Fatigue and Cyclic Loading Package

Categories: Abaqus, Concrete structure, Course, Fatigue Analysis, Finite Element, Fracture & Failure Analysis, Non-linear FEA, Paper Based Models, Seismic Analysis, Steel structure, Structures

Peyman Karampour

Level

Intermediate
Duration

9 hours 14 minutes
Last Updated

August 23, 2025

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About Course

Introduction to Fatigue and Cyclic Loading Modeling & Simulation

1. The Context
Many engineering components, from aircraft wings and automotive crankshafts to bridges and offshore structures — are subjected not to a single static load, but to repeated (cyclic) loads over their lifetime. Even if these loads are well below the material’s ultimate strength, they can cause progressive damage leading to fatigue failure.
This makes fatigue analysis a cornerstone of design for safety, durability, and life prediction.

2. The Concept of Fatigue

Definition: Fatigue is the progressive structural damage that occurs when a material is subjected to fluctuating stresses and strains over time.
Failure Mode: It’s typically brittle in appearance (even in ductile metals), initiated by microscopic cracks that grow with each load cycle until catastrophic failure.
Stages of Fatigue:
1. Crack initiation at stress concentrators (surface defects, notches, inclusions).
2. Crack propagation under cyclic loading.
3. Final fracture when remaining cross-section can no longer carry the load.

3. Cyclic Loading

Loading Types: Can be fully reversed (tension-compression), pulsating, or random spectrum loading.
Characterization: Cyclic loads are often described by stress amplitude, mean stress, and load ratio $R=σmin/σmax$
Real-world Complexity: Load histories can be irregular (e.g., variable amplitude loading from road conditions or wind gusts), requiring cycle counting methods like Rainflow Counting.

4. Modeling Approaches

Stress-Life (S–N) Approach
- Empirical relationship between cyclic stress amplitude and number of cycles to failure.
- Suitable for high-cycle fatigue (low stress, elastic deformation).
- Often uses Basquin’s equation and correction for mean stress (Goodman, Gerber).
Strain-Life (ε–N) Approach
- Captures low-cycle fatigue (high stress, plastic deformation).
- Uses Coffin–Manson relation for plastic strain and Basquin for elastic strain.
Fracture Mechanics Approach
- Models crack growth rate using Paris’ Law or similar relations.
- Useful for predicting remaining life after a crack is detected.
Multiaxial and Variable Amplitude Loading Models
- More advanced methods account for multi-directional stresses and realistic service loading histories.

5. Simulation Tools & Techniques

Finite Element Analysis (FEA):
- Provides local stress/strain fields under cyclic loads.
- Often coupled with fatigue life prediction software (e.g., nCode, fe-safe, Ansys nCode DesignLife).
Load Spectrum Simulation:
- Time histories from real-world measurements (road profiles, flight data) are processed into equivalent stress cycles.
Damage Accumulation Models:
- The most common is Miner’s Rule (linear damage accumulation).
- Nonlinear models attempt to account for load sequence effects.

6. Purpose of Modeling & Simulation

Predict component life before physical prototypes are built.
Optimize design for weight, cost, and durability.
Reduce the need for expensive full-scale fatigue testing.
Ensure safety and regulatory compliance.

7. Challenges & Considerations

Material variability and microstructure effects.
Surface treatments, residual stresses, corrosion, and temperature influence.
Accurate representation of load spectra and boundary conditions.

Course Content

Example-1: Analysis of low cyclic fatigue damage based on hysteresis energy
In this section, the analysis of low cyclic fatigue damage based on hysteresis energy in Abaqus software is investigated. It is well known that after several repetitive loading cycles, the response of an elastic-plastic structure, such as an automobile exhaust manifold subjected to large temperature fluctuations and clamping loads, may lead to a stabilized state in which the stress-strain relationship in each successive cycle is the same as in the previous one. The classical approach to obtain the response of such a structure is to apply the periodic loading repetitively to the structure until a stabilized state is obtained. This approach can be quite expensive, since it may require the application of many loading cycles before the stabilized response is obtained. To avoid the considerable numerical expense associated with a transient analysis, a direct cyclic analysis can be used to calculate the cyclic response of the structure directly. In the direct cyclic analysis, the Fourier representation of the solution and the residual vector are used to obtain the stabilized cyclic response directly. The damage initiation criterion is a phenomenological model used to predict the onset of damage due to stress reversals and the accumulation of inelastic strain in low-cycle fatigue analysis. Once the damage initiation criterion is satisfied at a material point, the damage state is calculated and updated based on the accumulated inelastic hysteresis energy density per cycle, Δw, for a stabilized cycle. The rate of damage in a material point per cycle is given by dD/dN=c3(deltaW/deltaW0)/L Abaqus uses the above damage initiation and evolution based on Hysteresis energy in the direct cyclic loading. Damage evolution for ductile materials can be defined for any element that can be used with the damage initiation criteria for a low-cycle fatigue analysis in Abaqus/Standard

