1. An Introduction to Abaqus Damping
What is Abaqus damping, and why is it important?This passage delves into the world of Abaqus damping, with a particular focus on material damping Abaqus, Rayleigh damping Abaqus, structural damping Abaqus, and Abaqus global damping. Damping in Abaqus is a vital concept, aimed at reducing or controlling movement in dynamic systems. It finds application in various scenarios, including viscoelastic Abaqus, where the Prony series Abaqus formulation is employed. Material damping Abaqus is explored in depth, covering its use in both directintegration and modebased dynamic analyses. Structural damping in Abaqus is discussed, emphasizing its suitability for models involving frictional behavior or local friction effects. Abaqus global damping is presented as a way to improve performance in preliminary design. This passage offers valuable insights for those seeking to understand and apply Abaqus damping techniques and includes references to Abaqus viscoelastic tutorials for further learning.
As mentioned above, damping is an influence within or upon a dynamic system that has the effect of reducing, restricting, or preventing its movements. In physical systems, damping is produced by processes that dissipate energy. Damping forces come from several sources simultaneously, such as energy loss during hysteretic loading, viscoelastic material properties, contact friction and so on. If would like to know more about the basic concepts of damping, you can simply click on “whatisdamping?“
Damping in a rolling bearing [Ref]
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2. Sources of Damping
Generally, we can have damping resulting from:
1. Material nonlinearity ⇒ inelastic dissipation
2. Internal friction ⇒ material behavior
3. External friction ⇒ joint behavior
3. Why do we use Abaqus Damping?
We take the profit of Abaqus damping to accurately models the energy loss in a dynamic system. Damping is also beneficial when modeling very fast phenomena and noisy dynamics. It will play a critical role to have a meaningful solution.
So, there are two main reasons for adding damping to a model: to limit numerical oscillations or to add physical damping to the system.
4. How can we Model Damping in Abaqus?
The most widely used damping form called viscous damping, in which the damping force is velocity proportional. In fact, the complex damping may be proportional to the square of velocity, such as the damping force of solid motion in liquid, and sometimes, it even has nothing to do with speed, such as the friction at the supports. 
Two primary aspects for defining Abaqus damping are available:
* Velocityproportional
Viscous damping
** Displacementproportional
Abaqus Structural damping (imaginary stiffness) is used in frequency domain dynamics and in modebased transient dynamics.
5. How can we enter data for damping in Abaqus?
In general, Abaqus has five categories of damping definition sources:
5.1. Material Damping Abaqus
You specify Material damping in Abaqus when defining material. When a structure is subjected to oscillatory deformations, its state is represented by a mix of kinetic and potential energy. Some of this energy is lost per deformation cycles in real structures, which is known as material damping.(will further discuss)
5.2. Element Damping
Abaqus damping for this type Includes contributions from complex spring elements, dashpot elements and connector elements (using connector damping)
5.3. Abaqus Global Damping
Abaqus global damping is assumed when the damping coefficient is constant in all materials. It is essentially a crude approximation aimed at improving performance, especially during preliminary design.
5.4. Abaqus Modal Damping
Applies only to modebased linear dynamic analyses, so it can only be used in Abaqus/Standard.
5.5. Artificial Damping
Damping associated with the time integration method (numerical damping).
Here, we only focus on material damping in Abaqus. Other types will discuss later in future articles.
6. Material Damping Abaqus
In most cases, the material model itself may provide damping in the form of plastic dissipation or viscoelasticity. For many applications such damping may be adequate. Another option is to use Rayleigh damping or structural damping.
Material damping Abaqus can be defined for both directintegration (nonlinear, implicit or explicit) and modebased (linear) dynamic analyses.
Here are the main points for using material damping in Abaqus:

Simulate Realistic Dynamics: Realworld structures exhibit energy loss due to internal friction and other factors. Material damping allows you to capture this phenomenon in your Abaqus model, leading to more accurate simulations of dynamic behavior like vibrations or impacts.

Control Unwanted Oscillations: Damping helps prevent numerical oscillations that can sometimes arise in simulations, especially when dealing with very fast phenomena or noisy dynamics. This improves the stability and convergence of your Abaqus analysis.

Focus on Key Responses: By introducing damping, you can expedite the decay of transient vibrations in your model. This allows you to focus on the longterm response or steadystate behavior of the structure, potentially saving computational time.

