
The Name 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 Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is elte.
Isotropic-Anisotropic Sample: Elastic Wave Propagation. Application Library path Acoustics_Module/Elastic_Waves/isotropic_anisotropic_sample
Ground Motion After Seismic Event: Scattering off a Small Mountain. Application Library path Acoustics_Module/Elastic_Waves/ground_motion_seismic_event
Propagation of Seismic Waves Through Earth. Application Library path Acoustics_Module/Elastic_Waves/seismic_waves_earth
Filter Parameters for Absorbing Layers
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. In the Filter Parameters for Absorbing Layers section you can change and control the values set for the filter used in the Absorbing Layers in Elastic Waves, Time Explicit. The values of the filter parameters defined here are used in all absorbing layers added to the model and they override the value of filter parameters enabled in the material model (Elastic Waves, Time Explicit Model). The default values of the filter parameters α, ηc, and s are set to 0.2, 0.01, and 2, respectively. Inside the absorbing layer, it is important to use a filter that is not too aggressive since this will result in spurious reflections.
For general information about the filter see the Filter Parameters section under Wave Form PDE in the COMSOL Multiphysics Reference Manual.
2D Approximation
The out-of-plane components of the velocity and the strain are not computed per default in 2D. This can be changed by selecting Include out-of-plane components check box. It can be relevant in some cases, for example for anisotropic materials, where the out-of-plane velocity may become different from zero for in-plane loads. This formulation is often referred to as 2.5D. Note that this comes at an extra computational cost.
This section is only visible in 2D components.
Thickness
Enter a value for the thickness d. The default value is 1[m], which represents a unit-thickness slice. Make sure that the same thickness assumption is used everywhere when you manually combine the Elastic Waves, Time Explicit interface with other physics interfaces that have an explicit thickness property. When using other unit systems than the default SI system, you need to pay special attention to the values of this property.
This section is only visible in 2D components.
Transient Mesh Settings
Enter the Maximum frequency to resolve fmax (the default is 1000[Hz]). This value is used to set up the physics-controlled mesh for the Elastic Waves, Time Explicit interface.
Discretization
In this section you can select the discretization for the Structural velocity and Strain tensor, Voigt notation. Per default both are set to Quartic (4th order). Using quartic elements together with a mesh size equal to approximately half the wavelength to be resolved, leads to the best performance when using the dG method.
When solving Elastic Waves, Time Explicit, it is important to have consistent settings for the Geometry Shape Function and the Discretization of the physics. The Automatic setting for the Geometry shape function (in the Curved Mesh Elements section on the Components node’s settings) may results in a linear geometry representation, if other physics are present in the model. This can lead to numerical errors when solving as the default is to use fourth-order (Quartic) spatial discretization of the dependent variables. To remedy this change the Geometry shape function to Quadratic Lagrange.
Dependent Variables
The dependent variables (field variables) are the Structural velocity and Structural velocity, components, and the Strain tensor, Voigt notation and Strain tensor, Voigt notation, components. The names can be changed, but the names of fields and dependent variables must be unique within a model.