The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the applic... more The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the application of the quasistatic peridynamic model to two-dimensional, linear elastic, plane stress and plane strain problems, with special attention to the modeling of plain and reinforced concrete structures. We consider just one deviation from linearitythat which arises due to the irreversible sudden breaking of bonds between particles. The peridynamic model starts with the assumption that Newton's second law holds true on every infinitesimally small free body (or particle) within the domain of analysis. A specified force density function, called the pairwise force function, (with units of force per unit volume per unit volume) between each pair of infinitesimally small particles is postulated to act if the particles are closer together than some finite distance, called the material horizon. The pairwise force function may be assumed to be a function of the relative position and the relative displacement between the two particles. In this paper, we assume that for two particles closer together than the specified "material horizon" the pairwise force function increases linearly with respect to the stretch, but at some specified stretch, the pairwise force function is irreversibly reduced to zero.
The thermal performance of economical housing located in hot climates remains a pending subject, ... more The thermal performance of economical housing located in hot climates remains a pending subject, especially in emerging economies. A cellular concrete mixture was designed, considering its thermophysical properties, to apply the new material into building envelopes. The proposed materials have low density and thermal conductivity to be used as a nonstructural lightweight construction element. From the design stage, a series of wall systems based on cellular concrete was proposed. Whereas in the second phase, the materials were analyzed to obtain the potential energy savings using dynamic simulations. It is foreseen that the energy consumption in buildings located in these climates will continue to increase critically due to the temperature increase associated with climate change. The temperatures predicted mean vote (PMV), electric energy consumption, and CO2 emissions were calculated for three IPCC scenarios. These results will help to identify the impact of climate change on the e...
The peridynamic model described in (Silling 1998; Gerstle et al. 2005), being a central-force mod... more The peridynamic model described in (Silling 1998; Gerstle et al. 2005), being a central-force model, is limited to modeling materials with a Poisson’s ratio of one-quarter. In this paper, the peridynamic model is generalized by adding peridynamic moments to simulate linear elastic materials with varying Poisson’s ratios. This micropolar peridynamic model is placed within a finite element context to enable efficacious application of boundary conditions and efficient computational solutions using an implicit, rather than an explicit, solution algorithm. The algorithm is suitable for quasistatic simulation of damage and cracking in concrete structures. Very simple constitutive models at the peridynamic level appear to be sufficient to model the complex damage and fracture phenomena observed in concrete structures. The peridynamic model predicts significant elastic boundary effects that are not predicted by classical stress-strain models. As a consequence, the peridynamic model predicts...
In a number of applications, large size structures subjected to loads that cause highly non-linea... more In a number of applications, large size structures subjected to loads that cause highly non-linear behavior need to be analyzed. With the peridynamic theory, proposed by Stewart Silling in 2000 and 2007, elasticity and damage in quasibrittle structures such as plain and reinforced concrete structures can be modeled with the peridynamic theory. To model these structures, lattice models with brittle beam elements are used to model concrete. A shortcoming of lattice and particle models is that they are highly demanding of computational power. Molecular dynamics may be, in some cases an appropriate tool for analyzing microcracks in quasibrittle materials in compression, but molecular dynamics becomes infeasible at scales larger than a few million atoms. For example, in masonry structures, cracks form in the brick mortar joints, and concrete blocks can be assumed to have a uniform displacement field. This allows us to use the peridynamic finite element model, which is an improvement over discrete lattice models. This model assumes a continuous displacement field within each finite element, with displacement discontinuities allowed to develop between finite elements. The objective of this work is to model cracks in quasibrittle structures, with the peridynamic model. The peridynamic finite element model is shown to be much more computer time-and memoryefficient than the similar discrete particle-based models. Results show that this implementation appears to be more computationally efficient than particle or lattice models.
Reinforced concrete structures subjected to loads that cause the formation and propagation of cra... more Reinforced concrete structures subjected to loads that cause the formation and propagation of cracks exhibit a behavior where continuum mechanics is no longer applicable, because most conventional models do not consider the discontinuities that appear and propagate because of concrete tension failure. In an effort to correct the shortcomings of continuum models, the peridynamic bond-based model was proposed in 2000 and the peridynamic state-based model in 2007. The micropolar peridynamic model improves the bond-based peridynamic model by allowing different values of the Poisson's ratio. A numerical scheme for the calculation of the micropolar peridynamic stress was developed where results show convergence with classical linear elastic solutions for small values of the material horizon. With this approach, the stress tensor can be analyzed at points in failure zones. Fractures patterns using physical experimentation are obtained and compared with the model.
