Regularized eXtended Finite Element Method Research Articles

Performance prediction of interlock woven composites by independent mesh method

High fidelity analysis methods have shown significant success in predicting performance and durability in laminated tape composites. This paper uses a combination of a regularized extended finite element method (Rx-FEM) for discrete damage modeling (DDM), which was previously validated for ply-level analysis in tape laminates, and the independent mesh method (IMM) to predict the progression of damage throughout an angle-interlock woven composite at the mesoscale. The Virtual Textile Morphology Suite (VTMS) performed process simulations to predict the as-woven tow architecture, using the digital chain technique. Process parameters were calibrated such that the crimp within the tows for the virtually generated meso-volume closely matched X-Ray images. The mesoscale simulations captured experimentally observed failure modes for tension and compression in warp and weft direction. The predicted strength values based on the virtual mesovolume were higher than experimental average from 1 to 25% for the warp compression damage mode.

A reduced-input cohesive zone model with regularized extended finite element method for fatigue analysis of laminated composites in Abaqus

A cohesive zone model (CZM) for fatigue crack propagation was integrated within the Regularized eXtended Finite Element Method (Rx-FEM) discrete damage modeling framework. This CZM constitutive model, which is formulated in terms of S-N stress-life curves rather than the more usual rates of crack propagation described with a Paris law, can predict both crack initiation and propagation by relying on the intrinsic relationships between S-N and the Paris law. This feature of the model is of significant practical interest since S-N curves can be synthesized with few parameters and simple engineering assumptions, while the experimental characterization of the Paris law parameters for all required stress ratios, mode mixities, and material interfaces in a composite structure is very difficult and often impractical. Used in combination with the Rx-FEM method, this CZM can predict mesh-independent crack networks in composite structures subjected to cyclic or quasi-static loads. The Rx-FEM methodology for fatigue damage was implemented in Abaqus using two superimposed sets of standard Abaqus elements to represent the enriched displacement field. The capabilities of the proposed methodology are demonstrated by comparing the experimental and predicted response of a mixed-mode bending (MMB) test, as well as a Clamped Tapered Beam (CTB) sub-element designed to study matrix crack initiation, delamination propagation, and subsequent delamination migration from one ply interface to another.

Implementation of the regularized extended finite element method in Abaqus framework for fracture modeling in laminated composites

The Regularized eXtended Finite Element Method (Rx-FEM) is a fracture mechanics based technique for progressive failure simulation when multiple damage events such as matrix cracks and delamination are introduced into the finite element model via mesh independent displacement discontinuities. In the Rx-FEM, the Heaviside step function that is used in the eXtended Finite Element Method (x-FEM) is replaced by a continuous function approximated by using the FE shape functions. This regularization offers unique possibility for the implementation of the Rx-FEM methodology in commercial FE software as a superposition of native elements as opposed to a single user defined element which is the approach taken by x-FEM implementation to date. The advantages of the novel Rx-FEM implementation lie in the ability to utilize the capabilities of the host software including contact, geometric nonlinearity as well as post-processing, and visualization. The proposed implementation of the Rx-FEM methodology is illustrated for commercial software Abaqus on a number of examples of mesh-independent crack modeling in composite laminates, and delamination between plies. The validity of the proposed implementation is demonstrated by comparing with experimental data and benchmark solutions.

Delamination initiation and migration modeling in clamped tapered laminated beam specimens under static loading

The Clamped Tapered Beam Specimen (CTBS) designed to study the initiation of matrix cracking and delamination and their propagation including delamination migration from one interface to another was considered. Regularized eXtended Finite Element Method (Rx-FEM), which allows modeling the matrix cracking in a direction independent of finite element boundaries, was used for the analyses. The key parameters which were compared with the data obtained during the simultaneously conducted experimental program included peak loads, matrix crack initiation locations and delamination migration locations. The predicted peak loads were within the experimental range when high transverse strength values obtained from three point bend tests were used in the predictions. The matrix crack initiation location as well as delamination migration locations were correctly predicted by taking into account residual thermal stresses and implementing energy dissipation based load control algorithms to model delamination migration during unstable crack propagation.

Discrete damage modeling of static bearing failure in laminated composites

Discrete Damage Modeling (DDM) of double shear lap bolted joint was performed. Regularized eXtended Finite Element Method (Rx-FEM) was used for the simulation of matrix cracking at initially unknown locations and in directions independent of the mesh orientation in a ply level 3D model. A set of input properties combining directly measured ply properties and properties empirically reduced from laminate level testing by using common industry practices was used for blind prediction of test data for 1.5D and 3.0D edge distance specimens with clamp-up. The simulations predicted the bearing strength characteristics for 1.5D configuration within 10% window, whereas for the 3.0D case the ultimate bearing strength was underpredicted by 20.3%. X-ray CT imaging of post-peak loaded specimens was performed. The observed failure modes and locations agreed with the experiment in most cases. A limited number of input parameters including fiber failure fracture toughness were varied in a parametric study.

Probabilistic mesh-independent discrete damage analyses of laminate composites

In this paper, probabilistic failure response and damage patterns in laminate composites was investigated by considering spatially varying and cross-correlated strength properties. The effect of statistical parameters such as the correlation length, variance and correlation coefficient between normal and shear strength within Discrete Damage Modeling (DDM) framework was examined for the first time. For this purpose, an efficient random field modeling framework for multiple cross-correlated random fields is proposed whereby different sets of uncorrelated random variables in Karhunen–Loève (KL) expansion corresponding to independent auto-correlation functions are generated and transformed to sets of correlated random variables. DDM is performed by means of Regularized eXtended-Finite Element Method (Rx-FEM) where multiple matrix cracks in different plies are modeled simultaneously with interplay delaminations in interactive fashion. Two composite laminates a quasi-isotropic carbon/epoxy [45/90/−45/90]s Hexply IM7/8552 and [45/−45/90]s T300/976 were modeled by using probabilistic DDM. Significant effects of the statistical parameters on the failure behavior and ultimate component strength were observed, manifesting importance of accurate definitions of the statistical properties for predicting probabilistic failure behavior and damage tolerance of laminate composites. The average strength values predicted by probabilistic analysis with spatially correlated strength values were closer to experimental data than the predictions with uncorrelated strength values.