The meaning of specific internal energy and dissipated inelastic specific energy in VUMAT

Updating Internal and Dissipated Inelastic Energies in VUMAT

When writing a VUMAT, the following quantities must be defined:

» Stress at the end of an increment

» SDVs (if there is any) at the end of an increment

But internal and dissipated energies at the end of the increment may be defined.

If you have any problem with the VUMAT results (stresses, strains, etc.) it can not be due to updating energies. You should investigate stress updating terms.

Now, let me ask you a question. What about the UMAT subroutine? I mean, do you think we should check the stresses for this same issue in the UMAT subroutine? What are the differences between the UMAT and VUMAT subroutines, especially in the stress terms calculations? If you check out the “Writing UMAT subroutine” section in the Abaqus Free course, you will have your answers. Trust me, it’ll make it worth your while.

Energy balance in Abaqus

In Abaqus, an energy balance is a fundamental concept used to track the flow of energy within a system during a simulation. It involves accounting for different forms of energy, such as kinetic energy, potential energy, and internal energy, and their interconversion within the system.

The energy balance equation in Abaqus is derived from the principle of conservation of energy, stating that the total energy within a closed system remains constant unless energy is added to or removed from the system. The energy generated is frequently a crucial aspect of ABAQUS/Explicit analysis. Assessing and comparing different energy elements can aid in determining if the analysis is producing a suitable outcome.

We can express the overall energy balance of the model as follows:

The sum of the internal energy , viscous energy dissipation , frictional energy dissipation , kinetic energy , and work done by externally applied loads equals a constant value denoted as . In the numerical model, the value of remains approximately constant, typically with an error of less than 1%.

Specific Internal Energy and Dissipated Inelastic Specific Energy | Internal energy meaning

In Abaqus “specific internal energy” refers to the internal energy per unit mass of a material. It is a thermodynamic property that describes the energy stored within a material due to its microscopic structure and interactions between its constituent particles. The specific internal energy is a key parameter in Abaqus simulations that helps capture the thermodynamic behavior and energy distribution within a material or system.

The internal energy (IE) is the sum of the recoverable elastic strain energy, EE; the dissipated inelastic energy (dissipated through inelastic processes such as plasticity), PE; the energy dissipated through viscoelasticity or creep, CDE; and the artificial strain energy (includes energy stored in hourglass resistances and transverse shear in shell and beam elements), AE:

IE = EE + PE + CDE + AE

Specific here means per unit of mass.

What is dissipated energy?

In Abaqus, “dissipated energy” refers to the energy that is converted into other forms, typically in the form of heat or work, and is lost from the system during a simulation. It represents the energy that is not recoverable or stored within the system but is instead dissipated as a result of various phenomena such as material deformation, friction, or viscous effects.

Dissipated energy can arise from different sources depending on the nature of the analysis. For example, in a mechanical analysis, it can be associated with plastic deformation, material yielding, and the associated hysteresis effects. In a thermal analysis, it can be related to heat conduction, convection, and radiation losses.

Abaqus provides several methods to evaluate and quantify the dissipated energy during a simulation. These methods depend on the specific analysis being performed. For instance, in a structural analysis, the dissipated energy can be computed from the stress-strain relationship using the plasticity or damage models incorporated in the material properties. Abaqus provides output variables and history outputs that can be used to extract and track the dissipated energy during the simulation.

Understanding and monitoring the dissipated energy in Abaqus can provide valuable insights into the behavior and response of a system, such as identifying regions of high energy losses, assessing the efficiency of a design, or evaluating the fatigue life of a structure.

What is inelastic energy?

In Abaqus, “inelastic energy” refers to the portion of the total energy within a system that is associated with irreversible deformations or material behavior. It represents the energy that is dissipated or lost due to inelastic processes, such as plastic deformation, material yielding, or damage accumulation.

When a material undergoes inelastic behavior, such as plasticity or viscoelasticity, some of the energy input into the system is converted into heat or dissipated in other forms. This dissipated energy is considered as inelastic energy. It is not recoverable and does not contribute to the elastic or stored energy within the system.

Abaqus provides the capability to compute and evaluate the inelastic energy during simulations. The inelastic energy can be calculated based on the constitutive models and material properties used in the analysis. Abaqus offers various material models, such as plasticity models, damage models, and viscoelastic models, which enable the estimation of inelastic energy.

By analyzing the inelastic energy distribution and evolution, engineers and researchers can gain insights into the behavior of materials and structures under different loading conditions. It helps in assessing the extent of irreversible deformations, predicting failure or fatigue, and optimizing designs to minimize energy losses.

See Also:

Training Package: Introduction to UMAT and VUMAT Subroutines

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