On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis

Matsubara, Seishiro; Terada, Kenjiro

doi:10.1002/nme.5328

Cited by 13 publications

(5 citation statements)

References 20 publications

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“…For example, IGA is of advantage in dealing with frictional contact problems as demonstrated in Lu (2011De Lorenzis et al (2011), Temizer et al (2012; Nishi et al (2019a). Also, it is applied in other interesting areas such as damage/fracture (Verhoosel et al (2011), Borden (2012; , electromagnetics (Buffa et al, 2010), heat transfer (An et al (2018), , multiscale (Matsubara et al (2016) and structural optimization (Seo et al (2010); Dedè et al (2012); Nishi et al (2019b) problems. Nonetheless, IGA has never joined hands with the microplane damage model to the best of our knowledge.…”

Section: Incorporation Of Gradientenhanced Microplanementioning

confidence: 99%

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

Han¹,

Yin²,

Kaliske³

et al. 2021

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Purpose This study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries. Design/methodology/approach For the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results. Findings The implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results. Originality/value The paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

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Section: Incorporation Of Gradientenhanced Microplanementioning

confidence: 99%

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

Han¹,

Yin²,

Kaliske³

et al. 2021

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“…When using IGA to solve the RVE equilibrium boundary value problem, some extra considerations are necessary. As pointed out in the work of Matsubara et al, the generation of a parallelepiped RVE geometry using NURBS can cause problems due to the fact that the sharp corners need to be represented by smooth basis functions. The authors thus proposed a strategy that involves splitting the domain into different patches and enforcing continuity of the displacement field across patches as an additional constraint on top of the PBCs.…”

Section: Rve Boundary Conditionsmentioning

confidence: 99%

“…All of the aforementioned features make IGA an attractive choice of numerical tool for use in conjunction with computational homogenization. Indeed, in the work of Matsubara et al, IGA was used to perform NMT, with focus restricted to the infinitesimal deformation case.…”

Section: Introductionmentioning

confidence: 99%

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A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis

Alberdi

Zhang

Khandelwal

2018

Numerical Meth Engineering

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Summary This study presents an isogeometric framework for incorporating representative volume element–based multiscale models into computational homogenization. First‐order finite deformation homogenization theory is derived within the framework of the method of multiscale virtual power, and Lagrange multipliers are used to illustrate the effects of considering different kinematical constraints. Using a Lagrange multiplier approach in the numerical implementation of the discrete system naturally leads to a consolidated treatment of the commonly employed representative volume element boundary conditions. Implementation of finite deformation computational strain‐driven, stress‐driven, and mixed homogenization is detailed in the context of isogeometric analysis (IGA), and performance is compared to standard finite element analysis. As finite deformations are considered, a numerical multiscale stability analysis procedure is also detailed for use with IGA. Unique implementation aspects that arise when computational homogenization is performed using IGA are discussed, and the developed framework is applied to a complex curved microstructure representing an architectured material.

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“…In spite of these advantages, only few attempts have so far been made at computational homogenization along with the method of IGA to the best of the author's knowledge. The first trial in this context is carried out by Matsubara et al [38], who discuss the points of attention in modeling multiple patches for multiple materials and in treating constraint conditions unique to NMT and NPT. However, it does not necessarily state their belief in the superiority of IGbased computational homogenization over FE-based one.…”

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confidence: 99%

Isogeometric analysis for numerical plate testing of dry woven fabrics involving frictional contact at meso-scale

2019

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With a view to application to meso-macro decoupled two-scale draping simulations of dry woven fabrics, the method of isogeometric analysis (IGA) is applied to the numerical plate testing (NPT) for their periodic unit structures involving frictional contact at meso-scale. The meso-structure having periodicity only in in-plane directions is identified with a representative volume element to characterize the macroscopic mechanical behavior that reflects the interfacial frictional contact phenomenon between fiber bundles. NURBS basis functions are utilized to accurately solve macro-scale frictional contact problems and the mortar-based knot-to-surface algorithms are employed to evaluate the contact-and friction-related variables. A weaving process is simulated as a preliminary analysis to obtain the initial state of an in-plane unit cell that is subjected to bending of fiber bundles contacting with each other. Several numerical examples are presented to demonstrate the performance and capability of the proposed method of IGA-based NPT for characterizing the macroscopic structural responses of dry woven fabrics that can be substituted by macroscopic 'inelastic material' behaviors. Keywords Isogeometric analysis • Frictional contact • Numerical plate testing • Dry woven fabric • Homogenization 1 Introduction Owing to the superior performance while being lightweight , composite materials typified by fiber-reinforced plastics are widely used in various engineering fields such as aviation and automobile industries. At the same time, as various macroscopic material responses can be achieved according to the mechanical characteristics, distribution morphology and blend ratio of fiber and matrix materials, the concept of computer-aided engineering (CAE) has been introduced in the tailoring process of the macroscopic material properties by designing the micro-structures. The underlying idea B K. Terada

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On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis

Cited by 13 publications

References 20 publications

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis

Isogeometric analysis for numerical plate testing of dry woven fabrics involving frictional contact at meso-scale

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