The paper deals with the homogenization-based modelling of periodic porous structures saturated b... more The paper deals with the homogenization-based modelling of periodic porous structures saturated by a Newtonian fluid and locally controlable due to embedded piezoelectric segments which can induce a peristaltic deformation of the microchannels, in response to prescribed propagating voltage waves. To respect dynamic effects of the flow in bulged pores, where the advection term of the acceleration is important, two time scales are considered and an appropriate time scaling of the fast-slow dynamics is introduced in a proportion to the spatial scaling. The two-scale homogenized problem is nonlinear by the consequence of the advection term in the flow model. Further nonlinearity is introduced by deformation-dependent homogenized coefficients of the macroscopic equations. For this, a linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to the deformation induced by the macroscopic quantities is employed.
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media feat... more The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic skeleton, rigid inclusion and a void pore. Unilateral frictionless contact is considered between opposing surfaces of the pore. For the homogenized model derived in our previous work, we justify incremental formulations and propose several variants of two-scale algorithms which commute iteratively solving of the micro-and the macro-level contact subproblems. A dual formulation which take advantage of the assumed microstructure periodicity and a small deformation framework, is derived for the contact problems at the micro-level. This enables to apply the semi-smooth Newton method. For the global, macrolevel step two alternatives are tested; one relying on a frozen contact identified at the microlevel, the other based on a reduced contact associated with boundaries of contact sets. Numerical examples of 2D deforming structures are presented as a proof of the concept.
The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous... more The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due to piezoelectric segments embedded in the microstructure and locally actuated by voltage waves. The homogenization is employed to derive a macroscopic model of the poroelastic medium with effective parameters modified by piezoelectric properties of the skeleton. To capture the peristaltic pumping, the nonlinearity associated with deforming configuration must be respected. In the macroscopic model, this nonlinearity is introduced through homogenized coefficients depending on the deforming micro-configurations. For this, linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to deformation induced by the macroscopic quantities are employed. This enables to avoid the two-scale tight coupling of the macro-and microproblems otherwise needed in nonlinear problems. The derived reduced-order model is implemented and verified using direct numerical simulations of the periodic heterogeneous medium. Numerical results demonstrate the peristaltic driven fluid propulsion in response to the electric actuation and the efficiency of the proposed treatment of the nonlinearity. The paper shows new perspectives in homogenization-based computationally efficient modelling of weakly nonlinear problems where continuum microstructures are perturbed by coupled fields.
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media feat... more The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic skeleton, rigid inclusion and a void pore. Unilateral frictionless contact is considered between opposing surfaces of the pore. For the homogenized model derived in our previous work, we justify incremental formulations and propose several variants of two-scale algorithms which commute iteratively solving of the micro-and the macro-level contact subproblems. A dual formulation which take advantage of the assumed microstructure periodicity and a small deformation framework, is derived for the contact problems at the micro-level. This enables to apply the semi-smooth Newton method. For the global, macrolevel step two alternatives are tested; one relying on a frozen contact identified at the microlevel, the other based on a reduced contact associated with boundaries of contact sets. Numerical examples of 2D deforming structures are presented as a proof of the concept.
We present a new approach and an algorithm for optimizing the material configuration and behaviou... more We present a new approach and an algorithm for optimizing the material configuration and behaviour of a fluid saturated porous medium in a two-scale setting. The state problem is governed by the Biot model describing the fluid-structure interaction in homogenized poroelastic structures. However, the approach is widely applicable to multiphysics problems involving several macroscopic fields where homogenization provides the relationship between the microconfigurations and the macroscopic mathematical model. The optimization variables describe the local microstructure design by virtue of the pore shape which determines the effective medium properties-the material coefficients-computed by the homogenization method. The main idea of the numerical optimization strategy consists in a) employing a precomputed database of the material coefficients associated to the geometric parameters and b) applying the sequential global programming (SGP) method for solving the problem of macroscopically optimized distribution of material coefficients. Although there are similarities with the free material optimization (FMO) approach, only effective material coefficients are considered admissible, for which a well-defined set of corresponding configurable microstructures exist. Due to the flexibility of the SGP approach, different types of microstructures with fully independent parametrizations can easily be handled. The efficiency of the concept is demonstrated by a series of numerical experiments. We show that the SGP method can handle simultaneously multiple types of microstructures with nontrivial parametrizations using a considerably low and stable number of state problems to be solved.