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Example-2: Simulation of the 2D fatigue phenomenon of a steel plate
In this lesson, the simulation of the 2D fatigue phenomenon of the steel plate using the Direct Cyclic method in Abaqus is studied. The two-dimensional part for the steel and the wire part to define the initial crack length has been used. An elastic material coupled with the traction separation law to consider the fracture and crack growth in the plate has been implied. It is well known that after several repetitive loading cycles, the response of an elastic-plastic structure, such as an automobile exhaust manifold subjected to large temperature fluctuations and clamping loads, may lead to a stabilized state in which the stress-strain relationship in each successive cycle is the same as in the previous one. The classical approach to obtain the response of such a structure is to apply the periodic loading repetitively to the structure until a stabilized state is obtained. This approach can be quite expensive, since it may require the application of many loading cycles before the stabilized response is obtained. To avoid the considerable numerical expense associated with a transient analysis, a direct cyclic analysis can be used to calculate the cyclic response of the structure directly. In this case, the Paris Law for fatigue modeling is considered.

Example-3: Modeling of the 3D fatigue
In this case, the modeling of the 3D fatigue of a steel plate in Abaqus software is studied. In this simulation steel solid part is used with an elastic material coupled with the traction separation law to consider crack growth inside it. Direct cyclic step with a maximum of one hundred cycles has been used. To define fatigue behavior Paris law as an input file with the Power law to consider the fracture parameter is used. During the process, the crack growth and fatigue data are achievable in a visualization for each cycle.

Example-4: Analysis of a Concrete-Filled Steel Column in Abaqus under cyclic loading-Validation Analysis
In this section, the analysis of a Concrete-Filled Steel Column in Abaqus under cyclic loading-Validation Analysis- in Abaqus software is investigated. The steel box column, ribs, and stiffener plates are modeled as three-dimensional shell parts. The two concrete blocks are modeled as three-dimensional solid parts. Concrete-damaged plasticity is selected to model concrete behavior under cyclic loading. The concrete damage plasticity material model represents a constitutive model based on a combination of the theory of plasticity and the theory of damage mechanics. This material model is often used in solving geotechnical problems due to its realistic description of the mechanical behavior of concrete material. The elastic-plastic model is considered for the steel material. The analysis is done in two stages. In the first step, the axial load is applied through a static step, and in the second step, the cyclic load is applied to the column. The weld contact model is considered among all steel parts and surface-to-surface contact among the other parts.

Example-5: Cyclic loading simulation of a steel beam reinforced with epoxy and CFRP
In this lesson, the cyclic loading simulation of a steel beam reinforced with epoxy and CFRP sheet in Abaqus is investigated. The steel beam is modeled as a three-dimensional shell part. The epoxy and CFRP are modeled as three-dimensional solid parts. To model steel hardening behavior under cyclic loading, Abaqus recommends some models, like kinematic or combined hardening, to consider the effect of each cycle in the stress-strain curve. Epoxy is modeled as elastic with damage behavior as a traction-separation law. The CFRP is modeled as an elastic model. For the most part, plastic analysis and design have in the past been directed toward the study of proportional, Monotonically increasing loading to failure. This type of loading is not entirely realistic for many applications, however. The concepts of a shakedown analysis. while enlarging the scope of plastic analysis, results in a structure that ultimately responds elastically, after a few cycles of inelastic action. Severe earthquakes, on the other hand, may induce considerable repeated inelastic action in a structure, especially at the joints. This has motivated the study of steel members and connections subjected to repeated and reversed loading

Example-6: Modeling of the cyclic loading of a composite Column(UHPC + Steel box)
In this test, the modeling of the cyclic loading of a composite Column(UHPC + Steel box) in ABAQUS is investigated. The Ultra-High-Performance Concrete column is modeled as a three-dimensional solid part. The steel box cover is modeled as a three-dimensional shell part. The concrete-filled steel box has great potential for use in the construction of bridges and buildings. Although concrete is the most universally used material in building, there are still some limitations to its use, such as low tensile strength and brittleness. Ultra-High Performance Concrete (UHPC), a cutting-edge concrete, may be able to overcome these concerns. The Concrete Damaged Plasticity model is used to define UHPC column behavior under cyclic loading. The model is a continuum, plasticity-based, damage model for concrete. It assumes that the two main failure mechanisms are tensile cracking and compressive crushing of the concrete material. To define steel box behavior, the elastic-plastic model with ductile damage criterion to consider the damage during the cyclic loading is used. The general static step with some changes in the convergence model to avoid early non-convergence is considered. Two types of interaction between the UHPC column and steel are assumed: first, cohesive surface interaction, and second, perfect contact.

