Abaqus User Element Research Articles

Phase Field Coupled Finite Deformation Plasticity Formulation of Ductile Fracture With Nonlinear Kinematic Hardening and Modified Energy Release Function

ABSTRACTA ductile damage theory is presented by coupling the covariant formulation of finite deformation plasticity with the phase field modeling of fracture, including kinematic hardening for the ductile response of the materials. A phase field coupled nonlinear kinematic hardening equation is proposed in the reference configuration having equivalent representation through the Lie derivative of the kinematic hardening tensor by push‐forward operation in the spatial configuration, thus ensuring the satisfaction of frame invariance. To capture the correct physical response of the material by the phase field evolution equation, the fracture driving function, that is, the difference between the sum of elastic and plastic energies and threshold energy, after the damage initiation is modified by an energy release controlling function, which is an empirical relation of equivalent plastic strain. In defining the energy release controlling function, well‐defined points with physical significance in the experimental load versus displacement curve are used. To simulate the response of the material in relatively large time steps, a modified staggered scheme is presented, evaluating the fracture driving and energy release controlling functions from the previous converged step and using the updated phase field variable in the weak form of the momentum balance equation. To quantify different material parameters from available experimental results in the literature, the developed phase field coupled elasto‐plastic model uses a neural network optimization procedure consisting of neural network training together with optimization in MATLAB and finite element model evaluation in Abaqus user element subroutine UEL. Model capabilities are demonstrated by simulating the crack propagation in complex 3D geometries such as the second and third Sandia Fracture Challenges.

An interprocess communication-based two-way coupling approach for implicit–explicit multiphysics lattice discrete particle model simulations

In this study, the researchers have developed a Multiphysics-Lattice Discrete Particle Model (M-LDPM) framework that deals with coupled-fracture-poroflow problems. The M-LDPM framework uses two lattice systems, the LDPM tessellation and the Flow Lattice Element (FLE) network, to represent the heterogeneous internal structure of typical quasi-brittle materials like concrete and rocks, and to simulate the material’s mechanical and transport behavior at the aggregate scale. The researchers revisited the LDPM governing equations and added the influence of fluid pore pressure. They also derived the Flow Lattice Model (FLM) governing equations for pore pressure flow through mass conservation balances for uncracked and cracked volumes. The M-LDPM framework was implemented using Abaqus user element subroutine VUEL for the explicit dynamic procedure of LDPM and user subroutine UEL for the implicit transient procedure of FLM. The coupling of the two models was achieved using Interprocess Communication (IPC) between Abaqus solvers. The M-LDPM framework can simulate the variation of permeability induced by fracturing processes by relating the transport properties of flow elements with local cracking behaviors. The researchers validated the M-LDPM framework by comparing the numerical simulation outcomes with analytical solutions of classical benchmarks in poromechanics.

Modeling magnetic soft continuum robot in nonuniform magnetic fields via energy minimization

The emerging magnetic soft continuum robots (MSCRs) – a type of slender and soft rods with embedded hard-magnetic particles – hold great promise in endovascular intervention via remote magnetic actuation. Although numerous advantages of using permanent magnets have been demonstrated for manipulating MSCRs (e.g., simple systems with high actuation force, large operating workspace), the magneto-mechanical behavior of MSCRs in nonuniform magnetic fields, particularly those generated by permanent magnets, remains largely unexplored. In this work, a systematic study of MSCRs in the nonuniform field is presented, which includes theoretical modeling using hard-magnetic elastica theory, numerical analyses by energy minimization method, finite element simulations using ABAQUS user element (UEL), and experimental validation. Without solving governing differential equations, the large deflection of MSCRs is efficiently obtained via the minimization of the total potential energy using sequential quadratic programming (SQP). This efficient modeling method offers insights into the control of MSCRs using nonuniform magnetic fields. Two practical strategies are provided for precisely controlling MSCRs by manipulating a cubic magnet through the adjustment of the actuation distance, rotation angle, and spin angle, laying the foundation for applications of magnetically-assisted endovascular intervention.