Tailor Damping to Materials: Abaqus offers various material damping models, such as Rayleigh Damping, that let you specify damping properties relevant to the materials in your model. This enhances the realism of your simulations.
Overall, material damping in Abaqus is a crucial tool for accurately representing energy dissipation and achieving meaningful results in dynamic analysis.
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7. Forms of Material Damping in Abaqus
♦ Rayleigh damping (Viscous damping)
♦ Structural damping
♦ Viscoelasticity (for viscoelastic materials)
In the following sections, we’re going to fully discuss the forms of material damping. Now, let’s start with Abaqus Rayleigh damping.
7.1. Rayleigh Damping Abaqus
Some models do not have any dissipation sources (an example is a linear system with chattering contact, such as a pipeline in a seismic event). In such cases, it is often desirable to introduce some general damping. Abaqus provides Rayleigh damping for this purpose. It provides a convenient abstraction to damp lower (massdependent) and higher (stiffnessdependent) frequency range behavior. (material damping)
In the Rayleigh model, damping is linearly proportional to mass M and stiffness K matrices. A damping matrix C is added to the system. We define C as:
C matrices are generated for each material in the model. We define the Rayleigh damping factors (alpha, beta) as material properties in Abaqus:
Supposing that only Abaqus Rayleigh damping is present in the model and all the materials use identical Rayleigh damping factors, we can find a relation between the effective system damping ratio and the Rayleigh damping parameters. According to the orthogonality between mass matrix and stiffness matrix, for each natural frequency of the system ωi, the effective damping ratio is equal to:
To define Abaqus Rayleigh damping, we need to calculate alpha and beta. For this purpose, let’s assume our objective is to impose a 5% damping ratio on a structure. To accomplish this, we will perform a modal analysis to determine the frequencies, denoted as omega 1 and omega 2, associated with the first and second modes. Then, using these frequencies, we will calculate the alpha and beta values.
Reminder. Damping Ratio………………………………………………………………………………………………..
The fraction of critical damping or damping ratio is defined as:
And natural frequency is:
Where c, k and m are damping, stiffness and mass of each mode, respectively.
………………………………………………………………………………………………………………………………………………………………………..
Thus, massproportional damping dominates when the frequency is low, and stiffnessproportional damping dominates when the frequency is high:
The orange line shows stiffnessproportional damping, which is straightforward because the damping ratio goes up as frequency goes up. On the other hand, the green line represents massproportional damping, where the damping ratio decreases as frequency increases, making a wavy curve. Often, you’ll see both of these damping types together, and their combined effect is shown by the blue line. Here’s the fascinating part: when the natural frequency is low, massproportional damping is more important, but for higher natural frequencies, stiffnessproportional damping becomes more significant.
7.2. Abaqus Structural Damping
Assumes that the damping forces are proportional to the forces caused by stressing of the structure and are opposed to the velocity:
Where F and I are the damping force and the forces caused by stressing of the structure for every DOF, respectively.The user provides the “s” value when defining Abaqus structural damping in the material module.
Damping in real structures is frequencydependent. Therefore, this is best suited for frequency domain dynamic procedures.
The damping forces due to structural damping are intended to represent frictional effects (as distinct from viscous effects). Thus, structural damping is suggested for models involving materials that exhibit frictional behavior (hysteretic damping) or where local frictional effects are present throughout the model, such as dry rubbing of joints in a multilink structure.
7.3. Viscoelasticity
Let me provide a brief explanation of what viscoelastic materials are and how we can utilize them in Abaqus.
In the world of materials, elastic substances follow Hooke’s law, where stress is directly linked to strain.
This means that when we apply a load to an elastic material, there will be an instantaneous deformation. As long as we maintain the applied load, the deformation will remain constant. When we remove the load, all of the deformation will be fully recovered, demonstrating that elastic materials return to their original shape once the load is removed. On the other hand, viscous materials follow a different behavior, obeying the following law:
Where stress is directly proportional to strain rate not strain. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. The term viscous implies that they deform slowly when exposed to an external force. They cannot return to their first configuration. It is due to dissipation of energy. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties:
Viscoelastic Abaqus model is useful for materials in which dissipative losses primarily caused by viscous (internal damping) effects. The model must be combined with an elastic material model. Viscoelasticity cannot be combined with any of the plasticity models. To delve deeper into this subject, check out the next section “Abaqus viscoelastic tutorial”, which will guide you through the modeling and simulation process using Abaqus software.
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7.3.1. Defining viscoelasticity in Abaqus(Viscoelastic Abaqus)
Viscoelastic Abaqus can be defined as:
* Timedomain viscoelasticity
Viscoelasticity is a function of time for transient analysis. It describes isotropic ratedependent material behavior. We can use a Prony series formulation to enter data:
The Prony series Abaqus is an equation that describes the relationship between shear modulus (G) and time (T).
In this equation, T represents time, G(t) denotes the shear modulus at a given time, Gi represents the relaxation modulus, and τ represents the relaxation time. To fully characterize the parameters in the Prony series, we need to start by defining the instantaneous shear modulus. Additionally, we must define the relaxation modulus and relaxation time. Depending on the chosen value of ‘N’, we have to use a table that lists various values of relaxation modulus and relaxation time.
Furthermore, it’s important to define the instantaneous Young’s modulus, instantaneous Poisson’s ratio, and density to comprehensively describe the material’s behavior.
So, this was all about viscoelastic Abaqus using the Prony series. Check out our Free Course to access more information and become a professional in Abaqus. Let’s now explore Frequency domain viscoelasticity.
** Frequency domain viscoelasticity
Viscoelasticity in Abaqus is a function of frequency for steadystate smallvibration analyses. This analysis is limited to Abaqus/Standard.
For example, many applications of elastomers involve dynamic loading in the form of steadystate vibration, and often in such cases, the dissipative losses in the material must be modeled to obtain useful results.
Here are the main points about defining viscoelastic materials in Abaqus:

