FEA with Engineered Adhesives and Introduction to the Calcbond Engineering App

FEA (Finite Element Analysis) is a powerful tool used in engineering and manufacturing to simulate and analyze complex structures and systems. On the other hand, structural adhesives are an increasingly popular joining method in many industrial and automotive applications. By using FEA to simulate the behavior of the adhesive joint under various load conditions, engineers can optimize the joint design to ensure maximum durability and longevity.

Different methods for modeling adhesives in FEA

There are several methods for modeling adhesives in FEA.

Tie-break method: The simplest method for modeling adhesives in FEA is the tie-break method, which assumes that the adhesive layer behaves like an elastic spring. The spring is modeled as a beam element connecting the bonded surfaces. When the tensile or shear stress in the adhesive exceeds a certain threshold, the tie is broken, and the two surfaces separate. This method is computationally inexpensive but does not capture the nonlinear behavior of adhesives or the effects of damage or degradation.

Continuum models: Continuum models are used to predict the behavior of adhesives under various loading conditions, such as tension, compression, bending, and shear. These models assume that the adhesive behaves as a homogeneous and continuous material.

Cohesive zone model: The most complex method for modeling adhesives in FEA is the cohesive zone model. This method divides the adhesive layer into cohesive zones, which represent the region of the adhesive where the separation between the two surfaces begins. The cohesive zone properties, such as the fracture toughness and cohesive strength, are determined from experiments or simulations. The model then simulates the behavior of the adhesive as the cohesive zones propagate and the bond between the two surfaces is lost. This method is computationally expensive but provides the most accurate representation of adhesive behavior.

The method chosen depends on the level of accuracy required and the computational resources available. As outlined in our previous online events, in many cases, analytical methods are sufficient to ensure a durable and long-lasting adhesive joint. If you want to watch our "Vehicle Manufacturing Days 2022" presentation about the Calculation and Simulation of Adhesive Joints, click here.

Recommended continuum models for engineered adhesives

Linear elastic (-plastic) model

The linear elastic model is a mathematical model used to describe the mechanical behavior of materials that deform elastically (i.e., they return to their original shape when the applied stress is removed). This model assumes that the relationship between the stress and strain is linear, meaning that the stress is proportional to the strain.

In this model, the elastic modulus, also known as Young's modulus, is a measure of a material's stiffness. It is defined as the ratio of the stress applied to a material to the resulting strain in the material.

You also need to know the material's Poisson's ratio, which is a measure of the material's lateral strain when subjected to axial stress. Poisson's ratio is defined as the ratio of the transverse strain to the axial strain.

In addition to these mechanical properties, you must know the loading conditions and geometry of the structure or component you are analyzing. This includes the magnitude and direction of the applied load, the dimensions and shape of the structure, and any boundary conditions or constraints that affect its deformation.

On the other hand, the linear elastic-plastic model considers that some materials can undergo permanent deformation (plastic deformation) after a certain threshold stress level is reached. This means that the material will no longer respond linearly to the applied stress but instead will begin to deform plastically.

In the linear elastic-plastic model, the material is assumed to behave elastically up to a certain stress level, known as yield stress. Once the yield stress is exceeded, plastic deformation begins to occur, and the material undergoes irreversible changes in shape. However, the material still behaves elastically up to a certain point known as the ultimate stress, beyond which the material fails.

In summary, while the linear elastic model assumes that the material behaves elastically up to the point of failure, the linear elastic-plastic model considers that some materials can undergo plastic deformation before failure.

Sergej Harder - CAE engineer at Sika, recommends working with the linear elastic model whenever the strength of structural adhesives (SikaPower?, SikaFast?, SikaForce?) needs to be verified.

Hyperelastic model

The hyperelastic model describes the mechanical behavior of materials that deform non-linearly and elastically. This model assumes that the relationship between the stress and strain is non-linear and that the stress is a function of the strain energy density.

In the hyperelastic model, the strain energy density is a measure of the energy stored in a material as it deforms under stress. In addition to the strain energy function, you also need to know the material's Poisson's ratio, which is a measure of the material's lateral strain when subjected to axial stress, and its bulk modulus, which is a measure of the material's resistance to volumetric deformation.

The hyperelastic model requires a large amount of experimental data to accurately describe the mechanical behavior of a material, and different strain energy functions may be needed for different loading conditions or material properties.

Generally, highly elastic adhesives like our Sikaflex? PU/STP products are simulated with the hyperelastic model.

Criteria for Adhesive Joint Failure

To determine failure, the stress and strain distributions from the Finite Element Analysis (FEA) model are compared to a maximum allowable value, which serves as the failure criterion. The yield criterion is often used as a failure criterion for a conservative design, but this approach increases the adhesive joint's overengineering. For brittle adhesives, failure criteria based on the maximum principal stress or maximum shear stress have shown some success, but this analysis is challenging due to stress singularities at the joint corners.

