Browsing by Subject "Isogeometric analysis"

Now showing 1 - 10 of 10

Open Access
Boundary viscoelasticity theory at finite deformations and computational implementation using isogeometric analysis
(Elsevier BV, 2021-02-01) Dortdivanlioglu, B.; Javili, Ali
Use of surface elasticity theory has experienced a prolific growth recently due to its utility in understanding the mechanics of nanomaterials and soft solids at small scales. Various extensions of surface elasticity theory have been proposed. The main objective of this contribution is to formulate a finite deformation theory for boundary viscoelasticity in principal stretches by accounting for strain-dependent boundary stresses. We present a model that utilizes a nonlinear evolution law and thus is not restricted to the states that are close to the thermodynamic equilibrium. Boundary contributions include both surface and curve effects wherein boundary elasticity as well as boundary tension are accounted for. The boundary constitutive models are formulated such that fluid-like and solid-like viscoelastic behavior of boundaries are considered. A geometrically exact computational framework using isogeometric analysis inherently suited to account for boundaries is developed. Equipped with the theoretical and computational framework, the influence of boundary viscoelasticity on the material response is illustrated. Non-equilibrium counterpart of surface tension is introduced and its effects are elucidated via examples. Through numerical examples, various applications of the bulk–boundary coupled formulation which require further investigation are highlighted.
Open Access
Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers
(John Wiley and Sons Ltd, 2014) Temizer, I.
SUMMARY: A computational contact homogenization framework is established for the modeling and simulation of soft matter friction. The main challenges toward the realization of the framework are (1) the establishment of a frictional contact algorithm that displays an optimal combination of accuracy, efficiency, and robustness and plays a central role in (2) the construction of a micromechanical contact test within which samples of arbitrary size may be embedded and which is not restricted to a single deformable body. The former challenge is addressed through the extension of mixed variational formulations of contact mechanics to a mortar-based isogeometric setting where the augmented Lagrangian approach serves as the constraint enforcement method. The latter challenge is addressed through the concept of periodic embedding, with which a periodically replicated C1-continuous interface topography is realized across which not only pending but also ensuing contact among simulation cells will be automatically captured. Two-dimensional and three-dimensional investigations with unilateral/bilateral periodic/random roughness on two elastic micromechanical samples demonstrate the overall framework and the nature of the macroscopic frictional response. © 2014 John Wiley & Sons, Ltd.
Open Access
Hierarchical NURBS in frictionless contact
(Elsevier, 2016) Temizer, İ.; Hesch, C.
This work investigates mortar-based frictionless contact in the context of NURBS discretizations that are subjected to local hierarchical refinement. The investigations emphasize three sets of choices which lead to different contact algorithms that have distinct advantages and disadvantages. First, on the optimization side, both exterior and interior point methods are applied, thus spanning inexact constraint enforcement algorithms of the penalty or barrier type as well as exact ones of the primal-dual type. Second, on the discretization side, the hierarchical basis set of the mortar variables is inherited either directly from the discretization of the slave surface or after an intermediate normalization step to satisfy the partition of unity. Third, in interaction with both optimization and discretization, the kinematic mortar variable is recovered from the actual normal gap through the full or lumped solution of a linear system of equations. The implications of different choices are highlighted through benchmark problems which monitor the solution quality at the global level through the structural force evolution and at the local level through the contact pressure distribution. © 2015 Elsevier B.V.
Open Access
An interior point method for isogeometric contact
(Elsevier, 2014) Temizer, I.; Abdalla, M. M.; Gürdal, Z.
The interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented Lagrangian approach. The method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region. The derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by NURBS-based isogeometric volume discretizations. Various interior point algorithms are discussed, including a primal-dual approach that satisfies the unilateral contact constraints exactly, in addition to two primal approaches that retain an arbitrary barrier parameter. The developed algorithms can easily be pursued starting from an augmented Lagrangian implementation. Numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework, but also highlight current limitations that suggest paths for future research. Overall, the results indicate that the interior point method can challenge the augmented Lagrangian method in contact mechanics, even displaying potential for higher efficiency and robustness. © 2014 Elsevier B.V.
