Research Papers

Isogeometric Implementation of High-Order Microplane Model for the Simulation of High-Order Elasticity, Softening, and Localization

[+] Author and Article Information
Erol Lale

Department of Civil Engineering,
Istanbul Technical University,
Maslak, Istanbul 34469, Turkey
e-mail: lale@itu.edu.tr

Xinwei Zhou

ES3, 550 West C Street,
San Diego, CA 92101
e-mail: xinwei.zhou@es3inc.com

Gianluca Cusatis

Associate Professor
Department of Civil and
Environmental Engineering,
Northwestern University,
2145 Sheridan Road Tech A125,
Evanston, IL 60208-3109
e-mail: g-cusatis@northwestern.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 20, 2016; final manuscript received September 16, 2016; published online October 14, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(1), 011005 (Oct 14, 2016) (10 pages) Paper No: JAM-16-1411; doi: 10.1115/1.4034784 History: Received August 20, 2016; Revised September 16, 2016

In this paper, a recently developed higher-order microplane (HOM) model for softening and localization is implemented within a isogeometric finite-element framework. The HOM model was derived directly from a three-dimensional discrete particle model, and it was shown to be associated with a high-order continuum characterized by independent rotation and displacement fields. Furthermore, the HOM model possesses two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C1 continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. Nonuniform rational B-splines (NURBS) based isogeometric elements are implemented in a 3D setting, with both displacement and rotational degrees-of-freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Furthermore, the proposed approach allows the natural formulation of a localization limiter able to prevent strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.

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Fig. 1

Global and microplane system of references

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Fig. 2

Boundary conditions for the high-order microplane model

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Fig. 3

Numerical results for the cantilever beam problems: (a) elastic curves for various meshes and comparison with beam theory solution, (b) calculated response for different internal length values, and (c) change of normalized bending stiffness with respect to thickness

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Fig. 4

Plate with a hole under tension: (a) schematic sketch of loading and boundary conditions, (b) typical finite-element mesh, and (c) mesh zoom-in with highlighted isogeometric element with corresponding control points

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Fig. 5

Load–displacement and strain profile curves for a bar under uniaxial tension: (a) local formulation, (b) high-order formulation with no regularization, (c) high order formulation with regularization on the total high-order stresses, and (d) high-order formulation with regularization on the high-order stress increments

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Fig. 6

Voronoi tessellation of unit sphere with 66 facets




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