Michal Kotoul - Academia.edu (original) (raw)

Papers by Michal Kotoul

Springer eBooks, Mar 25, 2008

Materials Science Forum, Dec 1, 2007

The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the... more The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The combination of the discretization, numerical and analytic methods is used. The discretization method, such as common finite element method (FEM), is served to include the boundary condition to the GSIF solution and to describe the remote stress and displacement field region with the low influence of the singularity of the crack tip. The Lekhnickii-Eshelby-Stroh (LES) formalism is used to derive the approach solution for the near stress field of the crack tip and the singularity problem in an orthotropic 'trimaterial' using the Schwartz-Neumann's alternating technique. The problem of the stress singularity is treated as a non-linear eigenvalue problem, which leads to the characteristic equation for the stress singularities of the form rδ −1 , 0

Engineering Mechanics ..., May 16, 2024

Engineering Fracture Mechanics, 1990

ABSTRACT This paper deals with the numerical simulation of the inception of plastic instability a... more ABSTRACT This paper deals with the numerical simulation of the inception of plastic instability and neck formation using damage mechanics and finite difference method. The incorporation of inertia forces into the computations makes it possible to model the dynamic redistribution of reversible strain energy which occurs as a consequence of the inception of plastic flow localization. It is shown that void kinetics stimulate this process. Numerical results suggest that the continuous process of plastic strain localization is accompanied by a sequence of abrupt changes. Such behaviour is evidenced by the discrete character of the time history of radial particle velocity at the chosen point of the sample. The measurements of acoustic emission in low carbon steel show similar discrete burst signals behind the plastic stability limit. It is concluded from the above mentioned results that plastic flow localization forms the intensive source of acoustic emission in ductile materials which may be more intensive as the sources generated by the microvoids activity.

Key Engineering Materials, Sep 1, 2007

The increasing use of fibre-reinforced composites in high performance structures has brought a re... more The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks, wedges, and multi-material wedges in anisotropic materials. This paper will address three crucial stages of the general stress concentrator analysis: i) numerical procedures for the determination of eigenvalues and eigenvectors in Williams-like asymptotic expansion for multi-material wedge; ii) approaches to an accurate calculation of the near crack tip fields – the application of so-called two-state (or mutual) conservation integrals; iii) application of fracture criteria for the assessment of fracture inception at the general stress concentrators - concept of the so called finite fracture mechanics.

Springer eBooks, Jan 4, 2008

The increasing use of fibre-reinforced composites in high performance structures has brought a re... more The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks in anisotropic materials. Most matrices of the advanced composite material are brittle. They prone to cracking under very low applied stresses and failure frequently occurs in the form of multiple matrix cracking. The orientations of these cracks may vary depending

Key Engineering Materials, Dec 1, 2019

The contribution deals with modelling and prediction of failure of mechanically loaded open cell ... more The contribution deals with modelling and prediction of failure of mechanically loaded open cell ceramic foam structures by using 3D volume FE models constructed from CT scans of real foam specimens. The condition for crack initiation in particular struts comes from the coupled stress-energy criterion which combines two fracture-mechanics parameters of the investigated material – tensile strength and its fracture toughness. By combining of both stress and energy condition one obtains information about the crack initiation length which is later used (together with the tensile strength) for determination of the strut failure in the complex 3D FE model of the ceramic foam structure. The crack onset is considered in the critical location at the moment when the (tensile) principal stress under the strut surface (in a depth corresponding to the crack initiation length) exceeded the tensile strength of the strut. Such approach enables us to define failure also on relatively coarse meshes of the FE models where potential stress concentrations are not described precisely and therefore it is not possible to decide about the failure just based upon the value of tensile stress on the strut surface.

Materials Science Forum, Dec 1, 2007

Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimil... more Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimilar elastic anisotropic materials. The link to the configurational forces approach is suggested.

Key Engineering Materials, Nov 1, 2006

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a hal... more The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half- space is analyzed for a general case of elastic anisotropy bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (ψ - integral) is discussed as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM.

