Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis ESDA2008.July 7-9, 2008, Haifa, Israe , 2020
The accuracy of the finite difference technique in solving
frictionless and frictional advancing... more The accuracy of the finite difference technique in solving
frictionless and frictional advancing contact problems is investigated
by solving the problem of a rigid punch on an elastic halfspace
subjected to normal loading. Stick and slip conditions between
the elastic and the rigid materials are added to an existing
numerical algorithm which was previously used for solving frictionless
and frictional stationary and receding contact problems.
The numerical additions are first tested by applying them in the
solution of receding and stationary contact problems and comparing
them to known solutions. The receding contact problem
is that of an elastic slab on a rigid half-plane; the stationary contact
problem is that of a flat rigid punch on an elastic half-space.
In both cases the influence of friction is examined. The results are
compared to those of other investigations with very good agreement
observed. Once more it is verified that for both receding
and stationary contact, load steps are not required for obtaining
a solution if the loads are applied monotonically, whether or not
there is friction.
Next, an advancing contact problem of a round rigid punch
on an elastic half-space subjected to normal loading, with and
without the influence of friction is investigated. The results for
frictionless advancing contact, which are obtained without load
steps, are compared to analytical results, namely the Hertz problem;
excellent agreement is observed. When friction is present,
¤Corresponding Author
load steps and iterations for determining the contact area within
each load step, are required. Hence, the existing code, in which
only iterations to determine the contact zone were employed, was
modified to include load steps, together with the above mentioned
iterations for each load step. The effect of friction on the stress
distribution and contact length is studied. It is found that when
stick conditions appear in the contact zone, an increase in the
friction coefficient results in an increase in the stick zone size
within the contact zone. These results agree well with semianalytical
results of another investigation, illustrating the accuracy
and capabilities of the finite difference technique for advancing
contact. .
Clinical implant dentistry and related research, 2018
Osseointegration of dental implants is a key factor for their success. It can be assessed either ... more Osseointegration of dental implants is a key factor for their success. It can be assessed either by destructive (eg, pullout or torque extraction), or nondestructive methods (eg, resonant frequency analysis). However, as of today there is a scarcity of models that can relate the outcome of destructive tests to the level of osseointegration. To study various percentages of bone to implant bonding (tie) using finite element simulations. While evolutions of the bone mechanical properties are not explicitly taken into account, emphasis is put on the 3-dimensional variable extent of the bone-implant bonding, its statistical distribution, and its influence on the measurable extraction and torque loads, seeking to obtain a quantitative relationship. We performed numerical simulations of randomly tied implants and calculated the evolution of the pullout force as well as that of the extraction torque. Within simplifying assumptions for the osseointegration represented by a tie (as opposed to...
... Email: Igor Zlotnikov (Igor.zlotnikov@mpikg.mpg.de). *Correspondence: Igor Zlotnikov, Faculty... more ... Email: Igor Zlotnikov (Igor.zlotnikov@mpikg.mpg.de). *Correspondence: Igor Zlotnikov, Faculty of Materials Engineering, Technion, Haifa, Haifa 32000, Israel. Publication History. ... 15 NA Kotov, T. Haraszti, L. Turi, G. Zavala, RE Geer, I. Dekany, JH Fendler, J. Am. Ceram. Soc. ...
Journal of the Mechanics and Physics of Solids, Nov 30, 2010
ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite compl... more ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion which was developed on experimental considerations (Rittel, et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software, and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.
