In this tutorial you will learn about Mass Scaling in Abaqus, Mass Scaling in Quasi-Static Problems, Principles and Rules of Mass Scaling, Mass Scaling in Dynamic Analysis, Stable Time Step in Explicit Analysis and how to Use Abaqus Mass Scaling in a model (you will learn the settings and how to apply Fixed Mass Scaling and Variable Mass Scaling in Abaqus).

If you have used Explicit solver in your problems, you should know that choosing a stable time step to solve this type of solver is very important. You are also familiar with the fact that the smallest size of the elements used for an Explicit analysis directly affects the time step of the solution. But have you ever thought about how much the solution time will increase if you have to use tiny elements in sensitive areas of your geometric model for any reason? Will this increase in resolution time also make reasonable help to solve accurately? In these cases, is Abaqus a solution to speed up the solution? Join us in this Abaqus tutorial to learn the answers to these questions scientifically and accurately.

**1. Introduction to Mass Scaling in Abaqus Software**

The Explicit Dynamics process is usually used to solve two categories of problems: the calculation of dynamic transient responses, as well as the analysis of quasi-static problems that have complex nonlinear effects (perhaps one of the most famous examples is contact problems). Because the Explicit or Central Difference Explicit method integrates equations in time, the discrete mass matrix in equilibrium equations plays a critical role in improving computational performance and accuracy in both of these problems. If Mass Scaling is used in the right and timely cases, in addition to improving the performance of the solution, it will also improve the accuracy in a specific group of problems. However, the appropriate Mass Scaling techniques for quasi-static problems may differ from those suitable for dynamic analysis techniques.

**1.1. Basic Concepts of Mass Scaling**

The Mass Scaling option in Abaqus is often used in the Abaqus / Explicit solver to increase computational efficiency in quasi-static analysis and some dynamic analysis involving a number of very small elements. As mentioned earlier, the size and dimensions of these small elements control the stable time steps of the solution and cause the dissolution time to increase dramatically. Mass Scaling can be used for the following purposes:

- Scale the mass of the entire model or individual elements (or even a set of elements);
- Scale the mass at the beginning of the solution or during the solution process.
- In analyzes that use several steps, Mass Scaling mode can be used in a specific step or stage.

**1.2. Methods of performing Mass Scaling in Abaqus**

- Multiply the mass of all elements by a user-defined fixed factor;
- Scale the mass of the specified elements at the same ratio, so that the minimum stable time step for solving each of the specified elements in this set is equal to the time step defined by the user.
- Scale only the mass of the elements in a set that cause the stable time step of the solution to be less than the value specified by the user so that the stable time step to solve these elements is equal to the value defined by the user.
- Scale the mass of all specified elements so that the steady time step for solving is the same as the number defined by the user.
- Perform the Mass Scaling process automatically based on the mesh geometry and the initial conditions of the problem.

**1.3. Mass Scaling in quasi-static analysis**

For quasi-static analyzes in which the behavior of the material is not rate-independent, it is not really important to scale the time in general. To achieve a cost-effective solution, the solution time must often be reduced or, on the contrary, the mass of the model artificially increased. This artificial increase in the mass of the model is called mass scaling. Both of the alternatives we mentioned lead to the same result in materials independent of the strain rate; However, mass scaling is a preferred solution in reducing solution time, even if the model includes the effects of strain rate dependence.

Mass scaling in quasi-static analysis is commonly used in all models. However, when different parts of the model have different mass and strength, it is better to scale only certain parts of our model or perform the desired operations separately on each part. However, what seems obvious is that in all cases, it is not possible to consider the mass of the model less than its physical and actual value, or to increase the mass arbitrarily, regardless of the accuracy of the solution and the results obtained. As a result, it is generally permissible to use a limited amount of Mass Scaling for most quasi-static problems, increasing the stable time step for Abaqus / Explicit solution and decreasing the solution time.

**Note:** It may have occurred to you to manually help reduce the dissolution time by increasing the density of the materials; But the options built into Abaqus are much more efficient and have much more flexibility.

**1.4. Mass Scaling in Dynamic Analysis**

Unlike quasi-static analysis, time scaling is always important in dynamic analysis and is necessary to extract the transient response, applying the exact physical mass and inertia of the model. However, many complex dynamic problems involve a few small elements, forcing Abaqus / Explicit to use small time steps to solve the problem. These small elements are the result of the use of complex and unconventional meshing techniques and are mainly known as controller elements (solution time controllers). By scaling the mass in these controller elements at the beginning of the solution step, without affecting the overall dynamic behavior of the structure, a stable time step for the solution can be effectively increased.

During a collision or impact process, elements close to the collision area undergo high deformation. The reduction in the dimensions of the elements of this savior during the analysis causes the problem-solving time to increase significantly; The use of Mass Scaling technique in these areas causes the solution time to be significantly reduced. In cases where the elements are compressed by a collision with a rigid body, the increase in mass in these very small elements will have very little effect on the dynamic response of the whole structure.

**1.5. Steady time step**

As you saw in the previous sections, the phrase “steady time step of an element” refers to the steady time of solution for an element. The terms “steady step-by-step time-element” and “steady-time step” also refer to the minimum steady time of an element between a set and the steady time step of solving a model, respectively.

