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EditorialComputational Methods for Fracture 2015

Timon Rabczuk,1,2 Xiaoying Zhuang,1,3 and Trung Nguyen-Thoi4

1 Institute of Structural Mechanics, Bauhaus-Universitat Weimar, Marienstraße 15, 99423 Weimar, Germany2School of Civil, Environmental and Architectural Engineering, Korea University, Republic of Korea3State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University,Shanghai 200092, China4Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Correspondence should be addressed to Timon Rabczuk; [email protected]

Received 13 August 2015; Accepted 13 August 2015

Copyright © 2015 Timon Rabczuk et al.This is an open access article distributed under theCreative CommonsAttribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cracks are the progenitors of material failure. The successof devising better, lighter, and stronger materials relies alsoon how much we understand and how well we can predictand control fracture. Therefore, the modelling of fracturehas always been a ubiquitous and foundational topic acrossengineering and sciences. From the early study of weldingfracture of steel structures in the 1930s to nowadays the designand development of novel nanomaterials, researchers andengineers cannot emphasize more the power of simulationin assisting the improvement of materials performance.The rapid advances in computational methods for fracture,especially in the past two decades, have enhanced such powerto the level where the prediction of complex fractures can berealized with multifields andmodels at different length scalesbeing considered at the same time.This special issue is, as wehoped to share with readers, a showcase on the state-of-the-art in the modelling of fractures.

The two key ingredients in the simulations of fractures aresuitable physical models and computational methods. Withthe contributions from colleagues, we are glad to presentthis special issue addressing certain aspects of the above-mentioned key ingredients: from the fundamental stressinteraction analysis ofmultiple 3D cracks using complex vari-able functions to meshfree numerical methods for fracturepropagation, from fractures in composites and piezoelectricmaterials to fractures in rocks and concrete, from staticfracture modelling to dynamic fractures, and from puremechanical problems to coupled field problems.

Multifield models for fracture propagation are an appeal-ing topic in computational mechanics. In this special issue,models have been developed with special emphasis onrock mechanics and multifield problems in fracture withapplications, for example, to coupled thermohydromechan-ical problems for compressed air energy storage and rockfailure. Besides, the influence of fractures in functionallygraded piezoelectric materials is investigated using mesh-free methods. Special electromechanical-coupling enrichedapproximation near crack tip is devised. A review focusingon the state-of-the-art on developments in multiscale andmultiphase modelling of hydraulic fracturing is carried outas well.

Composite structures are investigated including fracturesinmultilayered concrete/steel composite structures.The eval-uation of fracture and delamination of the structure subjectedto various jacking forces and ground conditions is studied andcompared to the full-scale experimental results.

Dynamic fracture is in itself a wide field of study. Paperin this issue focuses on explicit dynamics and tackles, inparticular, stochastic material parameter distribution andstabilized nodal integrated element-free Galerkin method fordynamic and implosive or explosive loading.

Fundamental solutions to curved and inclined 3D cracksurfaces using complex stress functions are studied.Theworkfeatures the curved length coordinate method and suitablequadrature rule is used to solve the integral equations whichare compared with numerical examples.

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 890890, 2 pageshttp://dx.doi.org/10.1155/2015/890890

2 Mathematical Problems in Engineering

Through these studies, the issue presents a fair reflectionof the current state-of-the-art, with a focus on modeling andsimulation methods. It should inspire our colleagues withnew ideas and trends for future research in the area.

Timon RabczukXiaoying Zhuang

Trung Nguyen-Thoi

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