Example-7: Analysis of cyclic loading of an Ultra-High-Performance-Fiber-Reinforcement Concrete column
In this section, the analysis of cyclic loading of an Ultra-High-Performance-Fiber-Reinforcement Concrete column in Abaqus software is studied. The UHPFRC column is modeled as a three-dimensional solid part. Ultra-high performance fiber reinforced concrete (UHPFRC) is a special type of concrete produced with Portland cement, reactive admixtures, small-size aggregates, inert admixtures, superplasticizers, and surface-treated steel fibers. The grading optimization of the mixture constituents provides a high packing density to the hardened composite, and consequently, ultra-high strength, ductility, and durability can be obtained. Cement-based matrices with high strength present sudden failure after the first crack. The addition of fibers delays the fast interconnection between early age microcracks and activates toughening mechanisms between fiber and matrix. Due to these effects, UHPFRC presents a pseudo-strain hardening behavior after cracking initiation. Then, strain localization occurs at peak load, and the bearing capacity of the composite decreases until rupture. The inelastic phenomena associated with the entire process, as matrix cracking, fiber debonding, and slip, provide a notable ductility and capacity of energy absorption to the cement-based material. The Concrete Damaged Plasticity model is used to model UHPFRC material under cyclic loading. The data can be extracted from the reference papers. The general static step with some changes in the convergence model is selected. To achieve the Hysteresis diagram, displacement and reaction force are required. The load is applied to the top surface of the column with an amplitude to consider a cyclic loading protocol.

Example-8: Simulation of the Ultra-High-Performance-Concrete beam-column joint under cyclic loading
In this case, the simulation of the Ultra-High-Performance-Concrete beam-column joint under cyclic loading is investigated. The UHPC beam-column joint is modeled as a three-dimensional solid part. The steel bars and strips are modeled as a three-dimensional wire part. Ultra-High Performance Concrete (UHPC) is an advanced technology in concrete industry with superior characteristics such as high strength in compression and tension, ductility, and durability. The UHPC materiel data is used to model beam-column behavior under cyclic loading. The CDP model needs compression and tensile data separately. The elastic-plastic material model is used for the steel bars and strips. To model cyclic loading, a general step with some changes in the divergence model is selected, and the proper outputs are requested to obtain a hysteresis diagram in the visualization. The embedded region constraint is considered for the embedded bars and strips inside the concrete host. The fixed boundary conditions are assigned to the two top and bottom surfaces of the column, and cyclic displacement to the free surface of the beam by using a protocol.

Example-9: Modeling of the concrete beam-column joint under cyclic loading
In this section, the modeling of the concrete beam-column joint under cyclic loading in Abaqus is studied. The concrete beam-column joint is modeled as a three-dimensional solid part. The strips and bars are modeled as three-dimensional wire parts. The steel material with elastic-plastic behavior is used for the strips and bars. The concrete Damaged Plasticity model to consider tensile damage of the concrete part during the cyclic loading is used. The model is a continuum, plasticity-based, damage model for concrete. It assumes that the two main failure mechanisms are tensile cracking and compressive crushing of the concrete material. The model assumes that the uniaxial tensile and compressive response of concrete is characterized by damaged plasticity. The goal of this simulation is to obtain the damage parameter for the concrete part. The general static step is appropriate for this type of analysis.

Example-10: Analysis of the steel beam-column structure under cyclic loading
In this section, the analysis of the steel beam-column structure under cyclic loading in ABAQUS to obtain damage behavior is simulated. The beam is modeled as a three-dimensional shell part, and two steel columns are modeled as three-dimensional shell parts. To model steel beams and columns under cyclic loading, elastic-isotropic plasticity coupled with a ductile damage criterion to predict damage during the simulation is used. The kinematic or combined plasticity can be used, but to predict damage, the isotropic plasticity and ductile damage can show better results. The general static step is appropriate for this type of analysis, and to avoid early non-convergence, some changes are made in the convergence model.