Open Access
Isogeometric analysis for numerical plate testing of dry woven fabrics involving frictional contact at meso-scale
(Springer, 2019-01) Temizer, İlker; Nishi, S.; Terada, K.
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.
Open Access
Isogeometric boundary element formulation for deformable particles in microchannel confinement
(2023-08) Gümüş, Özgür Can
Numerical simulations of deformable particles are essential to understand quantities that are not possible with experimental techniques. The boundary element method is an advantageous technique to analyze deformable particles in viscous flow conditions since it reduces the dimensionality of the problem by one for linear partial differential equations. Isogeometric boundary element formulation is proposed to model the motion of deformable particles which provides unique ad-vantages in terms of the higher-order continuity of elements and exact geometry representation. Moreover, it enables the calculation of surface normal and curvature analytically. Deformable particles, more specifically droplets, may undergo high deformation which deteriorates the mesh. Moreover, numerical inaccuracies result in a nonphysical change in the volume of the particle. Hence, volume correction and mesh relaxation algorithms are implemented in the isogeometric boundary element method to alleviate the aforementioned numerical artifacts. Without loss of generality, droplets in free and bounded flow cases are formulated and several benchmark problems are solved to assess the accuracy of the proposed formulation. Isogeometric boundary element method supported by stabilization methods explained in the study allows for obtaining stable and accurate results with low-resolution simulations.
Open Access
Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis
(John Wiley & Sons, Ltd., 2014) Temizer, I.
SUMMARY: A computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two-phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two-phase framework is cast within a self-consistent iterative scheme that acts as a first-order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar-based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non-uniform rational B-spline basis functions. Overall, the two-phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures. © 2013 John Wiley & Sons, Ltd.
Open Access
Radial and three-dimensional nonlocal pseudopotential calculations in gradient-corrected Kohn–Sham density functional theory based on higher-order finite element methods
(Elsevier BV, 2021-12-01) Temizer, İlker
Kohn–Sham density functional theory is an ab initio framework for electronic structure calculation that offers a basis for nonphenomenological multiscale approaches. In this work, higher-order finite element methods are applied in the context of this theory, with a particular focus on the use of nonlocal pseudopotentials. Specifically, an accurate class of pseudopotentials which are based on the generalized gradient approximation of the exchange–correlation functional with nonlinear core corrections are targeted. To this end, the suitable weak formulation of the underlying nonlinear eigenvalue problem is derived and additionally cast in a radial form. The weak forms are discretized through traditional Lagrange elements in addition to isogeometric analysis based on B-splines in order to explore alternative means of achieving faster routes to the solution of the resulting generalized eigenvalue problems with O(106–107) degrees of freedom. Numerical investigations on single atoms and larger molecules validate the computational framework where stringent accuracy requirements are met through convergence at optimal rates.
Open Access
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS
(2012) Temizer, I.; Wriggers, P.; Hughes, T. J. R.
A three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume. © 2011 Elsevier B.V.
Open Access
Variationally consistent Hellmann–Feynman forces in the finite element formulation of Kohn–Sham density functional theory
(Elsevier, 2023-01-01) Karaca, Kaan; Temizer, İlker
Hellmann–Feynman forces are derived within the numerical framework of the finite element method for density functional theory in the Kohn–Sham formalism. The variational consistency of the force expressions in all-electron and pseudopotential settings are carefully examined, with a particular focus on the implications arising from different representations for interaction terms that are associated with electrostatics. Numerical investigations in nonperiodic systems which range from diatomic molecules to carbon allotropes demonstrate the systematic convergence that is offered by the finite element framework, not only for energy and force but also for geometric configuration and molecular statics parameters. A range of higher-order discretizations employing fixed meshes are invoked within these examples based on classical finite elements as well as on isogeometric analysis. Overall, this work contributes to recent advances which demonstrate the viability of the finite element method for carrying out ab initio molecular dynamics.