ABSTRACT In this study, a newly developed nanoscale modulus mapping is applied in order to visual... more ABSTRACT In this study, a newly developed nanoscale modulus mapping is applied in order to visualize the 2D-distribution of mechanical characteristics in the aragonitic nacre layer of Perna canaliculus (green mussel) shells. Modulus maps provide lateral resolution of about 10 nm. They allow the aragonitic mineral (CaCO3) tablets and the interfaces between them to be clearly resolved, which are filled by an organic substance (mainly beta-chitin). The experimental data are compared with finite element simulations that also take into account the tip radius of curvature and the thickness of organic layers, as measured by means of scanning electron microscopy with back-scattered electrons. Based on this comparison, the Young modulus of beta-chitin is extracted. The obtained number, Eβ = 40 GPa, is higher than previously evaluated. The collected maps reveal that the elastic modules in the nacre layer change gradually across the ceramic/organic interfaces within a spatial range four times wider than the thickness of the organic layers. This is possibly due to inhomogeneous distribution of organic macromolecules within ceramic tablets. According to the data, the concentration of macromolecules gradually increases when approaching the organic/ceramic interfaces. A behavior of this type is unique to biogenic materials and distinguishes them from synthetic composite materials. Finally, three possible mechanisms that attempt to explain why gradual changes of elastic modules significantly enhance the overall resistance to fracture of the nacre layer are briefly discussed. The experimental findings support the idea that individual ceramic tablets, comprising the nacre, are built of the compositionally and functionally graded ceramic material. This sheds additional light on the origin of the superior mechanical properties of biogenic composites.
ABSTRACT The accuracy of the finite difference technique in solving frictionless and frictional a... more ABSTRACT The accuracy of the finite difference technique in solving frictionless and frictional advancing contact problems is investigated by solving the problem of a rigid punch on an elastic halfspace subjected to normal loading. Stick and slip conditions between the elastic and the rigid materials are added to an existing numerical algorithm which was previously used for solving frictionless and frictional stationary and receding contact problems. The numerical additions are first tested by applying them in the solution of receding and stationary contact problems and comparing them to known solutions. The receding contact problem is that of an elastic slab on a rigid half-plane; the stationary contact problem is that of a flat rigid punch on an elastic half-space. In both cases the influence of friction is examined. The results are compared to those of other investigations with very good agreement observed. Once more it is verified that for both receding and stationary contact, load steps are not required for obtaining a solution if the loads are applied monotonically, whether or not there is friction. Next, an advancing contact problem of a round rigid punch on an elastic half-space subjected to normal loading, with and without the influence of friction is investigated. The results for frictionless advancing contact, which are obtained without load steps, are compared to analytical results, namely the Hertz problem; excellent agreement is observed. When friction is present, load steps and iterations for determining the contact area within each load step, are required. Hence, the existing code, in which only iterations to determine the contact zone were employed, was modified to include load steps, together with the above mentioned iterations for each load step. The effect of friction on the stress distribution and contact length is studied. It is found that when stick conditions appear in the contact zone, an increase in the friction coefficient results in an increase in the stick zone size within the contact zone. These results agree well with semianalytical results of another investigation, illustrating the accuracy and capabilities of the finite difference technique for advancing contact.
ABSTRACT The penetration process in unconfined and confined thick polycarbonate (PC) plates was i... more ABSTRACT The penetration process in unconfined and confined thick polycarbonate (PC) plates was investigated experimentally and numerically. The confinement was applied by insertion of the PC plate into a conical steel ring. The response of such plates to the impact of long hard steel projectiles, having an ogive-head shape in the range of velocities of 151 < V < 271 [m/s], was investigated experimentally. The results indicate that confinement results in slightly shallower depths of penetrations. Failure parameters which were determined to fit these experimental results served in simulations of these results, and also to those of a 7.62 [mm] AP projectile impacting unconfined PC targets at velocities 600 < V < 900 [m/s]. A very good agreement regarding the trajectory of the projectile was obtained. The resisting force to the penetration depends on the failure strain, whose dependence on triaxiality, temperature and strain rate, should be further investigated. The triaxiality is defined as the ratio: tr=σm/σeq where σm=σii/3 and σeq is the Mises equivalent stress. The numerical results show that the confinement introduces a negative triaxiality within the confined plates prior to impact. The shallower penetration in confined targets is due to the higher negative triaxiality which reduces the ductile damage during penetration, while the hydrostatic pressure reduces the brittle fracture mechanism.