Regulační orgány jaderných reaktorů jsou zařízení, které slouží k regulaci jaderné reakce při sta... more Regulační orgány jaderných reaktorů jsou zařízení, které slouží k regulaci jaderné reakce při standardním provozu jaderného reaktoru a také k potlačení jaderné reakce v průběhu různých havarijních stavů. Vzhledem k nebezpečnosti nekontrolované jaderné reakce je nutné verifikovat funkci regulačních orgánů pro všechny havarijní stavy, přičemž je zřejmé, že ne všechny havarijní stavy jde simulovat experimentálně. V těchto případech je tedy vhodné sestavit matematický (výpočtový) model regulačního orgánu a provést numerické analýzy za účelem zjištění funkčnosti regulačního orgánu. V tomto příspěvku je popsán způsob vytvoření výpočtového modelu regulačního orgánu jaderného reaktoru VVER 440 a jsou představeny výsledky dynamické analýzy pro havarijní odstavení reaktoru při seismické události. 2 Matematický model regulačního orgánu reaktoru VVER 440 Na obrázku 1 je vidět struktura celého jaderného reaktoru s jedním vyznačeným regulačním orgánem, jehož dvě hlavní komponenty jsou pohon a vlastní regulační kazeta.
The objective of the paper is to demonstrate the homogenization approach applied to modelling the... more The objective of the paper is to demonstrate the homogenization approach applied to modelling the acoustic transmission on perforated interfaces embedded in the acoustic fluid. We assume a layer, with periodically perforated obstacles, separating two half-spaces filled with the fluid. The homogenization method provides limit transmission conditions which can be prescribed at the homogenized surface representing the “limit” interface. The conditions describe relationship between jump of the acoustic pressures and the transversal acoustic velocity, on introducing the “in-layer pressure” which describes wave propagation in the tangent directions with respect to the interface. This approach may serve as a relevant tool for optimal design of devices aimed at attenuation of the acoustic waves, such as the engine exhaust mufflers or other structures fitted with sieves and grillages. We present numerical examples of wave propagation in a muffler-like structure illustrating viability of the ...
Background: Krüppel-like factor5 (KLF5) has been reported to be involved in tumorigenicity of int... more Background: Krüppel-like factor5 (KLF5) has been reported to be involved in tumorigenicity of intestinal epithelium and is a transcription factor that affects tumor growth, invasion, and metastasis. The liver is the most common site of distant metastases of colorectal cancer and colorectal liver metastases is an important factor affecting its prognosis. Therefore, we examined the correlation between KLF5 expression level in colorectal liver metastases and clinicopathological factors and prognosis. Methods: KLF5 expression was evaluated immunohistochemically using surgical specimens of 98 patients who underwent initial hepatectomy for colorectal liver metastases. Results: KLF5 expression was detected in the cytoplasm of cancer cells. Of 98 cases, KLF5 was highly expressed in 42 cases. The number of metastatic tumors was relatively higher in the KLF5 high expression group (P=0.171). The tumor diameter was significantly larger in the KLF5 high expression group (P=0.007). In addition, there was a positive correlation between KLF5 expression and Ki67 expression (P=0.007). Overall survival rate after initial hepatectomy was significantly worse in the KLF5 high expression group compared with the KLF5 low expression group (P=0.029). Time to surgical failure (TSF) was significantly short in the KLF5 high expression group (P=0.017). Univariate analysis demonstrated that administration of preoperative chemotherapy, use of molecular targeted reagent, high serum carcinoembryonic antigen level, lymph node metastases of primary lesion, number of tumor (4), tumor diameter (5cm) and high expression level of KLF5 were significantly associated with a poor prognosis. Multivariate analysis demonstrated that number of tumor (4), tumor diameter (5cm) and high expression of KLF5 were independent risk factors for poor prognosis (P=0.040, P=0.001, P=0.045, respectively). Conclusion: KLF5 expression is an independent prognostic factor of patients with colorectal liver metastases. A novel treatment targeting KLF5 may improve the prognosis of patients with colorectal liver metastases.
