The simulation of polymer processes permits product designers to consider any geometric or processing condition, as crazy as it may be. It is known in the field of design that during the development of a product, the cost of fixing an error grows exponentially with the time it takes to detect the error. For that reason, the advantage of using simulation as a design tool can be very economical, but there are other reasons: such as decreasing the development time. Using a computer and software with material, process, and product data can lessen the need for tests (experiments) and reduce the costs related to material, staff, and machine time. For this, it is necessary to know as much as possible about the material variables, process conditions, and even the small details about the initial design of the product that will change during the process until the optimal design and/or processing result is obtained. The more information the designer has on it, the more accurate and more exact the simulation and the resulting values of the analysis will be.
HOW COMPUTER AIDED ENGINEERING WORKS
Before Computer Aided Engineering (CAE), it is necessary understand other concepts that are related to it. The development/optimization of products/processes has several areas that include computer-driven tools such as Computer Aided Design (CAD), Computer Aided Manufacturing (CAM), and the one of our interest: Computer Aided Engineering (CAE). Figure 1 shows a list the role of each computer-driven tool during the different phases of the development of the product which can be extrapolated to the industrial process optimization. CAD is used for creating a model of the product and transferring all the information (dimensions, tolerances, specifications) into the PC. CAD models are transferred to the CAE environment to analyze the performance and the processing of the product, and after the product is working perfectly, CAM creates the files for the machining operations and generates the real product . The process is not simple because CAE could find problems with the performance, and it is necessary to have feedback until the CAE results are adequate for the application. Also, the results must be manufacturable, so CAM may advise a return to CAD again. In recent years, CAD interfaces have become linked with CAM and CAE interfaces with different levels of precision.
Figure 1. Function of CAD, CAM and CAE during product development 
Thinking deeply about the natural extension of CAE, its analysis integrates processing, structure, and properties of silicone rubber. It simulates the product functionality and also the process variables for production of the part before the development. The main constituent of CAE is Finite Element Analysis (FEA), which is a numerical method to approximate the solutions of some equations (normally highly complex): in this case, heat transfer for curing or processing and external forces applied to the material, among others. FEA uses data given by the CAD software and converts it into elements that can be used to calculate the equations; once solved, each element contains the answer for the behavior of the material or product during the production process or the application. For silicone rubber, the CAE analysis focuses on the determination of stresses and temperatures in applications or processing, including failure . CAE analysis also must include the inherent characteristics of the silicone rubber such as incompressibility, high deformations (in comparison with metals or ceramics but lower than those of organic rubbers), and the material properties which greatly depend on pressure, temperature, and time. The challenge that the CAE system must also fulfill is to include the non-linearities inherent in the silicone rubber materials and the formulation, that is, the Poisson’s ratio for metals is approximately 0.33 but for polymeric materials it is 0.5 or more. The problem is that these values produce singularities in the simulations, which means, they have no real solutions or cause errors in the simulation.
The CAE functions can be explained in a simple way as follows: a CAD file is converted into discrete points and the points are used to create surfaces which delimit the interior and exterior of the part and therefore are called boundaries. The nodes and elements that form the material are called a mesh and the condition is that all the points must be connected at least with one other. In the early days, the designer had to create the mesh, but fortunately, nowadays mesh generation is automated. Here also, the type of analysis is defined and the reference values are set (that is, material properties such as elastic modulus, tension strength, compression strength, flexion strength, impact values, etc.), depending on the analysis to be done). The temperature and pressure conditions are applied to the exterior boundaries, and CAE determines how the points (the material) change in position and temperature as a function of the temperature, pressures, and time. The movement and change in the temperature are based on the equations and constraints that were previously fed into the system. The system has equilibrium relationships included which stipulate that the part could not be deformed into weird shapes that are not related to reality and are directly related to the boundary conditions.
The most important step during CAE analysis of silicone rubber is the optimization of curing conditions and their effect on the structure and properties of the final product. This analysis includes material changes and heat transfer analysis. When the best parameters are used, they lead to an excellent product quality, an increase in productivity, and energy savings. The numerical calculation of vulcanization can be done using different methods; the idea is to find how the degree of vulcanization changes with the temperature under isothermal conditions. Several models can be used, and, depending on the silicone modeled, they can be simple or more complex. Another of the applications for CAE with silicone rubber products is the analysis of processing and its effect on the part properties, and the correct selection of the mold, cooling and ejection temperature to avoid distortion, warpage, and residual stresses. It can be translated also into processing variables and even in changes in mold design. The third application is how external forces affect the silicone rubber properties or behavior during a specific application. The system uses strain-displacement functions, that is, models that explain how the silicone rubber is deformed by different stress conditions (tension, compression, flexion, etc.). The system uses the stiffness of the silicone rubber as a reference and decides if the equilibrium conditions are satisfactory or not.
CAE becomes more accurate and efficient depending on the computer performance and the types of mathematical models that can be handled. An Artificial Neural Network (ANN), for example, is a computational model based on biological networks which considers input variables, outputs variables, and hidden layers which contain information on the relationships between the input and output variables (which is normally non-linear). The information obtained with ANN even permits extrapolating to new conditions, so there is no need to create different conditions in CAE every time, which also reduces the computational time. As an example, ANN was used to analyze the extrusion processing conditions of specific products. The input variables were 10 curing temperatures and the respective torque value at specific time, and the output was the time to reach the torque value at a specific temperature. The hidden layer consists in hyperbolic tangent and logarithm sigmoid transfer functions which relate input and output variables. As result, the optimum cure time was determined in the temperature range, and calculations could also explore if a better optimum cure time exists outside the studied interval .
CAE: A CONCLUSION
As can be shown, CAE is an interesting method to design and analyze silicone rubber products. Although there are still restrictions with respect to the precise modeling of certain components of silicone properties such as incompressibility or hyperelasticity, the results are very accurate and can be considered a helpful tool for designers and engineers.
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