Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-ha...Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hard ening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor （SIF） before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are ~tudied. Results including plastic zone shape are compared with finite element method （FEM） to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work hardening material using RKPM.展开更多
The present work is concerned with a penny-shaped Dugdale crack embedded in an infinite space of one-dimensional （1D） hexagonal quasicrystals and subjected to two identical axisymmetric temperature loadings on the u...The present work is concerned with a penny-shaped Dugdale crack embedded in an infinite space of one-dimensional （1D） hexagonal quasicrystals and subjected to two identical axisymmetric temperature loadings on the upper and lower crack surfaces. Applying Dugdale hypothesis to thermo-elastic results, the extent of the plastic zone at the crack tip is determined. The normal stress outside the plastic zone and crack surface displacement are derived in terms of special functions. For a uniform loading case, the corresponding results are presented by simpli- fying the preceding results. Numerical calculations are carried out to show the influence of some parameters.展开更多
Polymers with reversible plasticity shape memory effect(RPSME)have attracted considerable attention due to their simple programming and large deformation.However,the exact mechanisms of RPSME are still not thoroughly ...Polymers with reversible plasticity shape memory effect(RPSME)have attracted considerable attention due to their simple programming and large deformation.However,the exact mechanisms of RPSME are still not thoroughly understood.In this work,the RPSME of SEBS/crystallizable paraffin was investigated by comparatively analyzing the performances and microstructures of samples with different paraffin content.It was found the shape fixing ratios(Rfs)of samples increased with the paraffin content,and interestingly,a significant improvement in Rf was observed when the paraffin content exceeded 60 wt%.Tensile test results showed that the deformation characteristics of samples changed from elastic to plastic as the paraffin content increased above 60 wt%.By exploring the crystallization behaviors of paraffin in various SEBS/paraffin samples,it was revealed that the microstructures of SEBS/paraffin were different when the paraffin content was below 50 wt%and above 60 wt%.In samples with low paraffin content(below 50 wt%),nearly all paraffin was co-crystallized with ethylene-co-butylene(EB)chains and its crystallization was severely restricted;while in samples with high paraffin content(above 60 wt%),“excess”paraffin appeared and this part of paraffin crystallized on the template of the EB/paraffin co-crystals,which might be responsible for the elastic-to-plastic transition and the sharp increase in Rf.Based on the above results,a possible structural model was proposed to explain the exact mechanism of RPSME in SEBS/paraffin.展开更多
Nickel-titanium shape memory alloy （NiTi SMA） which possesses crystal structure of B2 austenite at room temperature was subjected to plastic deformation at low temperature （-150 ℃） by means of local canning compr...Nickel-titanium shape memory alloy （NiTi SMA） which possesses crystal structure of B2 austenite at room temperature was subjected to plastic deformation at low temperature （-150 ℃） by means of local canning compression. The microstructural evolution of NiTi SMA at the different deformation degree was investigated by transmission electron microscopy （TEM） and high resolution transmission electron microscopy （HRTEM）. At the deformation degree by 15%, a high density of dislocations occurs in the deformed NiTi sample. At the deformation degree by 25%, the deformed NiTi sample exhibits the martensite morphology due to the pinning of dislocations at the grain boundaries. At the deformation degree by 50%, a small amount of nanocrystalline phase arises in the deformed NiTi sample. At the deformation degree by 80%, severe plastic deformation （SPD） leads to the occurrence of a great deal of amorphous and nanocrystalline phase,展开更多
Low-cost iron-based shape memory alloys（SMAs） show great potential for engineering applications. The developments of new processing techniques have recently enabled the production of nanocrystalline materials with i...Low-cost iron-based shape memory alloys（SMAs） show great potential for engineering applications. The developments of new processing techniques have recently enabled the production of nanocrystalline materials with improved properties. These developments have opened avenues for newer applications for SMAs. The influence of severe plastic deformation induced by the high-speed high-pressure torsion（HSHPT） process on the microstructural evolution of an Fe–Mn–Si–Cr alloy was investigated. Transmission electron microscopic analysis of the alloy revealed the existence of nanoscale grains with an abundance of stacking faults. The high density of dislocations characteristic of severe plastic deformation was not observed in this alloy. X-ray diffraction studies revealed the presence of ε-martensite with an HCP crystal structure and γ-phase with an FCC structure.展开更多
The recovery force or recovery strain is an important indicator of NiTi-based shape memory alloy devices. However, the restoring force or recoverable strain is partially restrained due to an interaction between reorie...The recovery force or recovery strain is an important indicator of NiTi-based shape memory alloy devices. However, the restoring force or recoverable strain is partially restrained due to an interaction between reorientation and reorientation-induced plasticity. Therefore, a macroscopic multi-mechanism constitutive model was constructed to describe the degeneration of shape memory effect based on the phase diagram. The residual strain after cooling consists of reorientation strain and reorientation-induced plastic strain. An internal variable, i.e., the detwinned stress, and its evolution equation were introduced into the transformation kinetics equation to describe the nonlinear hardening characteristics induced by the combined reorien- ration and detwinning mechanisms during mechanical loading. Finally, the proposed model was numerically implemented to simulate the experiments of shape memory effect at different peak strains. Comparisons between the experimental and simulated results show that the proposed model can reasonably describe the degeneration of shape memory effect.展开更多