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems desc... more SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by the NumPy package. For a particular problem two interfaces can be used: a declarative application programming interface (API), where problem description/definition files (Python modules) are used to define a calculation, and an imperative API, that can be used for interactive commands, or in scripts and libraries. After outlining the SfePy package development, the paper introduces its implementation, structure and general features. The components for defining a partial differential equation are described using an example of a simple heat conduction problem. Specifically, the declarative API of SfePy is presented in the example. To illustrate one of SfePy's main assets, the framework for implementing complex multiscale models based on the theory of homogenization, an example of a two-scale piezoelastic model is presented, showing both the mathematical description of the problem and the corresponding code.
Proceedings of the Eleventh International Conference on Computational Structures Technology
This paper deals with modeling wave dispersion in periodically heterogeneous plates characterised... more This paper deals with modeling wave dispersion in periodically heterogeneous plates characterised by high contrasts in elastic coefficients. We study two plate models based on the Reissner-Mindlin (R-M) theory and on the Kirchhoff-Love (K-L) theory. Models of homogenized plates were obtained using the two-scale unfolding method with the high contrast ansatz respected by scaling the elasticity coefficients of compliant inclusions. Consequently, dispersion properties are retained in the limit when the scale of the microstructure tends to zero. For some wavelengths, “mass density” coefficients can be negative, so that intervals of frequencies exist for which there is no propagation of elastic waves, the so-called band-gaps. Dispersion analysis for guided waves is performed for both types of the plates; occurrence of band gaps for the R-M plates is confirmed using numerical examples, however, the homogenized K-L plate model does not admit band gaps.
Progress in Computational Physics (PiCP) Vol 1: Wave Propagation in Periodic Media, 2012
This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation th... more This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation through heterogenous layers. The motivation is provided by the demand for a better understanding of meta-materials and their possible construction. We stress the analogies between the mathematical treatment of phononic, photonic and elastic meta-materials. Moreover, we treat the cloaking problem in more detail from an analytical and simulation oriented point of view. The novelty in the approach presented here is with the interlinked homogenization-and optimization procedure.
The paper deals with the homogenization-based modelling of periodic porous structures saturated b... more The paper deals with the homogenization-based modelling of periodic porous structures saturated by a Newtonian fluid and locally controlable due to embedded piezoelectric segments which can induce a peristaltic deformation of the microchannels, in response to prescribed propagating voltage waves. To respect dynamic effects of the flow in bulged pores, where the advection term of the acceleration is important, two time scales are considered and an appropriate time scaling of the fast-slow dynamics is introduced in a proportion to the spatial scaling. The two-scale homogenized problem is nonlinear by the consequence of the advection term in the flow model. Further nonlinearity is introduced by deformation-dependent homogenized coefficients of the macroscopic equations. For this, a linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to the deformation induced by the macroscopic quantities is employed.
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media feat... more The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic skeleton, rigid inclusion and a void pore. Unilateral frictionless contact is considered between opposing surfaces of the pore. For the homogenized model derived in our previous work, we justify incremental formulations and propose several variants of two-scale algorithms which commute iteratively solving of the micro-and the macro-level contact subproblems. A dual formulation which take advantage of the assumed microstructure periodicity and a small deformation framework, is derived for the contact problems at the micro-level. This enables to apply the semi-smooth Newton method. For the global, macrolevel step two alternatives are tested; one relying on a frozen contact identified at the microlevel, the other based on a reduced contact associated with boundaries of contact sets. Numerical examples of 2D deforming structures are presented as a proof of the concept.
The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous... more The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due to piezoelectric segments embedded in the microstructure and locally actuated by voltage waves. The homogenization is employed to derive a macroscopic model of the poroelastic medium with effective parameters modified by piezoelectric properties of the skeleton. To capture the peristaltic pumping, the nonlinearity associated with deforming configuration must be respected. In the macroscopic model, this nonlinearity is introduced through homogenized coefficients depending on the deforming micro-configurations. For this, linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to deformation induced by the macroscopic quantities are employed. This enables to avoid the two-scale tight coupling of the macro-and microproblems otherwise needed in nonlinear problems. The derived reduced-order model is implemented and verified using direct numerical simulations of the periodic heterogeneous medium. Numerical results demonstrate the peristaltic driven fluid propulsion in response to the electric actuation and the efficiency of the proposed treatment of the nonlinearity. The paper shows new perspectives in homogenization-based computationally efficient modelling of weakly nonlinear problems where continuum microstructures are perturbed by coupled fields.