Journal of Geological Resource and Engineering, 2018
According the Coulomb earth pressure theory, it is obtained that, for normally consolidated soils... more According the Coulomb earth pressure theory, it is obtained that, for normally consolidated soils, the lateral pressure coefficient of a soil at rest is equal to 1, and it is independent of the soil type, either granular or cohesive; or that the material is in a loose or compact state; hard or a soft cohesive soil. Also, a methodology to calculate the earth pressure for intermediate states between at rest condition and the active pressure is presented. In addition, a methodology to calculate the earth pressure for intermediate states between at rest condition and the passive pressure is presented. Two practical examples are presented: one for a frictionless wall; and another for a coarse wall. Practical recommendations are given for the use of the lateral earth pressure coefficient for different applications.
Journal of Geological Resource and Engineering, 2013
It is disclosed a method for the stability analysis of foundation piles and piers subjected to la... more It is disclosed a method for the stability analysis of foundation piles and piers subjected to lateral loading, both static and seismic conditions. The stability analysis for stratified soil is based upon the models of foundation soil-structure interaction and the Rankine´s theory of earth passive pressure. In addition, its application is simpler and it can be solved using a spreadsheet. The procedure described in this work can be used in homogeneous soils as in stratified soils, considers the horizontal drag forces exerted by the soil mass against the foundation during an earthquake, can be used easily in the four pile and piers boundary cases, and considers the pore pressure generated in a fine saturated soil during an earthquake or during a rapid application of the horizontal load. The solution of two examples are shown, one in static condition and one in seismic condition, detailing the procedure step by step.
The nuclear industry relies heavily upon reinforced concrete structures. It is therefore essentia... more The nuclear industry relies heavily upon reinforced concrete structures. It is therefore essential that we develop robust and reliable theoretical and computational models for simulating the behavior of reinforced concrete. We develop a simple rate-independent micropolar peridynamic constitutive model for concrete subject to monotonic deformation. Using this model, we demonstrate that many of the commonly observed, complex, behaviors of concrete emerge naturally: linear elasticity, distributed anisotropic damage, discrete cracking, dilatency, and shear bands. In addition, bond between reinforcing steel and concrete is modeled in a simple and natural way. Also, a boundary effect that has not been explicitly observed in the laboratory is predicted by the micropolar peridynamic model. The model is implemented in a computational simulation program written in MATLAB. Using this computer program, we use two example problems to demonstrate the efficacy of the peridynamic constitutive model...
There exists a great potential for application in soil mechanics with the use of mechanistic mode... more There exists a great potential for application in soil mechanics with the use of mechanistic models such as the finite element model, and other non-local models, such as the peridynamic model, since the soil mass can be modelled as a group of particles that interact with each other. In this work, we determine the bearing capacity of deep foundations where stresses are transmitted to deep deposits, which generally present better characteristics in terms of compressibility and shear strength. One of the main elements are driven piles, which must be previously designed, made and tested before their final use. In this work, a comparison with different methods is presented. The finite element method and the peridynamic model are used. Because the effect of consolidation was not taken into account, in these examples, the assumption is made that the structures are cemented in inert soil. Likewise, it is assumed that the water table has no influence on the simulations. Failure envelopes were observed where bonds between particles present high gradients of deformation and fracture. Bearing capacities were estimated and compared with those obtained from the Terzaghi and Meyerhof methods.
Journal of Geological Resource and Engineering, Jun 28, 2016
When Rankine or Coulomb theories to design of retaining wall are used, it is accepted beforehand ... more When Rankine or Coulomb theories to design of retaining wall are used, it is accepted beforehand that the retaining wall will experience a lateral displacement. This displacement is normally not calculated when a retaining wall is designed. This paper describes a method to estimate the lateral displacement of retaining walls. A practical example in the lateral displacement of a gravity retaining wall is presented.