Uncertainty qualification in seismic analysis of concrete dams based on model order reduction accelerated stochastic SBFEM

A pioneering framework for uncertainty quantification in seismic analysis of concrete dams rooted in the stochastic scaled boundary finite element method (SSBFEM) is proposed. For seismic analysis of dams, octree decomposition is used for mesh generation. SSBFEM is developed to predict the structural responses with randomly distributed material properties. The script in this paper can integrate octree mesh and SSBFEM into ABAQUS user element (UEL). Implementing octree SSBFEM on commercial software provides accurate and convenient full order models for uncertainty quantification. Monte Carlo simulation (MCs) is deployed to calculate the statistical characteristics of structural responses under random variables. Additionally, singular value decomposition (SVD) and radial basis function (RBF) are leveraged to refine traditional MCs. The solution space of MCs is decomposed into lower-order subspaces. Any structural responses can be rapidly evaluated from linear combinations of subspaces. Particularly, the method has been successfully applied to seismic analysis of concrete dams with different random material properties. Finally, several illustrative examples are provided to validate the accuracy and efficacy of the algorithm.

A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon

Numerical simulation of bone remodelling enables the investigation of short- and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90’s, and these models have been continuously refined since then. However, one issue which has been under discussion since those early days concerns a numerical instability known as checkerboarding. A literature review of recent approaches guided us to adopt a technique established in damage mechanics and topology optimisation, where similar mesh dependencies and instabilities occur. In our investigations, the so-called gradient enhancement is used to regularise the internal variable field, representing the evolution of the bone mass density. For this, a well-established mathematical model for load-adaptive bone remodelling is employed. A description of the constitutive model, the gradient enhancement extension and the implementation into an open-access Abaqus user element subroutine is provided. Parametric studies on the robustness of the approach are demonstrated using two benchmark examples. Finally, the presented approach is used to simulate a detailed femur model.

Heterogeneous Beam Element for Multiscale Modeling of Non-prismatic Composite Beam-like Structures

Anisotropy, heterogeneity, and geometry make full system-level three-dimensional (3D) finite element analysis (FEA) simulation of real composite beam-like structures, such as wind blades, impossible due to limitations on computing resources. A popular approach is to cut the structure into multiple cross-sections, from which the beam properties based on the Euler-Bernoulli or Timoshenko beam models are extracted using two-dimensional (2D) cross-sectional analyses. These properties are then utilized in beam elements for system-level analyses. However, the mechanics behind 2D cross-sectional analyses are based on prismatic beams, limiting the accuracy of this approach on non-prismatic structures, especially in predicting stresses. In this work, we present a new multiscale method based on Mechanics of Structure Genome to analyze beam-like non-prismatic composite structures. A beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with effective beam element stiffness matrices, which are then used as input for one-dimensional (1D) beam analysis using Abaqus User Element subroutine (UEL). Using the macroscopic beam analysis results as input, we can also perform dehomogenization to predict the stresses and strains in the original structure. We use three examples, a prismatic composite beam, an isotropic homogeneous tapered beam, and a composite tapered beam, to demonstrate the capability of HBE and show its advantages over the traditional cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry. HBE provides a new concept to model non-prismatic composite beams by modeling heterogeneous beam-like structures as equivalent beam elements rather than beam properties of material points of the reference line.

A generalized anisotropic damage interface model for finite strains

This contribution presents a generalized mechanical interface model for nonlinear kinematics. The interface’s response is non-coherent, i.e. allows for a jump in the deformations and for cohesive failure, and also includes interfacial (in)elasticity, which means that an additional membrane stiffness is introduced in the interface. This can result in a jump in the tractions across the interface and induces membrane stresses for in-plane stretches. An anisotropic cohesive law, i.e. dependent on the spatial interface normal, is formulated which induces for nonlinear kinematics additional shear-like stresses within the interface to satisfy the balance of angular momentum. The cohesive and membrane degradations are coupled via damage variables of the different deformation modes to account for an interaction. It is shown that the model is thermodynamically consistent, fulfills the balance equations and material frame indifference. An interface element with the generalized interface model is implemented as a user element in Abaqus. Numerical examples illustrate the influence of damage coupling on the mechanical response of adhesive layers.