We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinit... more We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinity of interfaces. The method is demonstrated on twin walls in PbTiO(3) single crystals. It is revealed that the region near the twin wall is significantly softer than the two domains surrounding it. A comparison with finite element simulations relates this effect to an anelastic relaxation due to point defect accumulation around the twin wall. Local softening around the twin wall can affect the overall elastic modulus in thin films and nanostructured ferroelectric materials, in which the average distance between twin walls is smaller than the thickness of the softer region.
ABSTRACT The quasi-static and dynamic mechanical and failure properties of a swaged tungsten-base... more ABSTRACT The quasi-static and dynamic mechanical and failure properties of a swaged tungsten-base heavy alloy rod have been investigated, with emphasis on the orientation of the specimens in the rod. Three orientations were considered, 0, 45, and 90 deg, with respect to the longitudinal axis of the rod. Compression, tension, and dominant shear tests were carried out. With the exception of the 0 deg orientation, all the orientations displayed quite similar mechanical characteristics in tension and compression. Dynamic shear revealed a critical strain for adiabatic shear failure of ɛ c ≈0.13, independent of the orientation and quite inferior to the quasi-static ductility. The present study confirms previous results obtained for one (generally unspecified) orientation and extends them to three orientations. Failure mechanisms were thoroughly characterized and it appears that significant damage does not develop prior to final failure. It is concluded that, for practical purposes, the swaged heavy alloy considered here can be regarded as isotropic from a mechanical and failure point of view, in spite of its microstructural anisotropy resulting from the swaging process.
Journal of the Mechanics and Physics of Solids, 2010
ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite compl... more ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion which was developed on experimental considerations (Rittel, et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software, and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.
ABSTRACT An experimental and numerical study of a non-uniform impact excitation of a circular bar... more ABSTRACT An experimental and numerical study of a non-uniform impact excitation of a circular bar is reported. In experiments, nine strikers with different contact area were accelerated against a circular bar. Axial surface strain of the impacted bar was measured at several distances from the impinged end to include the near and the far fields. The same experimental conditions were solved numerically using a commercial finite element code. It was demonstrated that the far-field response is insensitive to both the size and the form of the striker's colliding end. The distance at which such insensitivity is set is estimated to be approximately one and a half bar diameters.
Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis ESDA2008.July 7-9, 2008, Haifa, Israe , 2020
The accuracy of the finite difference technique in solving
frictionless and frictional advancing... more The accuracy of the finite difference technique in solving
frictionless and frictional advancing contact problems is investigated
by solving the problem of a rigid punch on an elastic halfspace
subjected to normal loading. Stick and slip conditions between
the elastic and the rigid materials are added to an existing
numerical algorithm which was previously used for solving frictionless
and frictional stationary and receding contact problems.
The numerical additions are first tested by applying them in the
solution of receding and stationary contact problems and comparing
them to known solutions. The receding contact problem
is that of an elastic slab on a rigid half-plane; the stationary contact
problem is that of a flat rigid punch on an elastic half-space.
In both cases the influence of friction is examined. The results are
compared to those of other investigations with very good agreement
observed. Once more it is verified that for both receding
and stationary contact, load steps are not required for obtaining
a solution if the loads are applied monotonically, whether or not
there is friction.
Next, an advancing contact problem of a round rigid punch
on an elastic half-space subjected to normal loading, with and
without the influence of friction is investigated. The results for
frictionless advancing contact, which are obtained without load
steps, are compared to analytical results, namely the Hertz problem;
excellent agreement is observed. When friction is present,
¤Corresponding Author
load steps and iterations for determining the contact area within
each load step, are required. Hence, the existing code, in which
only iterations to determine the contact zone were employed, was
modified to include load steps, together with the above mentioned
iterations for each load step. The effect of friction on the stress
distribution and contact length is studied. It is found that when
stick conditions appear in the contact zone, an increase in the
friction coefficient results in an increase in the stick zone size
within the contact zone. These results agree well with semianalytical
results of another investigation, illustrating the accuracy
and capabilities of the finite difference technique for advancing
contact. .
