Z. Mróz - Academia.edu (original) (raw)
Papers by Z. Mróz
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1984
The phenomenon of rock burst occurs when the static stability conditions of the rock mass are vio... more The phenomenon of rock burst occurs when the static stability conditions of the rock mass are violated and the dynamic failure process proceeds starting from the equilibrium state. In view of the difficulties in determining numerically the instability point, an alternative approach is advocated here: after solving the initial static problem the mode and onset of dynamic failure are studied by superposition of dynamic disturbances. In this way quantitative analyses of rock burst phenomena may be handled in a relatively simple manner.
Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria
Structural Optimization, 1993
The semi-analytical, analytical and direct methods for numerical structural shape sensitivity ana... more The semi-analytical, analytical and direct methods for numerical structural shape sensitivity analysis are discussed for a beam model and the general three-dimensional case. While the two first methods are applied directly to the finite element model of a structure, the direct approach follows from a continuous formulation and only the final results can be discretized.
Advances in Engineering Software, 2015
The relative sliding motion of two elastic bodies in contact induces wear process and contact sha... more The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process tends to a steady state occuring at fixed contact stress and strain distribution. This state corresponds to the minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper extends the previous analyses [1-5] of the steady state conditions to cases of periodic sliding of contacting bodies, assuming cyclic steady state conditions for both mechanical and thermal fields.
Journal of Theoretical and Applied Mechanics, 2004
The present paper is concerned with the modelling of fatigue crack initiation and propagation by ... more The present paper is concerned with the modelling of fatigue crack initiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mroz (1996, 1998). Using the linear elastic stress field at the front of a crack or sharp notch, the damage growth on a physical plane is specified in terms of mean values of the stress and strength function. The model is applied to study crack propagation under cyclically varying tension-compression conditions. The predictions are compared with experimental data.
Variational Methods in the Mechanics of Solids, 1980
ABSTRACT The application of standard stationarity conditions to the optimal design of a structure... more ABSTRACT The application of standard stationarity conditions to the optimal design of a structure against buckling (or other eigenvalue constraints) may actually lead to a reduction of its real strength in the sense that the “optimized” structure has been weakened with respect to higher modes to the extent that these have now become fundamental. In this case a true optimum occurs when the magnitudes of several eigenvalues coalesce, and the corresponding optimality condition is then no longer stationary. This singular condition is derived and applied to several examples of major practical significance, together with a method of obtaining an approximate solution to the resulting set of nonlinear equations.
The present paper is concerned with the modelling of fatigue crack ini-tiation and propagation by... more The present paper is concerned with the modelling of fatigue crack ini-tiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mróz (1996, 1998). Using the linear elastic stress field at the front of a crack or sharp notch, the damage growth on a physical plane is specified in terms of mean values of the stress and strength function. The model is applied to study crack propagation under cyclically varying tension-compression conditions. The predictions are compared with experimental data. Key words: fatigue, damage accumulation, crack propagation 1.
Acta Mechanica, 2017
The present work provides a formulation of a constitutive model for metals with the aim to simula... more The present work provides a formulation of a constitutive model for metals with the aim to simulate cyclic deformation under axial extension or compression assisted by cyclic torsional (or shearing) straining of specified amplitude and frequency. Such a mode of deformation was recently implemented in technological processes such as extrusion, forging and rolling, cf.
Journal of Computational and Applied Mechanics, 2015
The relative sliding motion of two elastic bodies in contact induces wear process and contact sha... more The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process at the constant relative velocity between the bodies tends to a steady state occurring at fixed contact stress and strain distribution. This state corresponds to a minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper is devoted to analysis of wear processes occurring for periodic sliding of contacting bodies, assuming cyclic steady state conditions for mechanical fields. From the condition of the rigid body wear velocity a formula for summarized contact pressure in the periodic steady state is derived. The optimization problem is formulated for calculation of the contact surface shape induced by wear in the steady periodic state.