International Journal of Fracture, Sep 1, 2007

Journal of Intelligent Material Systems and Structures, Jul 30, 2020

Engineering Fracture Mechanics, Oct 1, 2018

International Conference on Mechatronics - Mechatronika, Dec 1, 2018

In this contribution, a design of novel cantilever beam energy harvester, composed of several cer... more In this contribution, a design of novel cantilever beam energy harvester, composed of several ceramic layers with introduced high residual stresses, is proposed. The main aim of residual stresses is to protect the piezoelectric layer from cracking during the service of the harvester. A way to optimize composition of the multilayer energy harvester to receive both high apparent fracture toughness of the structure and simultaneously high electrical power of the harvester during its operation is presented. Both an analytical and a numerical model of the vibrational energy harvester are developed for this purpose. The increased resistance to fracture is achieved by means of high compressive stresses in the external ceramic layers. The electrical power output of the harvester is further optimized with respect to connected resistive load and excitation acceleration of vibrations. It was found that the optimal resistive load also leads to lowest mechanical stresses in particular laminate layers.

Materials Science Forum, Apr 1, 2005

A micromechanics study is presented of the matrix cracking of fibres-reinforced ceramic composite... more A micromechanics study is presented of the matrix cracking of fibres-reinforced ceramic composites when subject to tensile stressing normal to fibres. Stability and/or instability of the straight micro-crack paths is investigated for a periodic array of originally collinear, slowly growing microcracks with fibres located in between the neighbouring micro-cracks tips. The relevant application e.g. refers to matrix cracking in 90° plies of cross-ply ceramic composites. The problem is solved using the technique of distributed dislocations and an approximate fundamental solution for a single edge dislocation lying in a general point between inclusion centres. The Muschelishvili complex potentials and the Galerkin method for a numerical evaluation of coefficients of suitable chosen bas functions are employed. Numerical results are presented showing an influence of mutual microcracks-fibres geometry and the mismatch of elastic properties on micro-crack path stability/instability.

Key Engineering Materials, Aug 1, 2018

The aim of the paper is quantify the material length scale parameter of the simplified form of th... more The aim of the paper is quantify the material length scale parameter of the simplified form of the strain gradient elasticity theory (SGET) using first principles density-functional theory (DFT). The single material length scale parameterlis extracted from phonon-dispersions generated by DFT calculations and, for comparison, by adjusting the analytical SGET solution for the displacement field near the screw dislocation with the DFT calculations of this field. The obtained results are further used in the SGET modeling of cracked nanopanel formed by the single tungsten crystal where due to size effects and nonlocal material point interactions the classical fracture mechanics breaks down.

Solid State Phenomena, Dec 1, 2016

To better understand response or fracture conditions of the ceramic foam materials to the mechani... more To better understand response or fracture conditions of the ceramic foam materials to the mechanical loading, a finite element (FE) analysis of these structures has to be employed. The cellular structure of foams can be modelled either using a detailed realistic FE model based on the computer tomography scans or by using of simplified, beam element based, models. Nevertheless a main drawback of the realistic foam modelling consists in its high demandingness on computational resources. Therefore, simplified models are welcome substitutions (at least for analysis of the global mechanical foam response). The regular foam structure, based e.g. on Kelvin cells, is simple from the modelling point of view, but it doesn´t exactly capture the fully random character of the real foam structures and corresponding response to the external load. Definition of the random beam foam structure (respecting the real cell shapes and their distribution within volume), can thus improve this deficiency. The main aim of this work is thus to compare these different modelling approaches and quantify the influence of the foam irregularity on the response of ceramic foams to external (tensile) loading for various model sizes.

International Journal of Fracture, Nov 1, 1989

ABSTRACT Using the constitutive model for brittle tensile fracture derived by Grady and Kipp and ... more ABSTRACT Using the constitutive model for brittle tensile fracture derived by Grady and Kipp and the theory of moving singular surfaces, an analytical approach to the description of stress wave/fracture interaction has been proposed. The propagation of a one dimensional tensile stress pulse in a linear elastic medium with an inherent flaw structure is investigated. The nonlinearity in the constitutive description induced by the fracture process is effectively treated in terms of nonlinear waves with internal state variables.