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media feat... more The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic skeleton, rigid inclusion and a void pore. Unilateral frictionless contact is considered between opposing surfaces of the pore. For the homogenized model derived in our previous work, we justify incremental formulations and propose several variants of two-scale algorithms which commute iteratively solving of the micro-and the macro-level contact subproblems. A dual formulation which take advantage of the assumed microstructure periodicity and a small deformation framework, is derived for the contact problems at the micro-level. This enables to apply the semi-smooth Newton method. For the global, macrolevel step two alternatives are tested; one relying on a frozen contact identified at the microlevel, the other based on a reduced contact associated with boundaries of contact sets. Numerical examples of 2D deforming structures are presented as a proof of the concept.
We present a new approach and an algorithm for optimizing the material configuration and behaviou... more We present a new approach and an algorithm for optimizing the material configuration and behaviour of a fluid saturated porous medium in a two-scale setting. The state problem is governed by the Biot model describing the fluid-structure interaction in homogenized poroelastic structures. However, the approach is widely applicable to multiphysics problems involving several macroscopic fields where homogenization provides the relationship between the microconfigurations and the macroscopic mathematical model. The optimization variables describe the local microstructure design by virtue of the pore shape which determines the effective medium properties-the material coefficients-computed by the homogenization method. The main idea of the numerical optimization strategy consists in a) employing a precomputed database of the material coefficients associated to the geometric parameters and b) applying the sequential global programming (SGP) method for solving the problem of macroscopically optimized distribution of material coefficients. Although there are similarities with the free material optimization (FMO) approach, only effective material coefficients are considered admissible, for which a well-defined set of corresponding configurable microstructures exist. Due to the flexibility of the SGP approach, different types of microstructures with fully independent parametrizations can easily be handled. The efficiency of the concept is demonstrated by a series of numerical experiments. We show that the SGP method can handle simultaneously multiple types of microstructures with nontrivial parametrizations using a considerably low and stable number of state problems to be solved.
Regulační orgány jaderných reaktorů jsou zařízení, které slouží k regulaci jaderné reakce při sta... more Regulační orgány jaderných reaktorů jsou zařízení, které slouží k regulaci jaderné reakce při standardním provozu jaderného reaktoru a také k potlačení jaderné reakce v průběhu různých havarijních stavů. Vzhledem k nebezpečnosti nekontrolované jaderné reakce je nutné verifikovat funkci regulačních orgánů pro všechny havarijní stavy, přičemž je zřejmé, že ne všechny havarijní stavy jde simulovat experimentálně. V těchto případech je tedy vhodné sestavit matematický (výpočtový) model regulačního orgánu a provést numerické analýzy za účelem zjištění funkčnosti regulačního orgánu. V tomto příspěvku je popsán způsob vytvoření výpočtového modelu regulačního orgánu jaderného reaktoru VVER 440 a jsou představeny výsledky dynamické analýzy pro havarijní odstavení reaktoru při seismické události. 2 Matematický model regulačního orgánu reaktoru VVER 440 Na obrázku 1 je vidět struktura celého jaderného reaktoru s jedním vyznačeným regulačním orgánem, jehož dvě hlavní komponenty jsou pohon a vlastní regulační kazeta.
The objective of the paper is to demonstrate the homogenization approach applied to modelling the... more The objective of the paper is to demonstrate the homogenization approach applied to modelling the acoustic transmission on perforated interfaces embedded in the acoustic fluid. We assume a layer, with periodically perforated obstacles, separating two half-spaces filled with the fluid. The homogenization method provides limit transmission conditions which can be prescribed at the homogenized surface representing the “limit” interface. The conditions describe relationship between jump of the acoustic pressures and the transversal acoustic velocity, on introducing the “in-layer pressure” which describes wave propagation in the tangent directions with respect to the interface. This approach may serve as a relevant tool for optimal design of devices aimed at attenuation of the acoustic waves, such as the engine exhaust mufflers or other structures fitted with sieves and grillages. We present numerical examples of wave propagation in a muffler-like structure illustrating viability of the ...