**2. How to use Abaqus Mass Scaling in a model**

In general, two types of Mass Scaling are available in Abaqus / Explicit: Fixed Mass Scaling and Variable Mass Scaling. These two types of mass scaling can be applied to the model separately or simultaneously in a general scaling strategy. Also, the Mass Scaling technique can be used in all models or only part of the geometric model (or in a more specific case to a set of elements).

**2.1. Fixed Mass Scaling in Abaqus**

Fixed Mass Scaling is performed once at the beginning of the Step defined. There are two basic approaches to using this method: you can directly define the Mass Scaling coefficient or introduce the minimum stable step to time to Abaqus so that Abaqus / Explicit can calculate the relevant factor or coefficient. If you use both fixed and variable mass scaling techniques in one step, you should note that at the beginning of the desired time step of the solution, constant mass scaling will be performed and then after the solution, the main mass of the elements based on Mass settings Scaling variable will change.

Fixed Mass Scaling provides the user with a simple tool for improving the mass properties of a quasi-static problem at the beginning of the step of solving or improving the mass of a limited number of elements in a dynamic model. Because the scaling process is applied only once, at the beginning of the problem-solving step, Fixed Mass Scaling is very efficient and cost-effective in terms of computational cost.

To use the Fixed Mass Scaling technique in Abaqus, you must select one of the General-Dynamic, Explicit or General-Dynamic, temp-disp, Explicit solvers.

Then go to the Mass Scaling tab and select the Use scaling definition below option. Click on the Create button as shown below to enter the settings window.

In the settings window, select Semi-automatic Mass Scaling and in the Scale section, select at beginning of Step mode.

**2.2. Variable Mass Scaling in Abaqus**

Variable Mass Scaling is used to scale the mass of the elements at the beginning of the step and alternately during the solution process. When you use this type of Mass Scaling, you must specify the minimum optimal step time for the software so that Abaqus automatically calculates the coefficient or factor during the solution process. This type of Mass Scaling will be useful in cases where the Stiffness properties of the problem change dramatically during the solution step. This can occur in both quasi-static shaping analysis and dynamic modeling in which the elements are highly compressed. To activate and use Variable Mass Scaling in Abaqus, just repeat the 2.1 section, but this time in the last step, activate the Throughout Step mode.

**3. Define the scale factor directly**

Defining a scale factor directly is useful in quasi-static problems where the kinetic energy of the model must remain small. You can define a fixed mass scaling coefficient for a specific group of elements, which is applied to the principal mass of the elements. The mass of the elements is solved at the beginning of the step and is kept constant throughout the step unless the desired changes are applied by variable mass scaling. To apply the scale factor directly in Abaqus, you must follow the path below.

Step module à Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step, Scale by factor: scale_factor

**4. Define a stable time step of solving based on the element-to-element method**

To identify the steady time step used during a step, the Abaqus Explicit solver first identifies the smallest steady time step by studying the set element by element. A global estimation algorithm then determines the steady time step based on the largest model frequency. The largest number is selected from the two methods extracted above as the stable time step of the solution. In general, the stable time step determined by the global estimation method will be larger than the stable time step determined by the element-to-element estimation method. When constant or variable mass scaling with a constant element-to-element time step is used to scale the mass of a set of elements, the element-to-element stable time step is directly affected.

If all the elements of the model are scaled by defining a mass scaling, then the element-to-element estimation value will be equal to the element-to-element constant time step value unless the Penalty method is used for contact constraints. Penalty contact can cause the element-to-element estimate to be slightly less than the values assigned to the element-to-element stable time step. The actual stable time step used may be larger than the value assigned to the element-to-element stable time step because the global estimate is used. If mass scaling is applied to only part of the model, elements that have not been scaled may have a less stable time step than the value assigned to the element-to-element steady-state step, and in this case the steady-state element-to-element time step. Will be controlled by the above factor. As a result, if only part of the model is scaled, the time step used will generally not be equal to the value assigned to the stable time-to-element time step.

**5. Uniform mass scaling**

Uniform mass scaling will be useful in quasi-static problems where the kinetic energy of the model must remain small. This approach is similar to defining a direct scaling factor. In both cases, the mass of the identified elements is measured uniformly by the same factor. In the uniform method, however, the mass scaling factor is determined by Abaqus / Explicit rather than by the user. To define mass scaling uniformly in Abaqus, you must follow the path below.

Step module —> Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step or Throughout step, Scale to target time increment of: dt, Scale element mass: Uniformly to satisfy target

**6. Local and global mass scaling**

Creating a set of elements to use fixed or variable mass scaling causes the mass scaling process to become Local. By deleting a group or set of elements, the mass scaling process will become practically universal and applied to the whole set. Do not forget that both global and local mass scaling can be used simultaneously in one piece. In this case, the mass scaling process will be repeated on the specified location for the part by the specified set of the part. To apply this type of mass scaling, follow the path below in the Abacus step module:

Step module: Create Step: General, Dynamic, Explicit or Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling definitions below: Create: Semi-automatic mass scaling, Scale: At beginning of step or Throughout step, Region: Set: else.

The numerical structure research center has created various models using this template, which you can evaluate from the **link below** and order them if necessary.

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