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### Macroscale

## Macroscale Materials Simulation Tools

This page contains the following macroscale materials simulation tools:

- Creep deformation in RF-MEMS
- Gibbs— Symbolic Computation of Materials Thermodynamics
- OOF2
- Powder Compaction
- Thin-Film and Multi-Element Thermoelectric Devices Simulator
- One-Dimensional Finite Element Method Example

### Creep deformation in RF-MEMS

This tool simulates the response of a radio frequency MEMS switch fabricated at Purdue’s Birck Nanotechnology Center for our Center on the Prediction of Reliability, Integrity and Survivability of Microsystems (PRISM).

RF-MEMS devices are capacitive switches in which a membrane is moved to change the capacitance between the RF signal and ground. The metallic membrane in the PRISM device is made of polycrystalline Nickel with a thickness between 1 to 5 mm. The center metal conductor carries the RF signal and the actuation voltage. When no voltage is applied the membrane remains undeflected and the air gap of about 3 mm leads to a low capacitance; for sufficiently high applied voltages the membrane deflects and becomes in contact with the dielectric leading to an increase in capacitance of several orders of magnitude.

The deflection of the metal membrane due to the electrostatic force can be modeled using Euler-Bernoulli’s beam theory. To calculate the deflection, w(x), we assume that the middle plate remains flat while the four legs deform as cantilever beams of length L, width W and thickness t with an applied force F distributed equally among the four legs. The electrostatic force between the electrode and the beam is modeled using a parallel plate capacitor model.

**Gibbs— Symbolic Computation of Materials Thermodynamics**

### OOF2

OOF2 is public domain finite element analysis software created at the National Institute of Standards and Technology (NIST) to investigate the properties of microstructures. At the simplest level, OOF2 is designed to understand the effects of far fields (boundary conditions) on the local microstructural fields, or to assess the mechanical, electrical, and thermal reliability of a material with a complex topology.

OOF2 allows the user to study the thermal, electrical, and stress fields in a microstructure, along with couplings such as piezoelectricity, pyroelectricity, and thermal expansion. OOF2 can also perform crystallographic analyses of polycrystalline materials by using tensor form material properties.

The inputs necessary to perform a simulation include: 1) a microstructure (real micrograph or computer generated), 2) material properties and 3) boundary conditions. The specified information enables OOF2 to simulate the multiphysical properties, thus allowing to analyze and engineer the effect of microstructure.

The OOF2 manual can be found at: http://ww.ctcms.nist.gov/~langer/oof2man/index.html

You can find the OOF2 reference manual at: http://www.ctcms.nist.gov/~langer/oof2man/Chapter-Reference.html

OOF2 homepage: http://www.ctcms.nist.gov/oof/oof2

#### Related Content

### Powder Compaction

This tool calculates the microstructure evolution of compressible granular systems at high levels of confinement. The microstructure evolution is determined from three-dimensional particle mechanics static calculations of noncohesive frictionless monodispersed granular systems comprised by weightless spherical particles with radius d=0.440mm. Two different elastic materials are considered and the die-compaction of mixtures of different volume fraction can be simulated. The walls of the cylindrical container and of the punches are assumed rigid.

### Thin-Film and Multi-Element Thermoelectric Devices Simulator

This tool simulates both micro-scale thin-film thermoelectric devices and large-scale multi-element thermoelectric modules for cooling and power generation. This simulation tool is intended to simulate the operations of TE devices under various circumstances and boundary conditions. Both micro-scale thin-film TE devices and large-scale multi-element TE modules can be simulated. One of the advantages of this tool is that users can choose an independent variable such as design parameters of the TE device, and simulation conditions, and simulate the device performances as a function of the independent variable. This is very useful for users to optimize their TE device design suitable for the operating conditions.

### One-Dimensional Finite Element Method Example

This tool is intended for use in understanding and practicing the basics of the finite element method (FEM) in one dimension (1D).

The tool consists of a pair of Jupyter notebooks. The scripts in these notebooks solve the one-dimensional problem described below. The notebooks allow these scripts to be modified, run, and downloaded.

One of the notebooks is written in Octave, which is similar to Matlab. The remaining script is written in Python 3.0. The scripts are functionally identical otherwise.

The scripts solve for the displacement **u** of the bar loaded as shown in Figure 1. Both the analytical and numerical solutions are presented in this resource.

Figure 1: A bar of cross-sectional area **A**, Young's modulus **E**, and length **L**, fixed at the left end and loaded with a force **F** at the right end. The displacement **u** at the right-hand side is to be determined.

Figure 2: Division of the rod into **N** elements and **N+1** nodes, with each element represented by an equivalent spring of stiffness **k _{i}**.