Computational simulation of reinforced concrete structures is challenging because concrete cracks... more Computational simulation of reinforced concrete structures is challenging because concrete cracks at an early stage. Also, as a composite material with steel reinforcement, it is unclear whether the reinforcement should be modeled explicitly or whether the steel-concrete composite should be considered as a single, homogeneous, material. Adding to the difficulty is the fact that concrete is a quasi-brittle material, with a gradually softening cohesive process zone. Over the past 40 years, many finite element approaches have been employed to model reinforced concrete structures. The three main approaches are the smeared crack approach (or continuum damage mechanics), the discrete crack approach (including linear elastic fracture mechanics and cohesive crack models), and the discrete element approach (including lattice and particle models). These three approaches have achieved varying degrees of success. In 1998, Silling published a report describing the peridynamic model. This model r...
The peridynamic model is applied to the computational analysis of plain and reinforced concrete s... more The peridynamic model is applied to the computational analysis of plain and reinforced concrete structures. The peridynamic model is essentially a size-scaleable, continuum version of a molecular dynamics model. No assumption about the continuity of displacements is required in the model. While the continuum mechanics model requires concepts of stress and strain, the peridynamic model does not. Elasticity, cracking, and distributed damage emerge naturally from the peridynamic theory. The basic theory and several example problems are presented. The peridynamic model is promising from both conceptual and computational points of view for simulating the behavior of reinforced concrete structures.
Featured Application: Authors are encouraged to provide a concise description of the specific app... more Featured Application: Authors are encouraged to provide a concise description of the specific application or a potential application of the work. This section is not mandatory. Abstract: A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: Describe briefly the main methods or treatments applied; (3) Results: Summarize the article's main findings; and (4) Conclusions: Indicate the main conclusions or interpretations. The abstract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions. Keywords: keyword 1; keyword 2; keyword 3 (List three to ten pertinent keywords specific to the article; yet reasonably common within the subject discipline.) 0. How to Use This Template The template details the sections that can be used in a manuscript. Note that each section has a corresponding style, which can be found in the 'Styles' menu of Word. Sections that are not mandatory are listed as such. The section titles given are for Articles. Review papers and other article types have a more flexible structure. Remove this paragraph and start section numbering with 1. For any questions, please contact the editorial office of the journal or [email protected].
The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the applic... more The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the application of the quasistatic peridynamic model to two-dimensional, linear elastic, plane stress and plane strain problems, with special attention to the modeling of plain and reinforced concrete structures. We consider just one deviation from linearitythat which arises due to the irreversible sudden breaking of bonds between particles. The peridynamic model starts with the assumption that Newton's second law holds true on every infinitesimally small free body (or particle) within the domain of analysis. A specified force density function, called the pairwise force function, (with units of force per unit volume per unit volume) between each pair of infinitesimally small particles is postulated to act if the particles are closer together than some finite distance, called the material horizon. The pairwise force function may be assumed to be a function of the relative position and the relative displacement between the two particles. In this paper, we assume that for two particles closer together than the specified "material horizon" the pairwise force function increases linearly with respect to the stretch, but at some specified stretch, the pairwise force function is irreversibly reduced to zero.
The thermal performance of economical housing located in hot climates remains a pending subject, ... more The thermal performance of economical housing located in hot climates remains a pending subject, especially in emerging economies. A cellular concrete mixture was designed, considering its thermophysical properties, to apply the new material into building envelopes. The proposed materials have low density and thermal conductivity to be used as a nonstructural lightweight construction element. From the design stage, a series of wall systems based on cellular concrete was proposed. Whereas in the second phase, the materials were analyzed to obtain the potential energy savings using dynamic simulations. It is foreseen that the energy consumption in buildings located in these climates will continue to increase critically due to the temperature increase associated with climate change. The temperatures predicted mean vote (PMV), electric energy consumption, and CO2 emissions were calculated for three IPCC scenarios. These results will help to identify the impact of climate change on the e...
The peridynamic model described in (Silling 1998; Gerstle et al. 2005), being a central-force mod... more The peridynamic model described in (Silling 1998; Gerstle et al. 2005), being a central-force model, is limited to modeling materials with a Poisson’s ratio of one-quarter. In this paper, the peridynamic model is generalized by adding peridynamic moments to simulate linear elastic materials with varying Poisson’s ratios. This micropolar peridynamic model is placed within a finite element context to enable efficacious application of boundary conditions and efficient computational solutions using an implicit, rather than an explicit, solution algorithm. The algorithm is suitable for quasistatic simulation of damage and cracking in concrete structures. Very simple constitutive models at the peridynamic level appear to be sufficient to model the complex damage and fracture phenomena observed in concrete structures. The peridynamic model predicts significant elastic boundary effects that are not predicted by classical stress-strain models. As a consequence, the peridynamic model predicts...