A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys （SMAs）. It is based on the concept that an SMA is a mixture composed of austenite and martensite...A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys （SMAs）. It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka＇s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelastieity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.展开更多
A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material...A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material,the paper derives the macroscopic constitutive laws for homogenous equivalent medium. By changing the shape parameter of circular particles,the effect of pore shape on macroscopic constitutive laws is explored. Yield surfaces with different pore shapes are obtained. About voids,a two-scale conception is introduced,which regards main void as macroscopic scale and secondary cavities as microscopic scale. The macroscopic potential involving main and secondary voids is achieved. The proposed macroscopic constitutive law taking microscopic features as influence factors is helpful for exploring the macroscopic mechanical properties of porous medium when numerical simulation is required.展开更多
A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement i...A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.展开更多
An effect of unequal deformation in development of advanced plasticprocessing technologies is researched by studying an in-plane bending process of strip metal underunequal compressing. The research results show the f...An effect of unequal deformation in development of advanced plasticprocessing technologies is researched by studying an in-plane bending process of strip metal underunequal compressing. The research results show the following: If appropriately controlled, unequalplastic deformation can play an important role not only in the improvement of quality of partsobtained by plastic processing technologies, but also in the development of new processes foradvanced plastic working technologies. A coordinated growth of unequal plastic deformation candevelop the deformation potentiality of material to the fall. The degree of unequal plasticdeformation can be used as bases for optimization design of processes and dies of plastic forming.展开更多
A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic defor...A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys (SMAs). Three phases, austenite A, twinned martensite and detwinned martensite , as well as the phase transitions occurring between each pair of phases (, , , , and are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases (A, , and and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.展开更多
Using the rigid visco-plastic Finite Element Method (FEM), the process offorging for long cone-shaped posts made of aluminum alloys was modeled and the correspondingdistributions of the field variables were obtained b...Using the rigid visco-plastic Finite Element Method (FEM), the process offorging for long cone-shaped posts made of aluminum alloys was modeled and the correspondingdistributions of the field variables were obtained based on considering aberrance of grids, dynamicboundary conditions, non-stable process, coupled thermo-mechanical behavior and other specialproblems. The difficulties in equipment selection and die analysis caused by the long cone shape ofpost, as well as by pressure calculation were solved.展开更多
The shape of strip is calculated by iterative method which combines strip plastic deformation model with rolls elastic deformation model through their calculation results, which can be called results coupling method. ...The shape of strip is calculated by iterative method which combines strip plastic deformation model with rolls elastic deformation model through their calculation results, which can be called results coupling method. Be- cause the shape and rolling force distribution are very sensitive to strip thickness transverse distribution% variation, the iterative course is rather unstable and sometimes convergence cannot be achieved. In addition, the calculating speed of results coupling method is low, which restricts its usable range. To solve the problem, a new model cou- pling method is developed, which takes the force distribution between rolls, rolling force distribution and strip＇s exit transverse displacement distribution as basic unknowns, and integrates strip plastic deformation model and rolls elas- tic deformation model as a unified linear equations through their internal relation, so the iterative calculation between the strip plastic deformation model and rolls elastic deformation model can be avoided. To prove the effectiveness of the model coupling method, two examples are calculated by results coupling method and model coupling method re- spectively. The results of front tension stress, back tension stress, strip^s exit gauge, the force between rolls and rolling force distribution calculated by model coupling method coincide very well with results coupling method. How- ever the calculation course of model coupling method is more steady than results coupling method, and its calculating speed is about ten times as much as the maximal speed of results coupling method, which validates its practicability and reliability.展开更多
A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately.In this research,the concrete damage plastici...A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately.In this research,the concrete damage plasticity constitutive model is used to develop the numerical model of a deck beam on a berthing jetty in the Abaqus finite element package.The model constitutes a solid section of 3D hexahedral brick elements for concrete material embedded with 2D quadrilateral surface elements as reinforcements.The model was validated against experimental results of a beam of comparable dimensions in a cited literature.The validated beam model is then used in a three-point load test configuration to demonstrate its applicability for preliminary numerical evaluation of damage detection strategy in marine concrete structural health monitoring.The natural frequency was identified to detect the presence of damage and mode shape curvature was found sensitive to the location of damage.展开更多
文摘Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hard ening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor （SIF） before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are ~tudied. Results including plastic zone shape are compared with finite element method （FEM） to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work hardening material using RKPM.