Example-11: Simulation of the cyclic loading of a steel pipe
In this lesson, the simulation of the cyclic loading of a steel pipe in Abaqus software is studied. The pipe is a #d model with a combined plasticity model to consider the cyclic loading effect. The general static step and an amplitude to apply the cyclic loading are selected.

Example-12: Modeling of the cyclic loading of a circular concrete beam
In this simulation, the modeling of the cyclic loading of a circular concrete beam in Abaqus software is investigated. The concrete is modeled as a three-dimensional solid part. The proper material properties from the Abaqus documentation are selected to demonstrate the hysteresis behavior of the beam.

Example-13: Analysis of the honeycomb steel beam under cyclic load
In this case, the analysis of the honeycomb steel beam under cyclic load in Abaqus is investigated. Honeycomb Castellated Beam has a deeper part than a Comparable Solid Beam, which has greater resistance to deflection. Therefore, the product is most often used in Long Span applications with light and medium loads, especially for the roof. Because the weight of the steel does not change, the structural efficiency of the bending section increases. The further advantage of the Castellated Beam is the hole in the network that has a path to serve inside. In this tutorial beam is modeled as three three-dimensional shell parts. The key point in this simulation is the material model which has used. Abaqus recommends kinematic and combined plasticity, and they are appropriate for cyclic loading and extracting a hysteresis diagram. A general static step with some modifications has been used.

Example-14: Simulation of the steel beam damage under cyclic loading
In this section, the simulation of the steel beam damage under cyclic loading in Abaqus software is done. Under cyclic loading conditions such as those introduced by earthquake ground motions, the local buckling is initiated in the compression flange. However, it disappears and reappears in subsequent cycles. The beam is modeled as three-dimensional shell parts. The linear elastic, isotropic plastic material model with a damage parameter to investigate damage distribution has been used. A general static step is appropriate for this type of analysis.

Example-15: Modeling of a steel column with stiffeners under cyclic loading
In this lesson, the modeling of a steel column with stiffeners under cyclic loading in Abaqus software is studied. The box column is modeled as a three-dimensional shell part, and the stiffener is modeled as a planar shell part. The stiffeners are used at the end of the column as a weld zone the fortify it, and the stiffeners should change the damage zone at the end to another place. Normally, kinematic or combined plasticity is used to model cyclic behavior because they have a variable yield surface, but in this simulation, the goal is to find the damage and failure location, so isotropic plasticity with ductile damage criterion is used to achieve it. The ductile damage criterion can predict the damage zone under cyclic loading. The general static step was used. The boundary for the end of the column and the bottom edges of the stiffeners are assumed as a weld zone, so the fixed boundary condition is used for them. The cyclic loading with a specific protocol to define the load amplitude is used. The mesh has a good effect on the accuracy.

Example-16: Analysis of the composite column (steel beam and concrete core) under cyclic loading
In this section, the analysis of the composite column (steel beam and concrete core) under cyclic loading in Abaqus software is investigated. The steel beam and the concrete parts are modeled as three-dimensional solid parts. The steel material is used for the steel beam as an elastic-plastic material with a ductile damage criterion to consider damage and failure during cyclic loading. The concrete is modeled as an elastic material with concrete damaged plasticity(CDP) to predict tensile and compressive damage. The general static step was used with ideal or perfect contact between the steel beam and concrete column surfaces.

Example-17: Simulation of the Kalthoff–Winkler experiment crack growth using a peridynamic model
In this case, the simulation of the Kalthoff–Winkler experiment crack growth using a peridynamic model under low velocity impact in Abaqus is studied. Both two- and three-dimensional models can be used to model the plate. Fracture and failure analysis has always been one of the major concerns in theoretical studies and engineering applications. For mode II dynamic loading conditions with high rates, experiments have demonstrated that failure in shear form can be easily obtained if suitable fixtures are applied. The technique of loading edge cracks by edge impact (LECEI) introduced by Kalthoff provides such a fixture, in which a loosely positioned flat plate (target) with two parallel notches is impacted by a projectile. During the impact process, a compressive stress wave is triggered, and the displacement associated with this stress wave creates a pure shear mode II loading condition in a very short period, and an effective mode II crack propagation path can then be observed. The Kalthoff-Winkler experiment is a benchmark dynamic fracture problem for predicting crack propagation in an impact-loaded pre-notched plate. In this tutorial, three cases are investigated. The crack angle in all three cases is matched with the experiment.

