Isogeometric cohesive elements for two and three dimensional composite delamination analysis

in Composites : Part B, Engineering (2013)

Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B ... [more ▼]

Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B-splines) to generate cohesive ele- ments along delamination planes in an automatic fashion. A complete computational framework is presented including pre-processing, processing and post-processing. They are explained in details and implemented in MIGFEM–an open source Matlab Isogemetric Analysis code developed by the authors. The composite laminates are modeled using both NURBS solid and rotation-free shell elements. Several two and three dimensional examples ranging from standard delamination tests (the mixed mode bending test) to the L-shaped specimen with a fillet, three dimensional (3D) double cantilever beam and a 3D singly curved thick-walled laminate are provided. To the authors’ knowledge, it is the first time that NURBS-based isogeometric analysis for two/three dimensional delamination modeling is presented. IGA provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. [less ▲]

Dealing with interfaces in partitioned model order reduction for application to nonlinear problems

Scientific Conference (2013)

We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of ... [more ▼]

We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of the interface tractions linking subdomains to each others will be performed in a FETI context. [less ▲]

ALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION

Scientific Conference (2012, March)

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼]

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲]

Error estimation in quantities of interest for XFEM using recovery techniques

in Yang, Z J (Ed.) 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME) (2012)

Accurate error estimate in energy norm using a nearly-equilibrated kinematically-admissible displacement recovery technique

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

Rationalised computational time in fracture simulation: adaptive model reduction and domain decomposition

Scientific Conference (2011, June)

Enhanced recovery techniques for accurate evaluation of error estimates in FE aproximations

in Laghrouche, O; El Kacimi, A; Woodwaed, P (Eds.) et al 19th UK National Conference of the Association for Computational Mechanics in Engineering (2011)

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes ... [more ▼]

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes. The development of design tools that enhance performance of the final product and give reliability on the calculations is essential in todays industrial environment, which increasingly seeks to reduce develop- ment times for new products while improving the quality. During the last years there has been an increasing interest on the use of error estimates which help to measure and control the error committed in standard or enriched finite element approximations. The error can be defined in terms of energy norm or in quantities relevant for design purposes (such as the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems). In this work, we discuss the use of different a posteriori recovery techniques to evaluate error estimates for different finite element (FE) approximations. These techniques are based on equilibrated supercon- vergent patch recovery or equilibrated moving least squares procedures and can be used in smooth or singular problems. Numerical results show the capabilities of the proposed techniques to provide good error estimates. [less ▲]

Accurate evaluation of stress intensity factors using error estimation in quantities of interest based on equilibrated recovery

in Oliver, J; Jirasek, M; Allix, O (Eds.) et al Computational Modeling of Fracture and Failure of Materials and Structures. Proceedings of CFRAC 2011 (2011)

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an ... [more ▼]

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an error indicator for goal oriented adaptivity procedures. In this paper we propose an a posteriori recovery-based error estimation procedure which considers the stress intensity factor K typical of singular problems as the quantity of interest in finite element (FE) approximations. In general, error estimators in quantities of interest have been based on residual techniques and, although recovery techniques have been often preferred when considering the error in energy norm due to their robustness and simplicity, so far, there is no available procedure which considers an equilibrated recovery technique that can be used in standard FE frameworks. In [1] a standard SPR recovery technique is used to obtain an error measure of the J-integral, which is closely related to the value of the SIF. However, it does not consider any equilibrium constraints or the singularity near the crack tip, thus the obtained recovered stress field is not well suited for this kind of problems. The technique proposed herein relies on the enhanced superconvergent patch recovery technique presented in [2] to evaluate highly accurate recovered stress fields of the primal and dual problems, which are then used to obtain a sharp error estimate. The primal problem is simply the problem under analysis. To formulate the dual problem we consider the linear interaction integral representing K to obtain the applied loads of the dual FE approximation to solve. The high accuracy of the recovered stress fields for both the primal and dual solutions is obtained by decomposing the raw stress field obtained from the finite element approximations into singular and smooth parts, and enforcing the fulfilment of boundary and internal equilibrium equations. The results indicate an accurate estimation of the error in K for benchmark problems with exact solution. [less ▲]

Alleviating the Mesh Burden in Computational Solid Mechanics

in Proceedings of ECT2010 (2010, December 12)

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment ... [more ▼]

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment; meshfree methods; extended finite element methods; isogeometric analysis; advanced remeshing techniques. [less ▲]