Wire Mesh: The Basics

What is wire mesh? Definition, features, and target markets

A great variety of shapes and applications

“Wire mesh” is a generic term. It refers to two- or three-dimensional lattices made from two or more metallic wires which are linked to one another by different processes such as welding, weaving, netting, or knitting. Wire mesh products are widely employed for reinforcing, armoring, protecting, fencing, carrying, and displaying operations in a large variety of areas. Therefore, we can say that wire mesh is an integral part of industry and everyday life.

Wire mesh materials and their main characteristics

Wires used for wire mesh can be made from carbon steel, galvanized steel, PVC coated steel, stainless steel, aluminum, copper, copper alloys (brass and bronze), and other metals or alloys. Let’s take a look at the differences between all of these materiales.

Mesh made of carbon steel wires has high strength, is magnetic, and can be galvanized or cladded with a PVC coating or painted to prevent corrosion. Mesh made from stainless steel wires, instead, does not require further surface treatment. While on the one hand, copper wire is ductile, has a high thermal and electrical conductivity, and is resistant to atmospheric corrosion; on the other, brass wire has excellent abrasion-resistance properties. Last but not least, bronze wire is effective against atmospheric agents, while aluminum wire can be used to fabricate extremely lightweight and corrosion-resistant mesh.

The material selection, the wire diameter, and the manufacturing method depend on the application of the mesh products and their conditions of use.

Welded wire mesh

Welded wire mesh is a metal wire screen usually made out of two low carbon steel wires or stainless steel wires which are joined to each other at right angles and welded at the crossing points. Typical examples are reinforcement meshes for concrete components. In addition, there are industrial meshes in light or heavy design that can be used as fences, partition walls, and protective gratings.
Three-dimensional welded wire meshes are used e.g. as shopping carts, shopping baskets, and goods displays in supermarkets, as well as trays for domestic appliances, ventilation grids, cable guides, and cages for animals. Another example are electro-welded gabions, which are intended to hold masses of stone together and are enjoying growing popularity in landscaping.
Welded wire mesh is characterized by high stability and rigidity, and can also be welded into frame constructions.

Wire fabrics

Wire fabrics, also called woven wire cloth, are flat structures made of two wire systems intersected by weaving.

Typical products are airbag filters and other reinforcement fabrics, transportation and process belts, sieves, as well as pulp and paper processing systems. Wire fabrics are also used in filtration, separation, and cleaning processes for the mining, petrochemical, pharmaceutical, and food processing industries. Furthermore, wire fabrics act as a radio and microwave shielding, spark protection, or as fly nets.
Last but not least, woven wire cloth is applied in architectural applications such as façade covering. Depending on the material of the wires and the wire cloth texture, wire fabrics can be as soft and flexible as silk, or as rigid and durable as a steel plate.

Wire nettings

Wire nettings include the so-called wire netting fences. Examples are the rectangular nettings which are often used to enclose properties. Hexagonal nettings are used in agriculture and forestry to enclose woodland plantations and protect them against animals. Such kind of netting also serves as a slope reinforcement and protection against rock slides and avalanches.
There is also a special group of nettings, that is round braids, which act as a reinforcement of hoses and cables or as shielding of cables against electromagnetic interferences.

Netting | Fishing, Crafts & Weaving

netting, in textiles, ancient method of constructing open fabrics by the crossing of cords, threads, yarns, or ropes so that their intersections are knotted or looped, forming a geometrically shaped mesh, or open space. Modern net fabrics are produced not only by the netting method but also by weaving, knitting, and crocheting and are usually machine-made. The meshes vary greatly in shape and size, and weights range from fine to coarse. Tulle is an extremely fine, soft net with hexagonal-shaped meshes, and bobbinet also has hexagonal meshes. Nets having square corners, with knots in each of the corners, are frequently used in fishing and are popular for curtains.

Apparel and home-furnishing uses of nets include veils, hat shapes, dresses, curtains, and trimmings. Industrial applications include fishing and cargo nets.

Concepts of Hexahedral Meshing

In general, there are two ways to define a hexahedral mesh. We will briefly introduce their principles before discussing details of the implementation in CST Studio Suite.

Automatic Mesh Generation with Expert System
This is probably the most effective way of working with CST Studio Suite. The mesh generator determines the important features of your structure and automatically creates a mesh, which represents your structure and the fields equally well. This means that the frequency range and dielectrics, metallic edges, etc. are considered by the expert system, but certain mesh properties for individual shapes can also be set manually. Project Templates facilitate the mesh creation, and with a little bit of experience, you will be able to obtain reliable solutions in minimal time.

Adaptive Mesh Refinement (Energy Based or Expert System Based)
Adaptive meshing replaces your expertise by repeatedly running the simulation and evaluating the solutions. Usually regions with high field concentration or field gradients are recognized where the mesh needs to be locally refined. If the deviation in the results falls below a given accuracy level, the adaptation terminates. This approach always improves the start solution at the expense of simulation time. Since the CST Studio Suite expert mesher always guarantees a reasonable initial mesh and thus a good starting solution for the mesh adaptation process, the number of passes will normally be small.