Seismic analysis of post-tensioned concrete gravity dams using scaled boundary finite elements implemented as ABAQUS UEL

This paper presents an efficient numerical framework for the seismic analysis of post-tensioned concrete gravity dams, which automatically inserts anchors into the structure. The proposed approach is implemented in the commercial finite element software ABAQUS by introducing a polygonal user element (UEL) derived by the scaled boundary finite element method (SBFEM). By inserting nodes in the polygonal structural mesh along the anchor layouts, duplicating the inserted nodes representing anchors, and generating cohesive elements on the node pairs, post-tensioned anchors are naturally embedded into the structure, and the bond–slip interactions are considered. Furthermore, an unbounded UEL derived by the SBFEM is implemented to simulate the unbounded foundation in the dam–reservoir–foundation interaction systems. The unbounded UEL only requires a small truncation area around the region of interest to rigorously capture the dynamic properties of the infinite foundation in terms of a displacement unit-impulse response. This ABAQUS implementation allows the use of built-in capabilities of ABAQUS for nonlinear dynamic analysis, including contact modeling and cohesive fracture. Weak structural interfaces existing in a concrete gravity dam (dam–foundation interface and construction joints) are modeled by a cohesive–frictional contact scheme. In the end, sophisticated numerical models dams featuring post-tensioned gravity dams with weak interfaces and anchors can be generated in a fully automatic manner, requiring no special treatments for mesh generation such as partitioning. The accuracy of the proposed technique is verified through a numerical example of the Manly dam strengthened by a vertical anchor. The efficiency of this approach is demonstrated through a dam with three construction joints anchored by multiple inclined anchors. The input files of the numerical examples are available from the authors upon request.

Non-linear thermoelastic analysis of thin-walled structures with cohesive-like interfaces relying on the solid shell concept

In this work, a thermodynamically consistent framework for coupled thermo-mechanical simulations for thin-walled structures with the presence of cohesive interfaces is proposed. Regarding the shell formulation, a solid shell parametrization scheme is adopted, which is equipped with the mixed Enhanced Assumed Strain (EAS) method to alleviate Poisson and volumetric locking pathologies. It is further combined with the Assumed Natural Strain (ANS) method leading to a locking-free thermo-mechanical solid shell element using a fully-integrated interpolation scheme. In order to model thermo-mechanical decohesion events in thin-walled structures with imperfect internal boundaries, an interface finite element for geometrical nonlinearities is herein extended to account for the thermal field and thermo-elastic coupling. The computational implementation of the current finite element formulation has been performed as a user element in ABAQUS via user-defined capabilities. The predictability of the model is demonstrated using several representative examples.

절단 육면체 요소의 Abaqus 사용자 요소 서브루틴(UEL) 개발

절단 육면체 요소의 Abaqus 사용자 요소 서브루틴(UEL) 개발

Finite-element-based moisture transport model for wood including free water above the fiber saturation point

Timber constructions and engineered wood products exhibit a strong moisture-dependent behavior, which needs to be sufficiently describable by models to avoid critical designs. For wood, several models exist, able to describe the specific heat and moisture transfer mechanisms under normal service conditions as well as for particular situations during the production process, like the kiln drying of sawn timber. However, a unified model combining free water transport with the multi-Fickian approach below the fiber saturation point and the corresponding stable numerical implementation able to handle several possible states of water (bound water, water vapor and free water) and applicable to both drying and infiltration problems, is still missing.In this work, we link models for all those transport processes by reasonable coupling mechanisms. Numerical difficulties occurring at transition between different states of water are handled appropriately, leading to a stable and reliable simulation tool, which is implemented through a three-dimensional Abaqus user element. Thus, this contribution extends the applicability of heat and moisture simulation tools for wood to more critical service conditions, where wooden components might get into direct contact with free water. This may happen due to insufficient supervision during construction or in the production process of new types of wood composites. We anticipate that with the developed tool potentially critical designs can be identified by simulation instead of by time-consuming experiments or experience. This is of importance because the presence of free water and the resulting reduction in stiffness and strength is associated with a higher risk of local failure. This would allow more targeted designs of engineered wood products and efficient optimization strategies, especially with respect to the moisture behavior.