Example-18: Modeling of the cyclic loading of a cracked and damaged concrete column reinforced with GFRP bar
In this section, the modeling of the cyclic loading of a cracked and damaged concrete column reinforced with GFRP bar is investigated. Cyclic loading analysis of damaged concrete columns reinforced with Glass Fiber-Reinforced Polymer (GFRP) bars is an important simulation for evaluating seismic performance and rehabilitation strategies. This analysis helps engineers understand how cracked concrete structures with non-corrosive GFRP reinforcement behave under repeated loading-unloading cycles typical of earthquake conditions. In this tutorial, to model a cracked concrete column, the Concrete Damaged Plasticity model is used. The strength of the concrete, because of the initial damage and cracks, is less than the intact one.

Example-19: Analysis of the seismic behavior of CFRP-strengthened seismic-composite steel-concrete frame column
In this lesson, the finite element analysis of the seismic behavior of the CFRP-strengthened seismic-composite steel-concrete frame column in Abaqus in Abaqus is done. The concrete and steel columns are modeled as three-dimensional solid parts. The steel reinforcements are modeled as wire parts. The CFRP box is modeled as a shell part. In this study, cyclic loading tests were performed on composite steel-concrete columns to investigate the effect of the strengthening of seismic-damaged composite steel-concrete with CFRP on the performance of frame columns. The tests included horizontal load testing, horizontal displacement testing, and recording of the load-displacement hysteresis loops of the specimen.

Example-20: Simulation of the cyclic behavior of exposed base plates with extended anchor bolts
In this section, the Cyclic behavior of exposed base plates with extended anchor bolts in Abaqus is studied. Column base connections are among the most critical components of Steel Moment Frames; their behavior profoundly influences the overall performance of SMFs. Early investigations on Column-base connections, alongside remarkable experimental programs on large-scale specimens, have provided insight into their behavior and failure modes. These tests led to the development of prominent analytical models to characterize the strength of Column-base connections. To do the cyclic loading, both general static and dynamic implicit steps can be used. In this example, a general static step with some changes in the convergence model is considered. Abaqus provides many material models for concrete and steel materials under all loading and situations. The Concrete Damage Plasticity material model for the concrete foundation and the proper hardening model in the cyclic loading for the steel members are selected.

Example-21: Modeling of the cyclic loading of a steel beam-column joint with welded steel angle and stiffeners
In this case, the simulation of the cyclic loading of a steel beam-column joint with welded steel angle and stiffeners in Abaqus is done through a comprehensive tutorial. Box column, steel beam angles, and stiffeners are modeled as the three-dimensional solid part. If a structural steel member is subjected to a cyclically varying load of sufficient amplitude, it may fail after a certain number of load repetitions, even though the maximum load in a single cycle is much less than that required to cause yielding or fracture. To model steel material under cyclic load, Kinematic and Combined hardening can be used to consider the stress-strain diagram in each cycle. The analysis procedure would be the general static approach. To define weld joints, surface-to-surface interaction or constraints can be selected. The proper boundary with the cyclic load protocol is applied to the beam.

Example-22: Analysis of the CFRP for seismic strengthening of a shear-controlled RC column
In this model, the analysis of the CFRP for seismic strengthening of a shear-controlled RC column in Abaqus is investigated. The concrete column is modeled as a three-dimensional solid part, the steel reinforcements are modeled as a three-dimensional wire part, and the CFRP is modeled as a shell part. To model seismic behavior of concrete, the Concrete Damaged Plasticity(CDP) material is selected to consider tension nd compression damage. The CFRP reinforcement is modeled as an elastic material that can be damaged model is also available. Recent post-earthquake surveys revealed the high vulnerability of existing Reinforced Concrete (RC) structures, often designed for gravity loads only, even to moderate seismic events. Indeed, the lack of proper seismic detailing and a wrong shear-flexure hierarchy often leads to columns' brittle failures due to shear before attaining the flexural yielding. Furthermore, short and wall-like RC columns are commonly subjected to such a brittle failure, governed by concrete diagonal compression failure. To prevent premature brittle failures of existing RC columns, the use of Externally Bonded Reinforcement (EBR) made of Fibre Reinforced Polymer (FRP) strips has been recognized as a reliable and cost-saving strategy for increasing members' lateral strength capacity. Plenty of researchers focused attention on the shear strengthening of RC beams, mainly due to gravity loads. Even though post-earthquake observed shear failures in columns are more diffuse than shear failures of beams

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Fatigue and Cyclic Loading Package

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Introduction to Fatigue and Cyclic Loading Modeling & Simulation

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