Clinical implant dentistry and related research, 2018
Osseointegration of dental implants is a key factor for their success. It can be assessed either ... more Osseointegration of dental implants is a key factor for their success. It can be assessed either by destructive (eg, pullout or torque extraction), or nondestructive methods (eg, resonant frequency analysis). However, as of today there is a scarcity of models that can relate the outcome of destructive tests to the level of osseointegration. To study various percentages of bone to implant bonding (tie) using finite element simulations. While evolutions of the bone mechanical properties are not explicitly taken into account, emphasis is put on the 3-dimensional variable extent of the bone-implant bonding, its statistical distribution, and its influence on the measurable extraction and torque loads, seeking to obtain a quantitative relationship. We performed numerical simulations of randomly tied implants and calculated the evolution of the pullout force as well as that of the extraction torque. Within simplifying assumptions for the osseointegration represented by a tie (as opposed to...
... Email: Igor Zlotnikov (Igor.zlotnikov@mpikg.mpg.de). *Correspondence: Igor Zlotnikov, Faculty... more ... Email: Igor Zlotnikov (Igor.zlotnikov@mpikg.mpg.de). *Correspondence: Igor Zlotnikov, Faculty of Materials Engineering, Technion, Haifa, Haifa 32000, Israel. Publication History. ... 15 NA Kotov, T. Haraszti, L. Turi, G. Zavala, RE Geer, I. Dekany, JH Fendler, J. Am. Ceram. Soc. ...
Journal of the Mechanics and Physics of Solids, Nov 30, 2010
ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite compl... more ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion which was developed on experimental considerations (Rittel, et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software, and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.
ABSTRACT In this study, a newly developed nanoscale modulus mapping is applied in order to visual... more ABSTRACT In this study, a newly developed nanoscale modulus mapping is applied in order to visualize the 2D-distribution of mechanical characteristics in the aragonitic nacre layer of Perna canaliculus (green mussel) shells. Modulus maps provide lateral resolution of about 10 nm. They allow the aragonitic mineral (CaCO3) tablets and the interfaces between them to be clearly resolved, which are filled by an organic substance (mainly beta-chitin). The experimental data are compared with finite element simulations that also take into account the tip radius of curvature and the thickness of organic layers, as measured by means of scanning electron microscopy with back-scattered electrons. Based on this comparison, the Young modulus of beta-chitin is extracted. The obtained number, Eβ = 40 GPa, is higher than previously evaluated. The collected maps reveal that the elastic modules in the nacre layer change gradually across the ceramic/organic interfaces within a spatial range four times wider than the thickness of the organic layers. This is possibly due to inhomogeneous distribution of organic macromolecules within ceramic tablets. According to the data, the concentration of macromolecules gradually increases when approaching the organic/ceramic interfaces. A behavior of this type is unique to biogenic materials and distinguishes them from synthetic composite materials. Finally, three possible mechanisms that attempt to explain why gradual changes of elastic modules significantly enhance the overall resistance to fracture of the nacre layer are briefly discussed. The experimental findings support the idea that individual ceramic tablets, comprising the nacre, are built of the compositionally and functionally graded ceramic material. This sheds additional light on the origin of the superior mechanical properties of biogenic composites.