In a number of applications, large size structures subjected to loads that cause highly non-linea... more In a number of applications, large size structures subjected to loads that cause highly non-linear behavior need to be analyzed. With the peridynamic theory, proposed by Stewart Silling in 2000 and 2007, elasticity and damage in quasibrittle structures such as plain and reinforced concrete structures can be modeled with the peridynamic theory. To model these structures, lattice models with brittle beam elements are used to model concrete. A shortcoming of lattice and particle models is that they are highly demanding of computational power. Molecular dynamics may be, in some cases an appropriate tool for analyzing microcracks in quasibrittle materials in compression, but molecular dynamics becomes infeasible at scales larger than a few million atoms. For example, in masonry structures, cracks form in the brick mortar joints, and concrete blocks can be assumed to have a uniform displacement field. This allows us to use the peridynamic finite element model, which is an improvement over discrete lattice models. This model assumes a continuous displacement field within each finite element, with displacement discontinuities allowed to develop between finite elements. The objective of this work is to model cracks in quasibrittle structures, with the peridynamic model. The peridynamic finite element model is shown to be much more computer time-and memoryefficient than the similar discrete particle-based models. Results show that this implementation appears to be more computationally efficient than particle or lattice models.
Reinforced concrete structures subjected to loads that cause the formation and propagation of cra... more Reinforced concrete structures subjected to loads that cause the formation and propagation of cracks exhibit a behavior where continuum mechanics is no longer applicable, because most conventional models do not consider the discontinuities that appear and propagate because of concrete tension failure. In an effort to correct the shortcomings of continuum models, the peridynamic bond-based model was proposed in 2000 and the peridynamic state-based model in 2007. The micropolar peridynamic model improves the bond-based peridynamic model by allowing different values of the Poisson's ratio. A numerical scheme for the calculation of the micropolar peridynamic stress was developed where results show convergence with classical linear elastic solutions for small values of the material horizon. With this approach, the stress tensor can be analyzed at points in failure zones. Fractures patterns using physical experimentation are obtained and compared with the model.
Journal of Geological Resource and Engineering, 2018
According the Coulomb earth pressure theory, it is obtained that, for normally consolidated soils... more According the Coulomb earth pressure theory, it is obtained that, for normally consolidated soils, the lateral pressure coefficient of a soil at rest is equal to 1, and it is independent of the soil type, either granular or cohesive; or that the material is in a loose or compact state; hard or a soft cohesive soil. Also, a methodology to calculate the earth pressure for intermediate states between at rest condition and the active pressure is presented. In addition, a methodology to calculate the earth pressure for intermediate states between at rest condition and the passive pressure is presented. Two practical examples are presented: one for a frictionless wall; and another for a coarse wall. Practical recommendations are given for the use of the lateral earth pressure coefficient for different applications.
Journal of Geological Resource and Engineering, 2013
It is disclosed a method for the stability analysis of foundation piles and piers subjected to la... more It is disclosed a method for the stability analysis of foundation piles and piers subjected to lateral loading, both static and seismic conditions. The stability analysis for stratified soil is based upon the models of foundation soil-structure interaction and the Rankine´s theory of earth passive pressure. In addition, its application is simpler and it can be solved using a spreadsheet. The procedure described in this work can be used in homogeneous soils as in stratified soils, considers the horizontal drag forces exerted by the soil mass against the foundation during an earthquake, can be used easily in the four pile and piers boundary cases, and considers the pore pressure generated in a fine saturated soil during an earthquake or during a rapid application of the horizontal load. The solution of two examples are shown, one in static condition and one in seismic condition, detailing the procedure step by step.