Engineering Fracture Mechanics, 2012

Theoretical and Applied Fracture Mechanics, Oct 1, 2012

Springer eBooks, Mar 25, 2008

Materials Science Forum, Dec 1, 2007

The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the... more The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The combination of the discretization, numerical and analytic methods is used. The discretization method, such as common finite element method (FEM), is served to include the boundary condition to the GSIF solution and to describe the remote stress and displacement field region with the low influence of the singularity of the crack tip. The Lekhnickii-Eshelby-Stroh (LES) formalism is used to derive the approach solution for the near stress field of the crack tip and the singularity problem in an orthotropic 'trimaterial' using the Schwartz-Neumann's alternating technique. The problem of the stress singularity is treated as a non-linear eigenvalue problem, which leads to the characteristic equation for the stress singularities of the form rδ −1 , 0

Engineering Mechanics ..., May 16, 2024

Engineering Fracture Mechanics, 1990

ABSTRACT This paper deals with the numerical simulation of the inception of plastic instability a... more ABSTRACT This paper deals with the numerical simulation of the inception of plastic instability and neck formation using damage mechanics and finite difference method. The incorporation of inertia forces into the computations makes it possible to model the dynamic redistribution of reversible strain energy which occurs as a consequence of the inception of plastic flow localization. It is shown that void kinetics stimulate this process. Numerical results suggest that the continuous process of plastic strain localization is accompanied by a sequence of abrupt changes. Such behaviour is evidenced by the discrete character of the time history of radial particle velocity at the chosen point of the sample. The measurements of acoustic emission in low carbon steel show similar discrete burst signals behind the plastic stability limit. It is concluded from the above mentioned results that plastic flow localization forms the intensive source of acoustic emission in ductile materials which may be more intensive as the sources generated by the microvoids activity.

Key Engineering Materials, Sep 1, 2007

The increasing use of fibre-reinforced composites in high performance structures has brought a re... more The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks, wedges, and multi-material wedges in anisotropic materials. This paper will address three crucial stages of the general stress concentrator analysis: i) numerical procedures for the determination of eigenvalues and eigenvectors in Williams-like asymptotic expansion for multi-material wedge; ii) approaches to an accurate calculation of the near crack tip fields – the application of so-called two-state (or mutual) conservation integrals; iii) application of fracture criteria for the assessment of fracture inception at the general stress concentrators - concept of the so called finite fracture mechanics.

Springer eBooks, Jan 4, 2008

The increasing use of fibre-reinforced composites in high performance structures has brought a re... more The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks in anisotropic materials. Most matrices of the advanced composite material are brittle. They prone to cracking under very low applied stresses and failure frequently occurs in the form of multiple matrix cracking. The orientations of these cracks may vary depending

Key Engineering Materials, Dec 1, 2019

The contribution deals with modelling and prediction of failure of mechanically loaded open cell ... more The contribution deals with modelling and prediction of failure of mechanically loaded open cell ceramic foam structures by using 3D volume FE models constructed from CT scans of real foam specimens. The condition for crack initiation in particular struts comes from the coupled stress-energy criterion which combines two fracture-mechanics parameters of the investigated material – tensile strength and its fracture toughness. By combining of both stress and energy condition one obtains information about the crack initiation length which is later used (together with the tensile strength) for determination of the strut failure in the complex 3D FE model of the ceramic foam structure. The crack onset is considered in the critical location at the moment when the (tensile) principal stress under the strut surface (in a depth corresponding to the crack initiation length) exceeded the tensile strength of the strut. Such approach enables us to define failure also on relatively coarse meshes of the FE models where potential stress concentrations are not described precisely and therefore it is not possible to decide about the failure just based upon the value of tensile stress on the strut surface.

Materials Science Forum, Dec 1, 2007

Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimil... more Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimilar elastic anisotropic materials. The link to the configurational forces approach is suggested.

Key Engineering Materials, Nov 1, 2006

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a hal... more The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half- space is analyzed for a general case of elastic anisotropy bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (ψ - integral) is discussed as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM.