ABSTRACT The accuracy of the finite difference technique in solving frictionless and frictional a... more ABSTRACT The accuracy of the finite difference technique in solving frictionless and frictional advancing contact problems is investigated by solving the problem of a rigid punch on an elastic halfspace subjected to normal loading. Stick and slip conditions between the elastic and the rigid materials are added to an existing numerical algorithm which was previously used for solving frictionless and frictional stationary and receding contact problems. The numerical additions are first tested by applying them in the solution of receding and stationary contact problems and comparing them to known solutions. The receding contact problem is that of an elastic slab on a rigid half-plane; the stationary contact problem is that of a flat rigid punch on an elastic half-space. In both cases the influence of friction is examined. The results are compared to those of other investigations with very good agreement observed. Once more it is verified that for both receding and stationary contact, load steps are not required for obtaining a solution if the loads are applied monotonically, whether or not there is friction. Next, an advancing contact problem of a round rigid punch on an elastic half-space subjected to normal loading, with and without the influence of friction is investigated. The results for frictionless advancing contact, which are obtained without load steps, are compared to analytical results, namely the Hertz problem; excellent agreement is observed. When friction is present, load steps and iterations for determining the contact area within each load step, are required. Hence, the existing code, in which only iterations to determine the contact zone were employed, was modified to include load steps, together with the above mentioned iterations for each load step. The effect of friction on the stress distribution and contact length is studied. It is found that when stick conditions appear in the contact zone, an increase in the friction coefficient results in an increase in the stick zone size within the contact zone. These results agree well with semianalytical results of another investigation, illustrating the accuracy and capabilities of the finite difference technique for advancing contact.
ABSTRACT The penetration process in unconfined and confined thick polycarbonate (PC) plates was i... more ABSTRACT The penetration process in unconfined and confined thick polycarbonate (PC) plates was investigated experimentally and numerically. The confinement was applied by insertion of the PC plate into a conical steel ring. The response of such plates to the impact of long hard steel projectiles, having an ogive-head shape in the range of velocities of 151 < V < 271 [m/s], was investigated experimentally. The results indicate that confinement results in slightly shallower depths of penetrations. Failure parameters which were determined to fit these experimental results served in simulations of these results, and also to those of a 7.62 [mm] AP projectile impacting unconfined PC targets at velocities 600 < V < 900 [m/s]. A very good agreement regarding the trajectory of the projectile was obtained. The resisting force to the penetration depends on the failure strain, whose dependence on triaxiality, temperature and strain rate, should be further investigated. The triaxiality is defined as the ratio: tr=σm/σeq where σm=σii/3 and σeq is the Mises equivalent stress. The numerical results show that the confinement introduces a negative triaxiality within the confined plates prior to impact. The shallower penetration in confined targets is due to the higher negative triaxiality which reduces the ductile damage during penetration, while the hydrostatic pressure reduces the brittle fracture mechanism.
We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinit... more We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinity of interfaces. The method is demonstrated on twin walls in PbTiO(3) single crystals. It is revealed that the region near the twin wall is significantly softer than the two domains surrounding it. A comparison with finite element simulations relates this effect to an anelastic relaxation due to point defect accumulation around the twin wall. Local softening around the twin wall can affect the overall elastic modulus in thin films and nanostructured ferroelectric materials, in which the average distance between twin walls is smaller than the thickness of the softer region.
ABSTRACT The quasi-static and dynamic mechanical and failure properties of a swaged tungsten-base... more ABSTRACT The quasi-static and dynamic mechanical and failure properties of a swaged tungsten-base heavy alloy rod have been investigated, with emphasis on the orientation of the specimens in the rod. Three orientations were considered, 0, 45, and 90 deg, with respect to the longitudinal axis of the rod. Compression, tension, and dominant shear tests were carried out. With the exception of the 0 deg orientation, all the orientations displayed quite similar mechanical characteristics in tension and compression. Dynamic shear revealed a critical strain for adiabatic shear failure of ɛ c ≈0.13, independent of the orientation and quite inferior to the quasi-static ductility. The present study confirms previous results obtained for one (generally unspecified) orientation and extends them to three orientations. Failure mechanisms were thoroughly characterized and it appears that significant damage does not develop prior to final failure. It is concluded that, for practical purposes, the swaged heavy alloy considered here can be regarded as isotropic from a mechanical and failure point of view, in spite of its microstructural anisotropy resulting from the swaging process.