The nuclear industry relies heavily upon reinforced concrete structures. It is therefore essentia... more The nuclear industry relies heavily upon reinforced concrete structures. It is therefore essential that we develop robust and reliable theoretical and computational models for simulating the behavior of reinforced concrete. We develop a simple rate-independent micropolar peridynamic constitutive model for concrete subject to monotonic deformation. Using this model, we demonstrate that many of the commonly observed, complex, behaviors of concrete emerge naturally: linear elasticity, distributed anisotropic damage, discrete cracking, dilatency, and shear bands. In addition, bond between reinforcing steel and concrete is modeled in a simple and natural way. Also, a boundary effect that has not been explicitly observed in the laboratory is predicted by the micropolar peridynamic model. The model is implemented in a computational simulation program written in MATLAB. Using this computer program, we use two example problems to demonstrate the efficacy of the peridynamic constitutive model...
There exists a great potential for application in soil mechanics with the use of mechanistic mode... more There exists a great potential for application in soil mechanics with the use of mechanistic models such as the finite element model, and other non-local models, such as the peridynamic model, since the soil mass can be modelled as a group of particles that interact with each other. In this work, we determine the bearing capacity of deep foundations where stresses are transmitted to deep deposits, which generally present better characteristics in terms of compressibility and shear strength. One of the main elements are driven piles, which must be previously designed, made and tested before their final use. In this work, a comparison with different methods is presented. The finite element method and the peridynamic model are used. Because the effect of consolidation was not taken into account, in these examples, the assumption is made that the structures are cemented in inert soil. Likewise, it is assumed that the water table has no influence on the simulations. Failure envelopes were observed where bonds between particles present high gradients of deformation and fracture. Bearing capacities were estimated and compared with those obtained from the Terzaghi and Meyerhof methods.
Journal of Geological Resource and Engineering, Jun 28, 2016
When Rankine or Coulomb theories to design of retaining wall are used, it is accepted beforehand ... more When Rankine or Coulomb theories to design of retaining wall are used, it is accepted beforehand that the retaining wall will experience a lateral displacement. This displacement is normally not calculated when a retaining wall is designed. This paper describes a method to estimate the lateral displacement of retaining walls. A practical example in the lateral displacement of a gravity retaining wall is presented.
Computational simulation of reinforced concrete structures is challenging because concrete cracks... more Computational simulation of reinforced concrete structures is challenging because concrete cracks at an early stage. Also, as a composite material with steel reinforcement, it is unclear whether the reinforcement should be modeled explicitly or whether the steel-concrete composite should be considered as a single, homogeneous, material. Adding to the difficulty is the fact that concrete is a quasi-brittle material, with a gradually softening cohesive process zone. Over the past 40 years, many finite element approaches have been employed to model reinforced concrete structures. The three main approaches are the smeared crack approach (or continuum damage mechanics), the discrete crack approach (including linear elastic fracture mechanics and cohesive crack models), and the discrete element approach (including lattice and particle models). These three approaches have achieved varying degrees of success. In 1998, Silling published a report describing the peridynamic model. This model r...
The peridynamic model is applied to the computational analysis of plain and reinforced concrete s... more The peridynamic model is applied to the computational analysis of plain and reinforced concrete structures. The peridynamic model is essentially a size-scaleable, continuum version of a molecular dynamics model. No assumption about the continuity of displacements is required in the model. While the continuum mechanics model requires concepts of stress and strain, the peridynamic model does not. Elasticity, cracking, and distributed damage emerge naturally from the peridynamic theory. The basic theory and several example problems are presented. The peridynamic model is promising from both conceptual and computational points of view for simulating the behavior of reinforced concrete structures.
Featured Application: Authors are encouraged to provide a concise description of the specific app... more Featured Application: Authors are encouraged to provide a concise description of the specific application or a potential application of the work. This section is not mandatory. Abstract: A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: Describe briefly the main methods or treatments applied; (3) Results: Summarize the article's main findings; and (4) Conclusions: Indicate the main conclusions or interpretations. The abstract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions. Keywords: keyword 1; keyword 2; keyword 3 (List three to ten pertinent keywords specific to the article; yet reasonably common within the subject discipline.) 0. How to Use This Template The template details the sections that can be used in a manuscript. Note that each section has a corresponding style, which can be found in the 'Styles' menu of Word. Sections that are not mandatory are listed as such. The section titles given are for Articles. Review papers and other article types have a more flexible structure. Remove this paragraph and start section numbering with 1. For any questions, please contact the editorial office of the journal or [email protected].
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