An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates

The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.

A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

SummaryOne of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker‐Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load‐displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain‐softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials.

Effectiveness of different base isolation systems for seismic protection: Numerical insights into an existing masonry bell tower

Recent earthquakes in Italy have emphasized the high seismic vulnerability of historical masonry constructions and the need of effective retrofitting interventions. This paper investigates the possibility of improving the seismic performance of a historical masonry bell tower using different types of commercial isolators: High Damping Rubber Bearing (HDRB), Lead Rubber Bearing (LRB) and Friction Pendulum System (FPS) Isolator. Detailed three-dimensional (3D) finite element (FE) models are created to characterize the behavior of the three types of isolators. Then, an Abaqus User Element (UEL) is used to represent the 3D behavior of the isolators for global seismic analyses of isolated structures. The results of cyclic shear analyses show that the proposed UEL model can accurately predict the behavior obtained through detailed 3D FE models. Non-linear dynamic analyses are performed to investigate the seismic response of the historical masonry bell tower in the original and base-isolated configurations subjected to moderate-to-high seismic actions: moreover, the effects of near fault earthquakes are analyzed. The results obtained from the numerical simulations show that the HDRBs do not ensure an adequate seismic protection of the masonry bell tower in terms of damage patterns and top displacements. On the other hand, the LRBs and FPS isolators are very effective in reducing the earthquake effects on the masonry tower: residual displacements are negligible and the isolator displacements are limited. In case of near fault earthquakes, an isolation system with higher damping and larger dimension is required to reduce the drifts of the tower and to accommodate the large displacements of the isolators.

Hybrid seismic base isolation of a historical masonry church using unbonded fiber reinforced elastomeric isolators and shape memory alloy wires

One of the most promising devices for seismic base isolation of structures is the Unbonded Fiber Reinforced Elastomeric Isolator (UFREI) due to its low manufacturing cost and horizontal stiffness. This paper investigates the possibility of combining UFREIs and shape memory alloy (SMA) wires to increase the energy dissipation capacity of the isolation system for the seismic protection of a historical masonry church. Detailed 3D finite element (FE) analyses are performed to characterize the response of UFREIs under cyclic displacements. The behavior of SMA is simulated through a thermomechanical constitutive model implemented in a user-defined material (UMAT) subroutine available in the software package Abaqus. To reduce the computational effort in non-linear dynamic analyses of large isolated structures, an Abaqus user element (UEL) is developed to represent the 3D behavior of the isolation system proposed in this study. Non-linear dynamic time history analyses are then carried out to evaluate the seismic response of a historical masonry church in different configurations (fixed-base model and model equipped with different base isolation systems) for moderate and severe seismic intensity levels. Numerical results show that the damage observed in the masonry church can be considerably reduced through the insertion of UFREIs. The utilization of SMA wires with a specific pre-strain significantly increases the energy dissipation capacity of the base isolation system and decreases the horizontal displacements of the masonry church.

Mode II modeling of adhesive materials degraded by fatigue loading using cohesive zone elements

Because of maintenance issues, the concept of safe life is an important philosophy for designing adhesive joints where the service load is cyclic. However, this philosophy needs a tool to be able to estimate the total fatigue life. The objective of this study is to develop a numerical tool to predict the fatigue life of adhesive joints for pure mode II loading conditions. To achieve this, a previously published mode I data degradation approach was extended for pure mode II. Fatigue tests were performed on end notched flexure (ENF) specimens to calibrate the degradation model. A triangular shape cohesive zone model (CZM) in combination with a data degradation method were considered in an Abaqus user element (UEL) subroutine. Based on the results, it was found that the proposed method can be applied for fatigue life estimation of adhesive joints in pure mode II conditions as well as pure mode I.