基金supported by the National Natural Science Foundation of China(No.11102171)Program for New Century Excellent Talents in University of Ministry of Education of China(NCET-13-0973)+1 种基金The support from Sichuan Provincial Youth Science and Technology Innovation Team(2013-TD-0004)Scientific Research Foundation for Returned Scholars(Ministry of Education of China)are acknowledged as well
文摘The present work is concerned with a penny-shaped Dugdale crack embedded in an infinite space of one-dimensional （1D） hexagonal quasicrystals and subjected to two identical axisymmetric temperature loadings on the upper and lower crack surfaces. Applying Dugdale hypothesis to thermo-elastic results, the extent of the plastic zone at the crack tip is determined. The normal stress outside the plastic zone and crack surface displacement are derived in terms of special functions. For a uniform loading case, the corresponding results are presented by simpli- fying the preceding results. Numerical calculations are carried out to show the influence of some parameters.
基金financially supported by the National Natural Science Foundation of China (Nos.51773040 and 52173056)。
文摘Polymers with reversible plasticity shape memory effect(RPSME)have attracted considerable attention due to their simple programming and large deformation.However,the exact mechanisms of RPSME are still not thoroughly understood.In this work,the RPSME of SEBS/crystallizable paraffin was investigated by comparatively analyzing the performances and microstructures of samples with different paraffin content.It was found the shape fixing ratios(Rfs)of samples increased with the paraffin content,and interestingly,a significant improvement in Rf was observed when the paraffin content exceeded 60 wt%.Tensile test results showed that the deformation characteristics of samples changed from elastic to plastic as the paraffin content increased above 60 wt%.By exploring the crystallization behaviors of paraffin in various SEBS/paraffin samples,it was revealed that the microstructures of SEBS/paraffin were different when the paraffin content was below 50 wt%and above 60 wt%.In samples with low paraffin content(below 50 wt%),nearly all paraffin was co-crystallized with ethylene-co-butylene(EB)chains and its crystallization was severely restricted;while in samples with high paraffin content(above 60 wt%),“excess”paraffin appeared and this part of paraffin crystallized on the template of the EB/paraffin co-crystals,which might be responsible for the elastic-to-plastic transition and the sharp increase in Rf.Based on the above results,a possible structural model was proposed to explain the exact mechanism of RPSME in SEBS/paraffin.
基金Funded by National Natural Science Foundation of China(No.51071056)the Fundamental Research Funds for the Central Universities of China(Nos.HEUCF121712 and HEUCF201317002)
文摘Nickel-titanium shape memory alloy （NiTi SMA） which possesses crystal structure of B2 austenite at room temperature was subjected to plastic deformation at low temperature （-150 ℃） by means of local canning compression. The microstructural evolution of NiTi SMA at the different deformation degree was investigated by transmission electron microscopy （TEM） and high resolution transmission electron microscopy （HRTEM）. At the deformation degree by 15%, a high density of dislocations occurs in the deformed NiTi sample. At the deformation degree by 25%, the deformed NiTi sample exhibits the martensite morphology due to the pinning of dislocations at the grain boundaries. At the deformation degree by 50%, a small amount of nanocrystalline phase arises in the deformed NiTi sample. At the deformation degree by 80%, severe plastic deformation （SPD） leads to the occurrence of a great deal of amorphous and nanocrystalline phase,
基金supported by Project PN.IIPT-PCCA-2011-3.1-0174,Contract 144/2012
文摘Low-cost iron-based shape memory alloys（SMAs） show great potential for engineering applications. The developments of new processing techniques have recently enabled the production of nanocrystalline materials with improved properties. These developments have opened avenues for newer applications for SMAs. The influence of severe plastic deformation induced by the high-speed high-pressure torsion（HSHPT） process on the microstructural evolution of an Fe–Mn–Si–Cr alloy was investigated. Transmission electron microscopic analysis of the alloy revealed the existence of nanoscale grains with an abundance of stacking faults. The high density of dislocations characteristic of severe plastic deformation was not observed in this alloy. X-ray diffraction studies revealed the presence of ε-martensite with an HCP crystal structure and γ-phase with an FCC structure.