Computer Methods in Applied Mechanics and Engineering, 2012
ABSTRACT The relative sliding motion of two elastic bodies in contact under compressive tractions... more ABSTRACT The relative sliding motion of two elastic bodies in contact under compressive tractions induces wear process and contact shape evolution. The transient process tends to a steady state at fixed contact stress and strain distribution. This state was assumed to correspond to the minimum of the wear dissipation power. The stationary condition of the response functional then provides the contact pressure distribution. The present paper is aimed at extending to results of previous analyses , , , and of steady state conditions to cases of periodic sliding of contacting bodies, assuming the existence of cyclic steady state conditions. The wear dissipation in the steady cyclic period is then minimized with respect to the contact pressure distribution. The solutions of several cases of wear processes induced by translational and rotational sliding illustrate the applicability of the proposed variational method.
International Journal of Solids and Structures, 1994
ABSTRACT
To determine limit states of mechanical structures has always been one of the most important desi... more To determine limit states of mechanical structures has always been one of the most important design issues in mechanical and civi l engineering and long before modern computational tools had been available, engineering scientists and mathematicians have developed methods to deal with this question. For this, most important is to identify failure mechanisms in their particular technical context, to model them and to understand the structural evolution leading to the according limit state. Among the large variety of scenarios, we deal here exclusively with failure caused directly by inelastic material behaviour, concentrating on ductile metal or metal-li ke materials. From methodological point of view, only so-called Direct Methods, in particular Limitand Shakedown Analysis are considered. Limit Analysis, applicable only in the case of monotone loading is considered as particular case of Shakedown analysis, valid for variable loads with not deterministicall y given loading histories. ...
International Journal of Solids and Structures, 1992
Abstract The stability of discrete elastic systems subjected to conservative loading is governed ... more Abstract The stability of discrete elastic systems subjected to conservative loading is governed by the potential energy, which is a function of the generalized coordinates. When dry friction is present, it affects the stability conditions and the post-critical response. Quasi-static loading is considered and the normal forces to the friction surface are assumed to be specified. General critical state conditions are obtained in terms of the potential energy and the dissipation function. Then several examples are presented to illustrate various types of behavior. It is seen that limit points, bifurcation points, and transition points (associated with slip activation or deactivation) may occur on the deformation path, and that a sudden “snap” from one state to another is a common phenomenon when the system includes dry friction.
Granular Matter, 2018
The present paper is aimed at developing the analytical description of the interaction of two con... more The present paper is aimed at developing the analytical description of the interaction of two contacting spheres for several classes of slip and sliding trajectories, typical in the experimental testing. The analysis accounts for memory effects in the slip regime and configurational effects in the sliding regime, expressed in terms of an active loading surface and memory surfaces within the space of contact forces. Analytical relations for contact response are derived for linear and piecewise-linear motion trajectories of the sphere. The problem of multiple contact interaction of the sphere moving over the regularly packed granular bed is also considered analytically. It is demonstrated that the dual contact activation-separation processes occur within the combined slip-sliding modes, essentially affecting the distribution of contact tractions. The results obtained are relevant for the class of contact problems requiring analysis of interaction of slip and sliding displacements, in particular in testing grain contact interaction aimed at specification of elastic, frictional and wear parameters.
Icf11 Italy 2005, May 24, 2013
A material element with distributed microcracks of arbitrary orientations is considered under ten... more A material element with distributed microcracks of arbitrary orientations is considered under tensile and compressive stress regimes. The frictional slip with accompanying dilatancy at rough crack interfaces is assumed and crack growth criterion is derived. The variation of material compliance is analyzed and the non-linear response is determined for proportional loading and unloading.
Journal of Theoretical and Applied Mechanics
The most important effects related to monotonic and cyclic response of contact interfaces of brit... more The most important effects related to monotonic and cyclic response of contact interfaces of brittle materials are analyzed in the paper. Next, the available constitutive models are reviewed with respect to their ability to describe these effects. Several micro-mechanical mechanisms are analyzed including decohesion, interaction of primary and secondary asperities, asperity wear and damage and formation of a third body granular layer. Finally, we propose new formulations of constitutive models for cyclic interface response.
