Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Orzechowski, Grzegorz; Frączek, Janusz

doi:10.1007/s11071-015-2167-1

Cited by 73 publications

(36 citation statements)

References 40 publications

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“…[39,40] fits well absolute coordinates approach adopted here); however, to keep the model as easy as possible, much simpler approach is proposed here.…”

Section: Simplified Model Of a Flexible Linkmentioning

confidence: 93%

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Wojtyra

2016

Multibody Syst Dyn

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Problems with uniqueness and high parametric sensitivity of the solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multibody system with closed-loop kinematic chains is discussed. Three different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints; the approximate Coulomb model, smoothed in the vicinity of zero relative velocity; and the LuGre model with presliding displacements represented in terms of auxiliary state variables. Firstly, a rigid body model is investigated. It is shown that in the case of constraint addition approach, problems with uniqueness of solution emerge in the static friction regime. In the case of continuous models of friction, the solution in the stiction regime and its vicinity is highly sensitive to some hardly measurable or arbitrarily chosen parameters of the model of friction. Origins of nonuniqueness and high sensitivity are investigated, and the questionable credibility of the stiction regime simulation results is discussed. Secondly, a simplified model of body and joint elasticity is introduced to investigate the impact of flexibility on the mechanism frictional behavior. It is shown that taking the flexibility into consideration may eliminate the uniqueness and sensitivity problems. Moreover, the quantities that represent flexibility may be regarded as the key factors influencing the results of stiction regime simulation. Five examples are provided to illustrate the presented considerations.

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“…[39,40] fits well absolute coordinates approach adopted here); however, to keep the model as easy as possible, much simpler approach is proposed here.…”

Section: Simplified Model Of a Flexible Linkmentioning

confidence: 93%

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Wojtyra

2016

Multibody Syst Dyn

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“…The hyperelastic material models, which are shown in this Section, are in the well-known form of the Mooney-Rivlin models (Bonet and Wood, 1997;Orzechowski and Frączek, 2015). These models are commonly used to represent incompressible rubber-like materials.…”

Section: Nearly Incompressible Polynomial Materials Modelsmentioning

confidence: 99%

“…(3.1) implicitly assume that the incompressibility is ensured by setting J equal to one. This condition is fulfilled by the penalty method (Maqueda and Shabana, 2007;Orzechowski and Frączek, 2015). In this technique, the volumetric energy penalty function U p is added to the expression of the strain energy function.…”

Section: Nearly Incompressible Polynomial Materials Modelsmentioning

confidence: 99%

“…However, commercial FEA packages restrict the work with incompressible materials to shell and solid elements (ANSYS® Academic Research, 2010), also when slender structures are considered that are otherwise modelled with beam elements. One can overcome this limitation in the mentioned kind of common applications by applying fully parameterized ANCF beam elements (Shabana, 2008;Orzechowski and Frączek, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…The previous paper by Orzechowski and Frączek (2015) showed an importance of volumetric locking elimination techniques in typical applications, however, only higher-order elements, like those presented in Orzechowski and Shabana (2016), which were also numerically expensive due to the high number of coordinates and integration points, provided a reasonable results. Therefore, exemplary techniques that may reduce the computational cost are introduced and validated with several numerical examples.…”

Section: Introductionmentioning

confidence: 99%

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Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Orzechowski

Frączek

2017

jtam

Self Cite

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The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F -bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

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An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

Shariyat

Abedi

2022

Z Angew Math Mech

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The current article is devoted to the nonlinear dynamic and impact response analyses of rectangular incompressible neo‐Hookean hyperelastic plates with uniform/nonuniform transverse distributions of stiff elastic reinforcing particles. The nonlinear finite element governing equations are derived by using the principle of minimum total potential energy and solved by an updating scheme that uses the Runge‐Kutta time integration and penalty methods. The impact energy expressions are written for the integrated plate‐indenter system. The novelties of the article are: (i) realistic modeling the energy absorption of a particle‐reinforced nonlinear hyperelastic matrix based on the volume fractions of the constituent phases instead of using wrong Voigt‐type models or impractical predefined gradation coefficients, (ii) considering non‐uniform distributions of the reinforcing particles, (iii) using a highly accurate asymmetric (all the available theories are symmetric) infinite‐order plate theory, (iv) including the inherent hyperelastic nature of the material in the definition of the parameters of the plate theory, (v) considering the thickness changes of the plate, (vi) including von Karman's kinematic nonlinearity, (vii) analyzing both the dynamic and impact behaviors, (viii) proposing an adaptive algorithm to match the description of the displacement field with the load/stress variations, (ix) updating not only the stiffness but also the mass matrix within the time steps, (x) incorporation of the nonlinear boundary conditions by the penalty method, and (xi) performing time‐dependent analyses instead of the natural frequency analyses. Results reveal the drastic effects of the volume fraction of the reinforcing particles on the dynamic responses and report the impact responses of the FG hyperelastic plates, for the first time.

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Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Cited by 73 publications

References 40 publications

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

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