Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids

Rohan, Eduard; Cimrman, Robert; Lukeš, Vladimír

doi:10.1016/j.compstruc.2006.01.008

Cited by 25 publications

(14 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The homogenization method has been discovered and extended to reduce the number of composite design parameters significantly by the introduction of effective characteristics using potential or complementary energy principles (Markovic and Ibrahimbegovic, 2006). Although this technique, in its modern version, is almost 40 years old (Bensoussan et al, 1978;Luciano and Willis, 2006), there are still some new ideas and applications, such as applications in food industry (Kanit, 2006), some composites made of wood (Lux, 2006), superconductors (Kamiń ski, 2005;Lefik and Schrefler, 1994), fully and partially saturated heterogeneous solids (Rohan et al, 2006). After fundamental discoveries concerning elastic, thermal and electric effective properties (Christensen, 1979;Milton, 2002), thermo-dynamic wave propagation (Zhang, 2007), various multiscale problems (Fish and Ghouali, 2001;Kamiń ski, 2005;Zhang, 2005), even for time-dependent cases by ''equation free" approach (Samaey et al, 2006); a variety of materially nonlinear multi-component composites can be homogenized also (Castaneda and Suquet, 1998;Friebel et al, 2006;Idiart, 2006;Ma and Hu, 2006).…”

Section: Introductionmentioning

confidence: 99%

Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method

Kamiński¹

2009

International Journal of Solids and Structures

View full text Add to dashboard Cite

a b s t r a c tThe main issue this paper addresses is the derivation and implementation of a general homogenization method, including the simultaneous determination of sensitivity gradients and probabilistic moments of the effective elasticity tensor. This is possible with an application of the perturbation method based on Taylor expansion and with the effective modules method. The computational procedure is implemented using plane strain analysis carried out with the finite element method (program MCCEFF) and the symbolic computations system MAPLE. The sensitivity gradients and probabilistic moments are commonly determined on the basis of partial derivatives for the homogenized elasticity tensor, calculated using the response function method with respect to some composite parameters. They are subjected separately to a normalization procedure (in deterministic analysis) and the relevant algebraic combinations (for the stochastic case). This enriched homogenization procedure is tested on a periodic fiber-reinforced two component composite, where the material parameters are taken as design variables and then, the input random quantities. The results of computational analysis are compared against the results of the central finite difference approach in the case of sensitivity gradients determination as well as the direct Monte-Carlo simulation approach. This numerical methodology may be further applied not only in the context of the homogenization method, but also to extend various discrete computational techniques, such as Boundary/Finite element and finite difference together with various meshless methods.

show abstract

Section: Introductionmentioning

confidence: 99%

Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method

Kamiński¹

2009

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…Moreover, this approach can be extended formally, in much the same way as in, e.g. [32,35], also for non-linear problems arising along with large deformations or material nonlinearities (cf. [15]).…”

Section: Discussionmentioning

confidence: 98%

Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

2013

Self Cite

View full text Add to dashboard Cite

In this paper, quasistatic models are developed for the slow flow of compressible fluids through porous solids, where the solid exhibits fading memory viscoelasticity. Problems of this type are important in practical geomechanics contexts, for example, in the context of fluid flow through unconsolidated reservoir sands and of wellbore deformation behaviour in gas and oil shale reservoirs, all of which have been studied extensively. For slow viscous fluid flow in the poro-viscoelastic media we are able to neglect the dynamic effects related to inertia forces, as well as the dissipation associated with the viscous flows. This is in contrast to the vast body of work in the poro-elastic context, where much faster flow of the viscous fluids may give rise to memory effects associated with microflows in pores of the solid media. Such problems have been treated extensively in both the dynamic and quasistatic cases. We are taking a specific type of the porous medium subject to slow deformation processes possibly inducing moderate pressure gradients and flow rates characterised by negligible inertia effects. As the result of homogenisation of such a two-phase medium, we observe the fading memory behaviour in the Biot modulus which controls the pressure increase due to skeleton macroscopic deformation and pore fluid content. Although our derivation leads to a result which is consistent with the formal phenomenological approach proposed by Biot (J Appl Phys 23:1482-1498, 1962, we offer the reader more insight into the structure of the poro-viscoelastic constitutive relations obtained; in particular, we can show that the Biot compressibility evolves in time according to the creep function while the skeleton stiffness is driven by the relaxation function.

show abstract

“…The form of the homogenized model obtained reveals an interesting relationship between the fading memory material viscoelasticity observed at the macroscale and the strain-induced microflow in the low permeable inclusions, which is a local phenomenon. Similar features were discussed in [19,20] in the context of upscaling the model of a large deforming medium describing behaviour of biological tissues. The methods used in the present paper may be adapted and applied to similar double-porous materials with more complex topology of the reference periodic cell Y .…”

Section: Resultsmentioning

confidence: 69%

On the homogenization of a diffusion–deformation problem in strongly heterogeneous media

Griso¹,

Rohan

2007

Ricerche mat.

Self Cite

View full text Add to dashboard Cite

show abstract

Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids

Cited by 25 publications

References 16 publications

Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method

Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method

Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

On the homogenization of a diffusion–deformation problem in strongly heterogeneous media

Contact Info

Product

Resources

About