Background: Krüppel-like factor5 (KLF5) has been reported to be involved in tumorigenicity of int... more Background: Krüppel-like factor5 (KLF5) has been reported to be involved in tumorigenicity of intestinal epithelium and is a transcription factor that affects tumor growth, invasion, and metastasis. The liver is the most common site of distant metastases of colorectal cancer and colorectal liver metastases is an important factor affecting its prognosis. Therefore, we examined the correlation between KLF5 expression level in colorectal liver metastases and clinicopathological factors and prognosis. Methods: KLF5 expression was evaluated immunohistochemically using surgical specimens of 98 patients who underwent initial hepatectomy for colorectal liver metastases. Results: KLF5 expression was detected in the cytoplasm of cancer cells. Of 98 cases, KLF5 was highly expressed in 42 cases. The number of metastatic tumors was relatively higher in the KLF5 high expression group (P=0.171). The tumor diameter was significantly larger in the KLF5 high expression group (P=0.007). In addition, there was a positive correlation between KLF5 expression and Ki67 expression (P=0.007). Overall survival rate after initial hepatectomy was significantly worse in the KLF5 high expression group compared with the KLF5 low expression group (P=0.029). Time to surgical failure (TSF) was significantly short in the KLF5 high expression group (P=0.017). Univariate analysis demonstrated that administration of preoperative chemotherapy, use of molecular targeted reagent, high serum carcinoembryonic antigen level, lymph node metastases of primary lesion, number of tumor (4), tumor diameter (5cm) and high expression level of KLF5 were significantly associated with a poor prognosis. Multivariate analysis demonstrated that number of tumor (4), tumor diameter (5cm) and high expression of KLF5 were independent risk factors for poor prognosis (P=0.040, P=0.001, P=0.045, respectively). Conclusion: KLF5 expression is an independent prognostic factor of patients with colorectal liver metastases. A novel treatment targeting KLF5 may improve the prognosis of patients with colorectal liver metastases.
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems desc... more SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by the NumPy package. For a particular problem two interfaces can be used: a declarative application programming interface (API), where problem description/definition files (Python modules) are used to define a calculation, and an imperative API, that can be used for interactive commands, or in scripts and libraries. After outlining the SfePy package development, the paper introduces its implementation, structure and general features. The components for defining a partial differential equation are described using an example of a simple heat conduction problem. Specifically, the declarative API of SfePy is presented in the example. To illustrate one of SfePy's main assets, the framework for implementing complex multiscale models based on the theory of homogenization, an example of a two-scale piezoelastic model is presented, showing both the mathematical description of the problem and the corresponding code.
Proceedings of the Eleventh International Conference on Computational Structures Technology
This paper deals with modeling wave dispersion in periodically heterogeneous plates characterised... more This paper deals with modeling wave dispersion in periodically heterogeneous plates characterised by high contrasts in elastic coefficients. We study two plate models based on the Reissner-Mindlin (R-M) theory and on the Kirchhoff-Love (K-L) theory. Models of homogenized plates were obtained using the two-scale unfolding method with the high contrast ansatz respected by scaling the elasticity coefficients of compliant inclusions. Consequently, dispersion properties are retained in the limit when the scale of the microstructure tends to zero. For some wavelengths, “mass density” coefficients can be negative, so that intervals of frequencies exist for which there is no propagation of elastic waves, the so-called band-gaps. Dispersion analysis for guided waves is performed for both types of the plates; occurrence of band gaps for the R-M plates is confirmed using numerical examples, however, the homogenized K-L plate model does not admit band gaps.
Progress in Computational Physics (PiCP) Vol 1: Wave Propagation in Periodic Media, 2012
This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation th... more This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation through heterogenous layers. The motivation is provided by the demand for a better understanding of meta-materials and their possible construction. We stress the analogies between the mathematical treatment of phononic, photonic and elastic meta-materials. Moreover, we treat the cloaking problem in more detail from an analytical and simulation oriented point of view. The novelty in the approach presented here is with the interlinked homogenization-and optimization procedure.
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Papers by Eduard Rohan