An efficient numerical approach to the micromorphic hyperelasticity

Hassani, R.; Ansari, R.; Rouhi, H.

doi:10.1007/s00161-019-00808-9

Cited by 9 publications

(2 citation statements)

References 44 publications

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“…Different types of boundary conditions were utilized to demonstrate the capability of the developed element. In another study, Hassani et al [460] proposed an efficient numerical approach to the micromorphic hyperelasticity which was the variational DQ-finite element method. In their novel method, the domain was transformed into some finite element methods, and then a variational discretization technique was utilized within each element.…”

Section: Linear/nonlinear Static Bending and Buckling Of Small-scale ...mentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

120

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Section: Linear/nonlinear Static Bending and Buckling Of Small-scale ...mentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

120

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“…Some numerical approaches are also proposed to study the size effects in mechanical problems for microheterogeneous structures. As example, we can mention here the paper by Hassani et al [4], where the sizedependent variational differential quadrature procedure is combined with the finite element method into a new technique. In this paper, by considering several numerical examples, it has been shown that the proposed size-dependent formulation and numerical solution approach have a good performance to study the large deformations of hyperelastic microstructured bodies.…”

Section: Introductionmentioning

confidence: 99%

On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

Tomczyk

Gołąbczak

Litawska

et al. 2019

Continuum Mech. Thermodyn.

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The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically micro-heterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to study certain problems of micro-vibrations and of wave propagation related to microfluctuations of displacement field caused by a periodic structure of the shells. These micro-dynamic problems will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling includes both the asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the combined model have constant coefficients depending also on a cell size. Hence, this model takes into account the effect of a microstructure size on the dynamic behaviour of the shells (the length-scale effect). It will be shown that the micro-periodic heterogeneity of the shells leads to cell-depending micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures. Keywords Uniperiodic shells • Asymptotic and tolerance modelling • Micro-dynamics Communicated by Andreas Öchsner.

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An efficient numerical method to solve the problems of 2D incompressible nonlinear elasticity

Hassani

Ansari

Rouhi

2022

Continuum Mech. Thermodyn.

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An efficient numerical approach to the micromorphic hyperelasticity

Cited by 9 publications

References 44 publications

A review of size-dependent continuum mechanics models for micro- and nano-structures

A review of size-dependent continuum mechanics models for micro- and nano-structures

On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

An efficient numerical method to solve the problems of 2D incompressible nonlinear elasticity

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