A computational library for multiscale modeling of material failure

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation.     

Alignment and Graphene‐Assisted Decoration of Lyotropic Chromonic Liquid Crystals Containing DNA Origami Nanostructures

Composites of DNA origami nanostructures dispersed in a lyotropic chromonic liquid crystal are studied by polarizing optical microscopy. The homogeneous aqueous dispersions can be uniformly aligned by confinement between two glass substrates, either parallel to the substrates owing to uniaxial rubbing or perpendicular to the substrates using ozonized graphene layers. These opportunities of uniform alignment may pave the way for tailored anisometric plasmonic DNA nanostructures to photonic materials. In addition, a decorated texture with nonuniform orientation is observed on substrates coated with pristine graphene. When the water is allowed to evaporate slowly, microscopic crystal needles appear, which are aligned along the local orientation of the director. This decoration method can be used for studying the local orientational order and the defects in chromonic liquid crystals.     

Free Vibration Analysis of FG-CNTRC Cylindrical Pressure Vessels Resting on Pasternak Foundation with Various Boundary Conditions

This study focuses on vibration analysis of cylindrical pressure vessels constructed by functionally graded carbon nanotube reinforced composites (FG-CNTRC). The vessel is under internal pressure and surrounded by a Pasternak foundation. This investigation was founded based on two-dimensional elastic analysis and used Hamilton’s principle to drive the governing equations. The deformations and effectivemechanical properties of the reinforced structure were elicited from the first-order shear theory (FSDT) and rule of mixture, respectively. The main goal of this study is to show the effects of various design parameters such as boundary conditions, reinforcement distribution, foundation parameters, and aspect ratio on the free vibration characteristics of the structure.     

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.     

A three-dimensional meshfree method for continuous multiple-crack initiation,propagation and junction in statics and dynamics

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.     

A simple and robust three-dimensional cracking-particle method without enrichment

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any “mesh” orientation bias.     

A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks

We will present a meshfree method based on the local partition of unity for cohesive cracks. The cracks are described by a jump in the displacement field for particles whose domain of influence is cut by the crack. Particles with partially cut domain of influence are enriched with branch functions. Crack propagation is governed by the material stability condition. Due to the smoothness and higher order continuity, the method is very accurate which is demonstrated for several quasi static and dynamic crack propagation examples.     

Extended meshfree methods without branch enrichment for cohesive cracks

An extended meshless method for both static and dynamic cohesive cracks is proposed. This new method does not need any crack tip enrichment to guarantee that the crack closes at the tip. All cracked domains of influence are enriched by only the sign function. The domain of influence which includes a crack tip is modified so that the crack tip is always positioned at its edge. The modification is only applied for the discontinuous displacement field and the continuous field is kept unchanged. In addition to the new method, the use of Lagrange multiplier is explored to achieve the same goal. The crack is extended beyond the actual crack tip so that the domains of influence containing the crack tip are completely cut. It is enforced that the crack opening displacement vanishes along the extension of the crack. These methods are successfully applied to several well-known static and dynamic problems.     

Reverse simulation for collaborative commerce: A study of integrating object-oriented database technology with object-oriented simulator

Collaborative commerce has been used for communication, design, planning, information sharing, and information discovery in business-to-business (B2B) applications. The collaboration between buyers and sellers enhances product quality and customer satisfaction. However, most effort currently focuses on information sharing with customers and suppliers instead of joint product development or manufacturing. Moreover, traditional analytical methods have limited capability in solving problems. This study presents a framework for doing reverse simulation, where designers can reuse past experiments and change system parameters in manufacturing system for collaborative commerce. The framework integrates the object-oriented simulator and the object-oriented database. In this framework, the object-oriented database records the whole experiment scenarios and allows multiple planners with different expertise to involve concurrently and collaboratively. Then, simulations of advanced planning and scheduling in a product manufacturing environment that involves several planners working collaboratively are used for demonstration.