Structural Optimization, 1998
An algorithm of optimal design of supports including their number , position and stiffness is pro... more An algorithm of optimal design of supports including their number , position and stiffness is proposed. The number of supports constitute topological design parameters , their positions correspond to configuration parameters. Both , elastic and rigid supports are considered and the optimization is aimed to minimize the total structure cost. The topology bifurcation points correspond to generation of new supports. The topological sensitivity derivative is used in deriving the optimality conditions 9 The optimization procedure provides number of supports , their position and stiffness of both supports and beam segments.
International Journal of Non-Linear Mechanics, 2006
To study the response of cementitious joints in rock masses or masonry structures, the model of i... more To study the response of cementitious joints in rock masses or masonry structures, the model of interphase is considered for which the contact stresses and strains interact with the internal stresses or strains within the joint. The frictional slip and sliding effects are then combined with the inelastic deformations of the joint. The constitutive model of the joint is analysed by assuming two interfaces separating the joint from the adjacent material. The case of a cementitious layer interposed between two rigid bodies is treated in detail. Sommario. Al fine di analizzare la risposta mcccanica dei giunti cementizi presenti negli ammassi rocciosi o nelle strutture murarie a blocchi, viene presentato il modello di interfase che permette di tenere in conto l'interazione fra le tensioni e le deformazioni di contatto con quelle interne al giunto. Pertanto, i fenomeni di scivolamento che si verificano al contatto fra blocchi e giunto sono combinati con le deformazioni anelastiche del materiale che costituisce il giunto stesso. Il modello costitutivo del giuntoè derivato dall'assunzione che il giunto sia separato dai blocchi attraverso due interfacce. Il caso di un giunto cementizio interposto fra due blocchi rigidi, soggetto a compressione, viene trattatto nel dettaglio.
Wear, 1999
A model of friction accounting for third body particles at the contact interface is derived from ... more A model of friction accounting for third body particles at the contact interface is derived from a simple micro-mechanical model of a particle interacting with a hard tool surface and a soft workpiece surface. Also a wear law coupled with this friction model is proposed. When wear of the tool surface is considered, the abrasive contribution of hard particles is only accounted for. The rate of wear is associated with frictional dissipation rate rather than with the product of normal pressure and slip velocity as in the classical Archard wear law. Numerical examples illustrate applicability and properties of the proposed friction and wear model.
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1984
The phenomenon of rock burst occurs when the static stability conditions of the rock mass are vio... more The phenomenon of rock burst occurs when the static stability conditions of the rock mass are violated and the dynamic failure process proceeds starting from the equilibrium state. In view of the difficulties in determining numerically the instability point, an alternative approach is advocated here: after solving the initial static problem the mode and onset of dynamic failure are studied by superposition of dynamic disturbances. In this way quantitative analyses of rock burst phenomena may be handled in a relatively simple manner.
Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria
Structural Optimization, 1993
The semi-analytical, analytical and direct methods for numerical structural shape sensitivity ana... more The semi-analytical, analytical and direct methods for numerical structural shape sensitivity analysis are discussed for a beam model and the general three-dimensional case. While the two first methods are applied directly to the finite element model of a structure, the direct approach follows from a continuous formulation and only the final results can be discretized.
Advances in Engineering Software, 2015
The relative sliding motion of two elastic bodies in contact induces wear process and contact sha... more The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process tends to a steady state occuring at fixed contact stress and strain distribution. This state corresponds to the minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper extends the previous analyses [1-5] of the steady state conditions to cases of periodic sliding of contacting bodies, assuming cyclic steady state conditions for both mechanical and thermal fields.
Journal of Theoretical and Applied Mechanics, 2004
The present paper is concerned with the modelling of fatigue crack initiation and propagation by ... more The present paper is concerned with the modelling of fatigue crack initiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mroz (1996, 1998). Using the linear elastic stress field at the front of a crack or sharp notch, the damage growth on a physical plane is specified in terms of mean values of the stress and strength function. The model is applied to study crack propagation under cyclically varying tension-compression conditions. The predictions are compared with experimental data.