However, toughened and flexible adhesives are ductile and can withstand significant plastic deformation before failure, which makes stress-based failure criteria unsuitable. Instead, maximum principal strain and maximum shear strain criteria have had more success in predicting the failure of ductile adhesives. But, joint geometry and the nature of the bonded materials can impose constraints that significantly alter the hydrostatic stresses experienced by the adhesive. This, in turn, affects the actual strain and stress of failure, making it very challenging to determine appropriate maximum values to trigger failure in constitutive models used to describe adhesives without extensive testing.

Failure criteria based on the strain energy density take into account all stress and strain components and are even more accurate. However, direct modeling of bond failure remains the primary limitation and requires the cohesive zone modeling approach described in the following section.

Cohesive Zone Model

In this model, the adhesive layer is treated as a thin layer between the two components being bonded. The properties of the adhesive layer are described by a set of cohesive laws that define the behavior of the adhesive layer under different loading conditions.

Several mechanical data are required to use the cohesive zone model with adhesives. These include:

Fundamental Material Properties: The mechanical properties of the adhesive material are important for the cohesive zone model. These include elastic modulus, density, and shear modulus. These properties can be measured using standard testing techniques such as tensile, compression, and shear testing.

Traction Separation Relation: These are the fundamental mechanical data required for the cohesive zone model. Cohesive laws describe the relationship between the separation of the two components and the stresses within the adhesive layer. They typically include parameters such as the maximum adhesive stress, the adhesive fracture energy, and the adhesive toughness.

Geometry: The geometry of the adhesive layer is important for the cohesive zone model. The thickness of the adhesive layer and the shape of the adhesive layer interface must be known to model the adhesive layer's behavior accurately.

Loading Conditions: The loading conditions applied to the adhesive joint are also important for the cohesive zone model. The cohesive zone element only considers normal and shear stresses in the element thickness direction. Therefore, the contribution of other stresses should be negligible.

I highly recommend downloading the paper "The Use of Finite Element Methods for Design with Adhesives" by Greg Dean and Louise Crocker from the National Physical Laboratory in the UK.

Introducing "calcbond - ecosystem for adhesive engineering"

Our friends from ar engineers GmbH have launched their innovative adhesive engineering app: calcbond. It helps you solve complex adhesive engineering problems without having to be an expert. You can use the calcbond Wiki to get started with adhesive engineering without long and extensive online research time.

This is the first online on-demand engineering software enabling you to work on adhesive engineering projects with access to material cards of leading adhesive manufacturers.

Automated FEA

• Perform design analysis for concrete adhesive joint use cases
• Strength & stiffness evaluation via 3D FEA
• Automated documentation and approval standards

Analytical Calculations

• Simplified lap joint configurations
• Retrieve data from the material database
• Generate and assess results within seconds
• Speed your decision-making for standard applications

Database for adhesive materials

• Easy-click access to the adhesive material database
• Compare and select adhesive products for your application
• Directly apply the selected material card for calculation

We have prepared an introductory video about calcbond and its features:

If you still have any questions related to calcbond, don't hesitate to contact Axel Reinsch, Fabian Nowacki or myself.

FAQ - Frequently Asked Questions

How can I get access to the material data of a specific adhesive?

Sika generally offers extensive material cards for a core range of adhesives saving our customers costs for external testing. Most of the available material cards are also displayed on calcbond.app.

How can safety/reduction factors be incorporated to analyze adhesive joints?

See my previous edition of the newsletter, in which I discuss the basics of "Dimensioning with Material Reduction Factors"

If we use fracture-toughness-based simulation approaches, what is the best way to build in safety that accounts for environmental aging?

Environmental aging is a vast field that can significantly contribute to material parameters. Generally, the engineer has to define the realistic aging conditions for their product and consider the effect in the design. This can be either done by testing where the specimens are artificially aged or by implementing a reduction factor based on a standard or literature values. For a fracture toughness-based approach implemented by cohesive zone material, the properties of elasticity, strength, and fracture toughness must be considered for environmental aging. If you need help, be sure to get in touch with a Sika engineer for assistance, who will be able to guide you through the process of defining the right parameters.

Get Support

Sika adhesive engineers are at your side to help you design with engineered adhesives. Our team of experts and engineering partners help your design engineers in the early stages of design conceptualization, calculation & simulation of adhesively bonded joints, and validation of prototype structures. We work with our customers to develop material models for new applications and provide you with our extensive experience from countless projects involving Sika-engineered adhesives!