This following diagram shows the comparison of Expert System meshing based on project templates and adaptive mesh refinement.

Mesh generation methods: Expert System based on project templates and Adaptive Mesh Refinement

However, modifications to the structure force conventional mesh adaptation algorithms to start again from the beginning with each and every change of a parameter. Therefore the adaptive expert system hexahedral mesh refinement trains the expert system for a given structure. It can then maintain the mesh properties while the associated structure parts are slightly modified.

You can increase your own expertise on mesh generation by analyzing the steps taken by the adaptive mesh refinement. You can use this knowledge to manually tune the mesh to increase the simulation speed for subsequent simulations.

The strategies for mesh generation are quite different for high frequency problems as compared to low frequency applications.

Automatic Mesh Generation with Expert System

After this overview of meshing techniques, we go into the details of CST Studio Suite’s hexahedral mesh generation for high frequency problems. The expert system uses lots of parameters controlling the mesh generation, having either local or global influence on the mesh. There are a few settings which you may frequently modify in order to obtain highly efficient meshes. Let's start with the most important global ones:

Maximum Cell: the largest allowed cell size (all cells should have dimensions smaller than this value). The maximum cell is given by cells per wavelength or geometrical dimensions of the structure. The highest frequency of interest determines the smallest wavelength and thus dominates this value for high frequency applications.

Minimum Cell: the smallest allowed cell size (all cells should have dimensions larger than this value). The minimum cell is defined as fraction (ratio) from maximum cell or as absolute value.

Refinement at PEC-edges: factor which determines how much finer the cells should be around PEC edges, which are known to have singular behavior of electric field values.

These parameters are also set by the Project Templates and the expert-system based  Adaptive Mesh Refinement. The global mesh settings can be changed in the Mesh Properties (Hexahedral) dialog.            

Recommended Initial Hexahedral Discretization

The purpose of this section is to provide guidelines for the discretization of some typical types of structures using hexahedral meshes. We also recommend visiting a special training class on this topic. Please contact your support center for details.

Coaxial Structures

The following picture shows the coarsest recommended discretization for a coaxial structure as it may, for example, be used as initial mesh for adaptive mesh refinements:

Make sure to adjust the Mesh settings so that you have mesh lines at the center of the coaxial structures as well as at the inner and outer radii.

Planar Structures

Planar structures are usually quite sensitive in regard to meshing. We strongly recommend using the corresponding Project Template to adjust the meshing parameters to this type of structure.

One of the most critical settings is the choice of the Minimum Cell parameter, which limits the allowed refinement. The expert system automatically identifies the small thickness of the conductors and avoids snapping the mesh lines to these tiny steps. Therefore, the Mesh line ratio limit can normally be chosen relatively large. However, sometimes planar structures have small distances between structure edges in the metallization planes. In such cases, it must be carefully decided whether to place mesh lines at these positions.

We strongly recommend that you inspect your mesh carefully and, in case of unwanted merging of mesh lines, increase the Mesh line ratio limit parameter accordingly.

Furthermore, we recommend using at least 1-2 mesh lines across the width of the microstrip’s top conductor and 1-3 mesh lines along the height of the substrate.

Helical Structures

The following picture shows the recommended initial discretization for a helical structure:

We recommend using at least 1-2 mesh lines across the diameter of the helix’s cross-section. Furthermore, 3-5 mesh lines should be used along the helix’s axis in between the turns.

In cases where the diameter of the cross-section is very small, you should also consider modeling the helix as an infinitely thin PEC wire.

Mesh Tuning

So far we have briefly discussed how to obtain first simulation results with a reasonable initial mesh with minimal effort spent on the meshing process. If you now feel confident with the global parameters and switches, let's go on to improve the mesh with respect to simulation time and memory requirements. Please note that there is an additional section on Transient Solver Performance Improvements .

Mesh Feedback

The mesh node of the Navigation Tree can provide useful feedback to the user about the discretization of the model onto the Hexahedral mesh.

The Transient solver and the TLM solver will show the connectivity of Wires, Discrete edge ports and Lumped edge Elements. The end points of these one dimensional entities that are connected to ground (metal) or dangling in free space will be color coded and marked on the 3D model.

The Connectivity Tree for the TLM solver will be shown here. This is very similar to the Connection Tree display that is provided for the Transient solver (Check > Electrical Connections > Connection Tree...). Groups of objects that are electrically connected will be shown and dots are displayed in the 3D view for each connection point between two objects. The TLM solver will report other issues that are encountered during discretization that are considered worthy of user attention. Long thin conductors could become broken into separated parts on coarse meshes. A single object could connect to itself on a mesh with cells that are larger than an important gap in the object. Wires or cables could intersect with discretized metal objects at unexpected locations. The solver will also report locations where it finds conductors that are ‘weakly connected’. This means two objects or two parts of the same object are connected together only on a single cell corner. Better current flow is established if the connection is on a cell edge or face and if the connectivity path here is critical a finer mesh is advised.