Base seismic isolation of a historical masonry church using fiber reinforced elastomeric isolators

This paper investigates the possibility of improving the seismic performance of a small historical masonry church using fiber reinforced elastomeric isolators in bonded (BFREI) and unbonded (UFREI) applications. Detailed three-dimensional (3D) finite element (FE) models are used to characterize the behavior of the two types of FREIs. An Abaqus User Element (UEL) is developed to simulate the 3D behavior of FREIs for large scale seismic analyses of complex isolated structures. The results of cyclic shear analyses show that the proposed UEL model can accurately predict the FREIs behavior obtained through detailed 3D FE models. A series of non-linear dynamic analyses are performed to investigate the seismic response of a small historical masonry church in the original and base-isolated configurations employing both BFREIs and UFREIs. Numerical results show that the fixed-base model of the church experiences severe and widespread damage, while UFREIs are found to be effective in significantly reducing the damage level of the church when subjected to moderate-to-high seismic actions. Moreover, it can be observed that both the isolator types satisfy the maximum lateral displacement requirements reported in the literature.

Implementation of a simple novel Abaqus user element to predict the behavior of unbonded fiber reinforced elastomeric isolators in macro-scale computations

The need for seismic protection of structures located in earthquake prone areas of developing countries has motivated several investigations of low-cost seismic isolators in recent years. One of the most promising device is the Unbonded Fiber Reinforced Elastomeric Isolator (UFREI): in UFREIs no bonding or fastening is provided between the bearing and top–bottom supports and expensive thick steel plates are not required. The behavior of UFREIs is characterized by rollover and full-contact deformations under horizontal loads: the former decreases the effective stiffness of the isolation system, thus reducing the seismic demand, while the latter plays a key role in generating a hardening phase, thus limiting the horizontal displacement of the isolator under severe earthquakes. Such remarkable advantages highlight a great potential for world-wide UFREIs applications. However, until now there is no representative UFREI model available in structural analysis software codes. In this work, a comprehensive but simple UFREI model is implemented in an ABAQUS user element (UEL), taking into account non-linear, hardening and hysteretic behavior of the bearing: in addition, multiple DOFs are considered to simulate the complex 3D behavior of UFREIs, which is characterized by horizontal and vertical displacements, rotation and torsion. The effectiveness of the UEL model is evaluated performing 3D FE dynamic time history analyses on a rigid slab supported by four different types of UFREI. The results show that the UEL model can reasonably fit the behavior of the detailed FE model, significantly reducing the computational efforts of the analyses. The UEL model proposed in this study can be particularly suitable for 3D dynamic time history analyses of complex base isolated structures.

Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper, the node based smoothed-strain Abaqus user element (UEL) in the framework of finite element method is introduced. The basic idea behind of the node based smoothed finite element (NSFEM) is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell [Liu, Dai and Nguyen-Thoi (2007)]. Therefore, the numerical integration is globally performed over smoothing domains. It is demonstrated that the proposed UEL retains all the advantages of the NSFEM, i.e., upper bound solution, overly soft stiffness and free from locking in compressible and nearly-incompressible media. In this work, the constant strain triangular (CST) elements are used to construct node based smoothing domains, since any complex two dimensional domains can be discretized using CST elements. This additional challenge is successfully addressed in this paper. The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity. The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

Seismic performance evaluation of timber-steel hybrid structure through large-scale shaking table tests

The experimental results and numerical simulation of shaking table tests on a two-thirds scale four-story timber-steel hybrid structure are reported in this paper. The hybrid structural system, developed recently, consists of prefabricated infill wood shear walls and moment-resisting steel frames serving as structural subassemblies to resist seismic loads together. The hybrid structure was subjected to earthquake ground motions at three different hazard levels with peak ground accelerations scaled to 0.14 g, 0.40 g, and 0.80 g, respectively. The responses of the structure, in terms of acceleration, inter-story drift, roof displacement, load sharing between the steel frames and infill walls, etc., were measured by different types of sensors. Peak shear force ratio (R) was defined to assess the proportion of the shear force resisted by the infill wood shear walls, and the results showed that the infill walls significantly contributed to the lateral resistance of the hybrid structure. The structure performed very well with little damage observed after severe earthquake excitations corresponding to the maximum credible earthquake. In addition, a non-linear numerical model of the hybrid structure was established in Abaqus with the Abaqus User Element to model the seismic behavior of the infill wood shear walls, and the numerical model was further validated by shaking table test results.