Journal of the Mechanics and Physics of Solids, 2010
ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite compl... more ABSTRACT The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion which was developed on experimental considerations (Rittel, et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software, and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.
ABSTRACT An experimental and numerical study of a non-uniform impact excitation of a circular bar... more ABSTRACT An experimental and numerical study of a non-uniform impact excitation of a circular bar is reported. In experiments, nine strikers with different contact area were accelerated against a circular bar. Axial surface strain of the impacted bar was measured at several distances from the impinged end to include the near and the far fields. The same experimental conditions were solved numerically using a commercial finite element code. It was demonstrated that the far-field response is insensitive to both the size and the form of the striker's colliding end. The distance at which such insensitivity is set is estimated to be approximately one and a half bar diameters.
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Papers by Avraham Dorogoy
frictionless and frictional advancing contact problems is investigated
by solving the problem of a rigid punch on an elastic halfspace
subjected to normal loading. Stick and slip conditions between
the elastic and the rigid materials are added to an existing
numerical algorithm which was previously used for solving frictionless
and frictional stationary and receding contact problems.
The numerical additions are first tested by applying them in the
solution of receding and stationary contact problems and comparing
them to known solutions. The receding contact problem
is that of an elastic slab on a rigid half-plane; the stationary contact
problem is that of a flat rigid punch on an elastic half-space.
In both cases the influence of friction is examined. The results are
compared to those of other investigations with very good agreement
observed. Once more it is verified that for both receding
and stationary contact, load steps are not required for obtaining
a solution if the loads are applied monotonically, whether or not
there is friction.
Next, an advancing contact problem of a round rigid punch
on an elastic half-space subjected to normal loading, with and
without the influence of friction is investigated. The results for
frictionless advancing contact, which are obtained without load
steps, are compared to analytical results, namely the Hertz problem;
excellent agreement is observed. When friction is present,
¤Corresponding Author
load steps and iterations for determining the contact area within
each load step, are required. Hence, the existing code, in which
only iterations to determine the contact zone were employed, was
modified to include load steps, together with the above mentioned
iterations for each load step. The effect of friction on the stress
distribution and contact length is studied. It is found that when
stick conditions appear in the contact zone, an increase in the
friction coefficient results in an increase in the stick zone size
within the contact zone. These results agree well with semianalytical
results of another investigation, illustrating the accuracy
and capabilities of the finite difference technique for advancing
contact. .
frictionless and frictional advancing contact problems is investigated
by solving the problem of a rigid punch on an elastic halfspace
subjected to normal loading. Stick and slip conditions between
the elastic and the rigid materials are added to an existing
numerical algorithm which was previously used for solving frictionless
and frictional stationary and receding contact problems.
The numerical additions are first tested by applying them in the
solution of receding and stationary contact problems and comparing
them to known solutions. The receding contact problem
is that of an elastic slab on a rigid half-plane; the stationary contact
problem is that of a flat rigid punch on an elastic half-space.
In both cases the influence of friction is examined. The results are
compared to those of other investigations with very good agreement
observed. Once more it is verified that for both receding
and stationary contact, load steps are not required for obtaining
a solution if the loads are applied monotonically, whether or not
there is friction.
Next, an advancing contact problem of a round rigid punch
on an elastic half-space subjected to normal loading, with and
without the influence of friction is investigated. The results for
frictionless advancing contact, which are obtained without load
steps, are compared to analytical results, namely the Hertz problem;
excellent agreement is observed. When friction is present,
¤Corresponding Author
load steps and iterations for determining the contact area within
each load step, are required. Hence, the existing code, in which
only iterations to determine the contact zone were employed, was
modified to include load steps, together with the above mentioned
iterations for each load step. The effect of friction on the stress
distribution and contact length is studied. It is found that when
stick conditions appear in the contact zone, an increase in the
friction coefficient results in an increase in the stick zone size
within the contact zone. These results agree well with semianalytical
results of another investigation, illustrating the accuracy
and capabilities of the finite difference technique for advancing
contact. .