International Journal of Fracture, Sep 1, 2007

Journal of Intelligent Material Systems and Structures, Jul 30, 2020

Engineering Fracture Mechanics, Oct 1, 2018

International Conference on Mechatronics - Mechatronika, Dec 1, 2018

In this contribution, a design of novel cantilever beam energy harvester, composed of several cer... more In this contribution, a design of novel cantilever beam energy harvester, composed of several ceramic layers with introduced high residual stresses, is proposed. The main aim of residual stresses is to protect the piezoelectric layer from cracking during the service of the harvester. A way to optimize composition of the multilayer energy harvester to receive both high apparent fracture toughness of the structure and simultaneously high electrical power of the harvester during its operation is presented. Both an analytical and a numerical model of the vibrational energy harvester are developed for this purpose. The increased resistance to fracture is achieved by means of high compressive stresses in the external ceramic layers. The electrical power output of the harvester is further optimized with respect to connected resistive load and excitation acceleration of vibrations. It was found that the optimal resistive load also leads to lowest mechanical stresses in particular laminate layers.

Materials Science Forum, Apr 1, 2005

A micromechanics study is presented of the matrix cracking of fibres-reinforced ceramic composite... more A micromechanics study is presented of the matrix cracking of fibres-reinforced ceramic composites when subject to tensile stressing normal to fibres. Stability and/or instability of the straight micro-crack paths is investigated for a periodic array of originally collinear, slowly growing microcracks with fibres located in between the neighbouring micro-cracks tips. The relevant application e.g. refers to matrix cracking in 90° plies of cross-ply ceramic composites. The problem is solved using the technique of distributed dislocations and an approximate fundamental solution for a single edge dislocation lying in a general point between inclusion centres. The Muschelishvili complex potentials and the Galerkin method for a numerical evaluation of coefficients of suitable chosen bas functions are employed. Numerical results are presented showing an influence of mutual microcracks-fibres geometry and the mismatch of elastic properties on micro-crack path stability/instability.

Key Engineering Materials, Aug 1, 2018

The aim of the paper is quantify the material length scale parameter of the simplified form of th... more The aim of the paper is quantify the material length scale parameter of the simplified form of the strain gradient elasticity theory (SGET) using first principles density-functional theory (DFT). The single material length scale parameterlis extracted from phonon-dispersions generated by DFT calculations and, for comparison, by adjusting the analytical SGET solution for the displacement field near the screw dislocation with the DFT calculations of this field. The obtained results are further used in the SGET modeling of cracked nanopanel formed by the single tungsten crystal where due to size effects and nonlocal material point interactions the classical fracture mechanics breaks down.

Solid State Phenomena, Dec 1, 2016

To better understand response or fracture conditions of the ceramic foam materials to the mechani... more To better understand response or fracture conditions of the ceramic foam materials to the mechanical loading, a finite element (FE) analysis of these structures has to be employed. The cellular structure of foams can be modelled either using a detailed realistic FE model based on the computer tomography scans or by using of simplified, beam element based, models. Nevertheless a main drawback of the realistic foam modelling consists in its high demandingness on computational resources. Therefore, simplified models are welcome substitutions (at least for analysis of the global mechanical foam response). The regular foam structure, based e.g. on Kelvin cells, is simple from the modelling point of view, but it doesn´t exactly capture the fully random character of the real foam structures and corresponding response to the external load. Definition of the random beam foam structure (respecting the real cell shapes and their distribution within volume), can thus improve this deficiency. The main aim of this work is thus to compare these different modelling approaches and quantify the influence of the foam irregularity on the response of ceramic foams to external (tensile) loading for various model sizes.

International Journal of Fracture, Nov 1, 1989

ABSTRACT Using the constitutive model for brittle tensile fracture derived by Grady and Kipp and ... more ABSTRACT Using the constitutive model for brittle tensile fracture derived by Grady and Kipp and the theory of moving singular surfaces, an analytical approach to the description of stress wave/fracture interaction has been proposed. The propagation of a one dimensional tensile stress pulse in a linear elastic medium with an inherent flaw structure is investigated. The nonlinearity in the constitutive description induced by the fracture process is effectively treated in terms of nonlinear waves with internal state variables.

Engineering Fracture Mechanics, 2012

Theoretical and Applied Fracture Mechanics, Oct 1, 2012