Local Mesh Properties for Hexahedral Mesh

Besides global mesh controls, acting on all objects and materials in a simulation domain, CST Studio Suite also offers local mesh properties, which only influence a certain number of objetcs. After selecting one or more objects and pressing the right mouse button, you can open the Local Mesh Properties dialog box from the context menu and afterwards apply special mesh settings for this selected group. Afterwards those local mesh properties are accessible in the Navigation Tree under Groups > Mesh Groups, where they can also be later changed.

Difference between New Default and Legacy Mesh Engine

Recently a new hexahedral mesh engine has been introduced, which behaves slightly different than the previous mesh engine. In most cases, the new engine should be more efficient and robust in terms of mesh quality, simulation speed and accuracy. The mesh engine, used as default until v2013, is still available under the name "legacy". CST-Projects generated in older versions (up to v2013) automatically use the legacy mesh, so results and run times should not show major changes.

The first visual difference:  the legacy uses so-called fixpoints, whereas as the new engine uses so-called snapping planes. Snapping planes have the advantage of being more general. With those snapping planes, volumes, planes, edges can be distinguished easier than in the older fixpoint-based system. In the "Specials..." Dialogue of new Mesh Engine, further powerful snapping options are available.

In addition, the following differences between legacy and new hexahedral mesh engines exist:

Performing a single simulation does not provide any information about the accuracy of the solution. The FI method guarantees that the discretization error decreases with an increasing number of mesh cells. This property can be used to check the accuracy by refining the mesh, re-running the simulation and comparing the results. It is, however, important to find a good compromise between mesh density (affecting the simulation time) and accuracy.

The Project Templates try to adjust the global mesh settings to the particular kind of structure in order to obtain reasonable accuracy. The resulting mesh can then be used as an initial mesh for a subsequent mesh adaptation run.

The following picture shows how the adaptive process is activated, e.g. for the transient solver by simply checking the Adaptive mesh refinement option:

he previous one. In other words, the number of mesh cells increases by about 70 % from pass to pass.
This adaptation strategy is a field-based approach that delivers mesh refinement in strategically important regions. The disadvantage of this method is that the refinement regions are coupled neither to the structure parts nor to the global meshing parameters. Parameter studies and optimizations will therefore lead to repeated adaption runs, which negatively affect the overall performance.

Adaptive expert system mesh refinement
The major difference between this strategy and the Energy based refinement is that the former adjusts the expert system’s parameters directly. As a result of this approach, the expert system is trained for a particular structure so that the same settings can be kept for subsequent calculations.
The contents of the adaptive mesh refinement dialog box change if the Refinement strategy is set to Expert system based:
The Mesh increment parameter determines the absolute increase for the "Maximum Cell"  values (Cells per wavelength, Fraction of max model edge) per adaptation pass.

At the end of a successful expert system based mesh adaptation, CST Studio Suite informs you that the expert system has been trained to yield accurate results for this structure. This means that it will not be necessary to start further adaptation runs with this structure since the quality of the mesh will be maintained even if you slightly change the geometry during parametric sweeps or automatic optimizations.

Finite Integration Method and Perfect Boundary Approximation

An outstanding feature of CST Studio Suite is the implementation of the

Finite Integration Method

(FI-Method) in conjunction with the

Perfect Boundary Approximation

(PBA). The simulated structure and the electromagnetic fields are mapped to hexagonal mesh.

PBA mesh: Besides the sufficient sampling of the fields, it is very important to obtain a good approximation of the structure within the mesh. This is performed by Perfect Boundary Approximation (PBA), which "maps" the structure from the continuous world into the mesh of the discrete world.

The figure below illustrates the convergence for the PBA algorithm compared to a standard staircase method for an example with analytic solution: the computation of one eigenvalue for a spherical resonator.

It is obvious that the PBA method quickly leads to a very good accuracy while the staircase method is converging very slowly.

Structure Treatment by Automesh: To make sure that the structure is represented as well as possible, the automatic mesh generator tries to create the mesh such that critical structure elements are located on mesh lines or planes. This is accomplished by creating a number of snapping planes for important structure parts. For a very accurate discretization of the structure these mesh lines might be necessary, but small local mesh steps increase the simulation time.

To avoid such problems, the Minimum cell can be limited (e.g. as fraction from Maximum Cell) . This forces the automatic mesh generator to produce a mesh where the absolute ratio between the highest and the smallest distance between mesh lines is below a certain limit (see Mesh Properties).

Mesh and PEC Edges: At PEC edges, singularities of the electromagnetic fields occur. This means that the fields vary significantly near such edges. To obtain a good approximation of this behavior, the most straight-forward method is to increase the spatial sampling rate there (see Special Mesh Properties - Refine), which is also done automatically by the project wizard for e.g. planar structures.

A second, more sophisticated possibility is to use the corner correction method, which is activated by default. The corner correction uses a singularity model for PEC edges. It is based on analytical models to obtain a better representation of the electromagnetic fields (see Special Mesh Properties - Discretizer).

See also

Mesh and Simulation, Mesh View (Hexahedral), Mesh Properties (Hexahedral), Adaptive Mesh Refinement (Transient), Special Mesh Properties (Hexahedral) - Refine, Local Mesh Properties (Hexahedral)