Understanding Finite Element Analysis (FEA)

What Makes FEA Essential?

FEA plays a critical role in simulating real-world conditions to test the durability and functionality of materials and structures. This enables engineers to:

• Enhance designs for better performance and safety.
• Reduce costs by identifying potential failures early.
• Accelerate product development cycles with accurate simulations.

Mathematics Behind FEA

The mathematics behind FEA involves solving partial differential equations (PDEs) that describe physical phenomena. These PDEs are often complex and cannot be solved analytically for most real-world problems. FEA simplifies these equations by discretizing the domain into finite elements and approximating the solution using interpolation functions. The process involves:

• Meshing: Dividing the domain into smaller elements.
• Formulating Element Equations: Using interpolation functions to approximate the PDEs within each element.
• Assembling Global Equations: Combining the element equations to form a global system of equations.
• Solving the System: Using numerical methods to solve the global system for unknown variables such as displacements, temperatures, or stresses.

Different FEA Methods

Following are the different methods are used in FEA, each suited for different types of problems:

• Finite Element Method – FEM: Divides the entire problem domain into smaller subdomains (elements) with predefined shape functions. FEM is versatile and commonly used for structural analysis, thermal problems, and fluid dynamics. It works well for complex geometries
• Finite Difference Method – FDM: Approximates the derivatives in PDEs using differences between values at discrete points on a grid. FDM is widely used in solving time-dependent problems like heat conduction, wave propagation, etc.
• Finite Volume Method – FVM: Solves the PDE by dividing the domain into control volumes and applying conservation laws (e.g., mass, momentum, energy) to each volume. Primarily used in fluid dynamics, especially in Computational Fluid Dynamics (CFD) simulations.
• Boundary Element Method - BEM: Only discretizes the boundaries of the domain, reducing the problem to a lower dimension. Often used in problems where the domain is infinite or semi-infinite, like acoustics, electromagnetism, and some fluid problems.

Types of FEA Solutions and Analysis

FEA can be used to perform various types of analyses, including:

1. Static Analysis: Evaluates the response of structures under steady loads.
2. Dynamic Analysis: Studies the behavior of structures under time-varying loads.
3. Modal Analysis: Determines the natural frequencies and mode shapes of structures.
4. Thermal Analysis: Analyzes heat transfer and temperature distribution.
5. Nonlinear Analysis: Deals with material and geometric nonlinearities, such as plastic deformation and large deformations.

Latest Trends and Diverse Applications of FEA in Medical Products

FEA has become an invaluable tool in the development of medical products. Recent trends include:

• Personalized Medicine: FEA is used to create patient-specific models for surgical planning and implant design, improving outcomes and reducing risks.
• Biomechanics: Simulations of human tissues and organs help in understanding their behavior under different conditions, aiding in the design of prosthetics and orthotics.
• Medical Device Design: FEA helps in optimizing the design of medical devices such as stents, pacemakers, and artificial joints, ensuring their safety and efficacy.
• Regulatory Compliance: FEA is increasingly used to meet regulatory requirements, providing detailed analysis and documentation for device approval.

Case Study - Detailed Report on FEA Thermal Analysis of a Stent Used in Bypass Surgery

Stents are small, tube-shaped devices inserted into arteries to keep them open. They are commonly used in procedures like angioplasty to treat coronary artery disease (CAD). Stents help maintain blood flow by propping open arteries that have been narrowed by plaque buildup.

Materials Used in Stents:

Stents are typically made from materials that offer a combination of strength, flexibility, and biocompatibility. Common materials include:

• Nitinol: Known for its super-elasticity and shape memory properties, making it ideal for self-expanding stents.
• Stainless Steel: Offers high strength and durability.
• Cobalt-Chromium Alloys: Provide excellent radial strength and biocompatibility.
• Polymers: Used in bioresorbable stents that gradually dissolve in the body.

FEA Thermal Analysis of Stents:

• Thermal analysis in FEA focuses on how the stent responds to temperature variations within the body, particularly during and after implantation. This is important because the thermal environment can affect the material properties, and in turn, the mechanical integrity and performance of the stent.
• Objective: To assess the temperature distribution in the stent and understand how different materials behave under body temperature.
• Methodology: The stent is modelled in an CAD software with detailed material properties. The boundary conditions mimic the thermal environment within the human body, typically around 37°C.

Simulation Setup

• Modelling: A 3D model of the stent is created using CAD software and imported into the FEA package.
• Material Properties: Thermal conductivity, specific heat, and density of the stent material i.e. Stainless Steel are inputted into the software.
• Boundary Conditions: The external surface of the stent is subjected to a body temperature of 37°C, while the internal temperature conditions mimic the cooling effects (Convection Cooling) of blood flow.
• Meshing: The stent model is discretized into small elements, allowing for detailed analysis of temperature distribution.

Results and Discussion

• The FEA simulation results typically show the temperature distribution across the stent over time.
• Temperature Distribution: The images depict the temperature gradients within the stent, showing how heat dissipates through the structure. Areas with higher temperatures may indicate potential risks for thermal stress, which could affect the stent's performance.
• Material Behaviour: The thermal analysis reveals that materials like nitinol, with higher thermal conductivity, distribute heat more evenly, reducing the risk of localized thermal stress. On the other hand, stainless steel may show more significant temperature gradients, which could affect its long-term performance.

The FEA thermal analysis of the stent provides critical insights into the thermal behaviour of different materials used in stents. Understanding these thermal effects is essential for ensuring the reliability and longevity of the stent after implantation.

Conclusion:

In conclusion, FEA is a powerful tool that combines advanced mathematics and computational techniques to solve complex engineering problems. Its applications in medical products are expanding, offering new possibilities for innovation and improving patient care.

How Decos helps its clients?

Decos provides cutting edge FEA services in healthcare domain which can help you to catapult your product development process and sustaining efforts. FEA Services provided by Decos include Structural Analysis, Thermal & Heat Transfer Analysis, Non-Linear Analysis and Drop Test.