Capture TimeDependent Behavior: Viscoelastic materials exhibit properties that change with time. Defining them in Abaqus allows you to simulate realworld materials like polymers, rubber, or some biomaterials that exhibit both elastic (recoverable) and viscous (irreversible) deformation under stress.

Advanced Material Modeling: Abaqus offers various viscoelastic material models, including Prony series, Prony series with relaxation spectrum, and others. These models capture the complex stressstrain response of viscoelastic materials over time.

Simulate Creep and Stress Relaxation: Creep refers to the increasing deformation under constant stress, and stress relaxation describes the decrease in stress over time under constant strain. Defining viscoelastic materials allows you to analyze these phenomena crucial for understanding longterm behavior of structures.

FrequencyDependent Analysis: Viscoelastic properties can vary with loading frequency. Abaqus allows you to define viscoelasticity in the time domain or frequency domain, enabling analysis of structures under dynamic or cyclic loading.

Increased Simulation Accuracy: By incorporating viscoelastic behavior, you can achieve more realistic simulations of structures made from these materials. This is crucial for applications like vibration analysis, fatigue prediction, or understanding the longterm performance of components.
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What is damping?
Damping is an influence within or upon a dynamic system that has the effect of reducing, restricting or preventing its movements. In physical systems, damping is produced by processes that dissipate energy.
What are the Sources of Damping?
Generally, Damping results from several sources, such as inelastic dissipation (Material nonlinearity), material behavior (Internal friction), and joint behavior (External friction).
How can we model damping in Abaqus?
There are two primary aspects for defining damping available in Abaqus. The most widely used damping form is called viscous damping, in which the damping force is velocityproportional. Sometimes the damping force is Displacementproportional such as the friction at the supports. This damping form is called Structural damping (imaginary stiffness).
What is the benefit of using damping in physical systems?
There are two main reasons for adding damping to a model: to limit numerical oscillations or to add physical damping to the system. Damping is also beneficial when modeling highspeed phenomena and noisy dynamics.
What is the damping definition sources in Abaqus?
In general, Abaqus has five categories of damping definition sources: Abaqus Material damping, Element damping (spring elements, dashpot elements, and connector elements), Abaqus global damping (constant damping coefficient), Modal damping (in modebased linear dynamic analyses), and Artificial damping (numerical damping).
What are the forms of Material Damping in Abaqus?
There are three options to provide material damping in Abaqus. The viscoelasticity model is useful for materials in which dissipative losses are primarily caused by viscous (internal damping) effects. Rayleigh damping Abaqus (Viscous damping) is used to introduce general damping in models without dissipation sources (an example is a linear system with chattering contact, such as a pipeline in a seismic event). Another option is to use Abaqus structural damping. The damping forces due to structural damping are intended to represent frictional effects (as distinct from viscous effects).
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