基金Financial supports by the National Natural Science Foundation of China （Nos. 11572265, 11532010）, the Excellent Youth Found of Sichuan Province （No. 2017JQ0019）
文摘The recovery force or recovery strain is an important indicator of NiTi-based shape memory alloy devices. However, the restoring force or recoverable strain is partially restrained due to an interaction between reorientation and reorientation-induced plasticity. Therefore, a macroscopic multi-mechanism constitutive model was constructed to describe the degeneration of shape memory effect based on the phase diagram. The residual strain after cooling consists of reorientation strain and reorientation-induced plastic strain. An internal variable, i.e., the detwinned stress, and its evolution equation were introduced into the transformation kinetics equation to describe the nonlinear hardening characteristics induced by the combined reorien- ration and detwinning mechanisms during mechanical loading. Finally, the proposed model was numerically implemented to simulate the experiments of shape memory effect at different peak strains. Comparisons between the experimental and simulated results show that the proposed model can reasonably describe the degeneration of shape memory effect.
基金Project supported by the National Natural Science Foundation of China (No. 10976032)
文摘A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys （SMAs）. It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka＇s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelastieity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10972162)
文摘A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material,the paper derives the macroscopic constitutive laws for homogenous equivalent medium. By changing the shape parameter of circular particles,the effect of pore shape on macroscopic constitutive laws is explored. Yield surfaces with different pore shapes are obtained. About voids,a two-scale conception is introduced,which regards main void as macroscopic scale and secondary cavities as microscopic scale. The macroscopic potential involving main and secondary voids is achieved. The proposed macroscopic constitutive law taking microscopic features as influence factors is helpful for exploring the macroscopic mechanical properties of porous medium when numerical simulation is required.
基金supported by the Fulbright Colombia-Colciencias Scholarship and Universidad Militar Nueva Granada
文摘A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.
基金National Natural Science Foundation of China (No.59475059) and the Aeronautical Science Foundation of China (No.94G53111).
文摘An effect of unequal deformation in development of advanced plasticprocessing technologies is researched by studying an in-plane bending process of strip metal underunequal compressing. The research results show the following: If appropriately controlled, unequalplastic deformation can play an important role not only in the improvement of quality of partsobtained by plastic processing technologies, but also in the development of new processes foradvanced plastic working technologies. A coordinated growth of unequal plastic deformation candevelop the deformation potentiality of material to the fall. The degree of unequal plasticdeformation can be used as bases for optimization design of processes and dies of plastic forming.
基金Financial supports by the National Natural Science Foundation of China (Grant 11532010)the project for Sichuan Provincial Youth Science and Technology Innovation Team, China (Grant 2013TD0004)
文摘A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys (SMAs). Three phases, austenite A, twinned martensite and detwinned martensite , as well as the phase transitions occurring between each pair of phases (, , , , and are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases (A, , and and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.
文摘Using the rigid visco-plastic Finite Element Method (FEM), the process offorging for long cone-shaped posts made of aluminum alloys was modeled and the correspondingdistributions of the field variables were obtained based on considering aberrance of grids, dynamicboundary conditions, non-stable process, coupled thermo-mechanical behavior and other specialproblems. The difficulties in equipment selection and die analysis caused by the long cone shape ofpost, as well as by pressure calculation were solved.
基金Sponsored by National Science and Technology Support Plan of China (2009AA04Z143)Science and Technology Support Plan of Hebei Province of China (10212101D)Important Natural Science Foundation of Hebei Province of China (E2006001038)
文摘The shape of strip is calculated by iterative method which combines strip plastic deformation model with rolls elastic deformation model through their calculation results, which can be called results coupling method. Be- cause the shape and rolling force distribution are very sensitive to strip thickness transverse distribution% variation, the iterative course is rather unstable and sometimes convergence cannot be achieved. In addition, the calculating speed of results coupling method is low, which restricts its usable range. To solve the problem, a new model cou- pling method is developed, which takes the force distribution between rolls, rolling force distribution and strip＇s exit transverse displacement distribution as basic unknowns, and integrates strip plastic deformation model and rolls elas- tic deformation model as a unified linear equations through their internal relation, so the iterative calculation between the strip plastic deformation model and rolls elastic deformation model can be avoided. To prove the effectiveness of the model coupling method, two examples are calculated by results coupling method and model coupling method re- spectively. The results of front tension stress, back tension stress, strip^s exit gauge, the force between rolls and rolling force distribution calculated by model coupling method coincide very well with results coupling method. How- ever the calculation course of model coupling method is more steady than results coupling method, and its calculating speed is about ten times as much as the maximal speed of results coupling method, which validates its practicability and reliability.
文摘A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately.In this research,the concrete damage plasticity constitutive model is used to develop the numerical model of a deck beam on a berthing jetty in the Abaqus finite element package.The model constitutes a solid section of 3D hexahedral brick elements for concrete material embedded with 2D quadrilateral surface elements as reinforcements.The model was validated against experimental results of a beam of comparable dimensions in a cited literature.The validated beam model is then used in a three-point load test configuration to demonstrate its applicability for preliminary numerical evaluation of damage detection strategy in marine concrete structural health monitoring.The natural frequency was identified to detect the presence of damage and mode shape curvature was found sensitive to the location of damage.