Variational Methods in the Mechanics of Solids, 1980
ABSTRACT The application of standard stationarity conditions to the optimal design of a structure... more ABSTRACT The application of standard stationarity conditions to the optimal design of a structure against buckling (or other eigenvalue constraints) may actually lead to a reduction of its real strength in the sense that the “optimized” structure has been weakened with respect to higher modes to the extent that these have now become fundamental. In this case a true optimum occurs when the magnitudes of several eigenvalues coalesce, and the corresponding optimality condition is then no longer stationary. This singular condition is derived and applied to several examples of major practical significance, together with a method of obtaining an approximate solution to the resulting set of nonlinear equations.
The present paper is concerned with the modelling of fatigue crack ini-tiation and propagation by... more The present paper is concerned with the modelling of fatigue crack ini-tiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mróz (1996, 1998). Using the linear elastic stress field at the front of a crack or sharp notch, the damage growth on a physical plane is specified in terms of mean values of the stress and strength function. The model is applied to study crack propagation under cyclically varying tension-compression conditions. The predictions are compared with experimental data. Key words: fatigue, damage accumulation, crack propagation 1.
Acta Mechanica, 2017
The present work provides a formulation of a constitutive model for metals with the aim to simula... more The present work provides a formulation of a constitutive model for metals with the aim to simulate cyclic deformation under axial extension or compression assisted by cyclic torsional (or shearing) straining of specified amplitude and frequency. Such a mode of deformation was recently implemented in technological processes such as extrusion, forging and rolling, cf.
Journal of Computational and Applied Mechanics, 2015
The relative sliding motion of two elastic bodies in contact induces wear process and contact sha... more The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process at the constant relative velocity between the bodies tends to a steady state occurring at fixed contact stress and strain distribution. This state corresponds to a minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper is devoted to analysis of wear processes occurring for periodic sliding of contacting bodies, assuming cyclic steady state conditions for mechanical fields. From the condition of the rigid body wear velocity a formula for summarized contact pressure in the periodic steady state is derived. The optimization problem is formulated for calculation of the contact surface shape induced by wear in the steady periodic state.
Computer Methods in Applied Mechanics and Engineering, 2012
ABSTRACT The relative sliding motion of two elastic bodies in contact under compressive tractions... more ABSTRACT The relative sliding motion of two elastic bodies in contact under compressive tractions induces wear process and contact shape evolution. The transient process tends to a steady state at fixed contact stress and strain distribution. This state was assumed to correspond to the minimum of the wear dissipation power. The stationary condition of the response functional then provides the contact pressure distribution. The present paper is aimed at extending to results of previous analyses , , , and of steady state conditions to cases of periodic sliding of contacting bodies, assuming the existence of cyclic steady state conditions. The wear dissipation in the steady cyclic period is then minimized with respect to the contact pressure distribution. The solutions of several cases of wear processes induced by translational and rotational sliding illustrate the applicability of the proposed variational method.
International Journal of Solids and Structures, 1994
ABSTRACT
To determine limit states of mechanical structures has always been one of the most important desi... more To determine limit states of mechanical structures has always been one of the most important design issues in mechanical and civi l engineering and long before modern computational tools had been available, engineering scientists and mathematicians have developed methods to deal with this question. For this, most important is to identify failure mechanisms in their particular technical context, to model them and to understand the structural evolution leading to the according limit state. Among the large variety of scenarios, we deal here exclusively with failure caused directly by inelastic material behaviour, concentrating on ductile metal or metal-li ke materials. From methodological point of view, only so-called Direct Methods, in particular Limitand Shakedown Analysis are considered. Limit Analysis, applicable only in the case of monotone loading is considered as particular case of Shakedown analysis, valid for variable loads with not deterministicall y given loading histories. ...
International Journal of Solids and Structures, 1992
Abstract The stability of discrete elastic systems subjected to conservative loading is governed ... more Abstract The stability of discrete elastic systems subjected to conservative loading is governed by the potential energy, which is a function of the generalized coordinates. When dry friction is present, it affects the stability conditions and the post-critical response. Quasi-static loading is considered and the normal forces to the friction surface are assumed to be specified. General critical state conditions are obtained in terms of the potential energy and the dissipation function. Then several examples are presented to illustrate various types of behavior. It is seen that limit points, bifurcation points, and transition points (associated with slip activation or deactivation) may occur on the deformation path, and that a sudden “snap” from one state to another is a common phenomenon when the system includes dry friction.
Granular Matter, 2018
The present paper is aimed at developing the analytical description of the interaction of two con... more The present paper is aimed at developing the analytical description of the interaction of two contacting spheres for several classes of slip and sliding trajectories, typical in the experimental testing. The analysis accounts for memory effects in the slip regime and configurational effects in the sliding regime, expressed in terms of an active loading surface and memory surfaces within the space of contact forces. Analytical relations for contact response are derived for linear and piecewise-linear motion trajectories of the sphere. The problem of multiple contact interaction of the sphere moving over the regularly packed granular bed is also considered analytically. It is demonstrated that the dual contact activation-separation processes occur within the combined slip-sliding modes, essentially affecting the distribution of contact tractions. The results obtained are relevant for the class of contact problems requiring analysis of interaction of slip and sliding displacements, in particular in testing grain contact interaction aimed at specification of elastic, frictional and wear parameters.
Icf11 Italy 2005, May 24, 2013
A material element with distributed microcracks of arbitrary orientations is considered under ten... more A material element with distributed microcracks of arbitrary orientations is considered under tensile and compressive stress regimes. The frictional slip with accompanying dilatancy at rough crack interfaces is assumed and crack growth criterion is derived. The variation of material compliance is analyzed and the non-linear response is determined for proportional loading and unloading.
Journal of Theoretical and Applied Mechanics
The most important effects related to monotonic and cyclic response of contact interfaces of brit... more The most important effects related to monotonic and cyclic response of contact interfaces of brittle materials are analyzed in the paper. Next, the available constitutive models are reviewed with respect to their ability to describe these effects. Several micro-mechanical mechanisms are analyzed including decohesion, interaction of primary and secondary asperities, asperity wear and damage and formation of a third body granular layer. Finally, we propose new formulations of constitutive models for cyclic interface response.
Structural Optimization, 1998
An algorithm of optimal design of supports including their number , position and stiffness is pro... more An algorithm of optimal design of supports including their number , position and stiffness is proposed. The number of supports constitute topological design parameters , their positions correspond to configuration parameters. Both , elastic and rigid supports are considered and the optimization is aimed to minimize the total structure cost. The topology bifurcation points correspond to generation of new supports. The topological sensitivity derivative is used in deriving the optimality conditions 9 The optimization procedure provides number of supports , their position and stiffness of both supports and beam segments.
International Journal of Non-Linear Mechanics, 2006
To study the response of cementitious joints in rock masses or masonry structures, the model of i... more To study the response of cementitious joints in rock masses or masonry structures, the model of interphase is considered for which the contact stresses and strains interact with the internal stresses or strains within the joint. The frictional slip and sliding effects are then combined with the inelastic deformations of the joint. The constitutive model of the joint is analysed by assuming two interfaces separating the joint from the adjacent material. The case of a cementitious layer interposed between two rigid bodies is treated in detail. Sommario. Al fine di analizzare la risposta mcccanica dei giunti cementizi presenti negli ammassi rocciosi o nelle strutture murarie a blocchi, viene presentato il modello di interfase che permette di tenere in conto l'interazione fra le tensioni e le deformazioni di contatto con quelle interne al giunto. Pertanto, i fenomeni di scivolamento che si verificano al contatto fra blocchi e giunto sono combinati con le deformazioni anelastiche del materiale che costituisce il giunto stesso. Il modello costitutivo del giuntoè derivato dall'assunzione che il giunto sia separato dai blocchi attraverso due interfacce. Il caso di un giunto cementizio interposto fra due blocchi rigidi, soggetto a compressione, viene trattatto nel dettaglio.
Wear, 1999
A model of friction accounting for third body particles at the contact interface is derived from ... more A model of friction accounting for third body particles at the contact interface is derived from a simple micro-mechanical model of a particle interacting with a hard tool surface and a soft workpiece surface. Also a wear law coupled with this friction model is proposed. When wear of the tool surface is considered, the abrasive contribution of hard particles is only accounted for. The rate of wear is associated with frictional dissipation rate rather than with the product of normal pressure and slip velocity as in the classical Archard wear law. Numerical examples illustrate applicability and properties of the proposed friction and wear model.