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A ductile damage criterion at various stress triaxialities

BRUENIG, Michael; CHYRA, Oliver; ALBRECHT, Daniel; DRIEMEIER, Larissa; ALVES, Marcilio
Fonte: PERGAMON-ELSEVIER SCIENCE LTD Publicador: PERGAMON-ELSEVIER SCIENCE LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.54%
The paper discusses the effect of stress triaxiality on the onset and evolution of damage in ductile metals. A series of tests including shear tests and experiments oil smooth and pre-notched tension specimens wits carried Out for it wide range of stress triaxialities. The underlying continuum damage model is based oil kinematic definition of damage tensors. The modular structure of the approach is accomplished by the decomposition of strain rates into elastic, plastic and damage parts. Free energy functions with respect to fictitious undamaged configurations as well as damaged ones are introduced separately leading to elastic material laws which are affected by increasing damage. In addition, a macroscopic yield condition and a flow rule are used to adequately describe the plastic behavior. Numerical simulations of the experiments are performed and good correlation of tests and numerical results is achieved. Based oil experimental and numerical data the damage criterion formulated in stress space is quantified. Different branches of this function are taken into account corresponding to different damage modes depending oil stress triaxiality and Lode parameter. In addition, identification of material parameters is discussed ill detail. (C) 2007 Elsevier Ltd. All rights reserved.; Deutsche Forschungsgemeinschaft (DFG) (German Research Foundation)[BR1793/10-1]; FAPESP[04/15404-0]

Dependence of brittle-to-ductile transition on crystallographic direction in diamond turning of single-crystal silicon

Jasinevicius, Renato Goulart; Duduch, Jaime Gilberto; Montanari, Luciana; Pizani, Paulo Sergio
Fonte: SAGE PUBLICATIONS LTD; LONDON Publicador: SAGE PUBLICATIONS LTD; LONDON
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.6%
The objective of this paper is to show the dependence relationship between the crystallographic orientations upon brittle-to-ductile transition during diamond turning of monocrystalline silicon. Cutting tests were performed using a -5 degrees rake angle round nose diamond tool at different machining scales. At the micrometre level, the feedrate was kept constant at 2.5 micrometres per revolution (mu m/r), and the depth of cut was varied from 1 to 5 mu m. At the submicrometre level, the depth of cut was kept constant at 500 nm and the feedrate varied from 5 to 10 mu m/r. At the micrometre level, the uncut shoulder generated with an interrupted cutting test procedure provided a quantitative measurement of the ductile-to-brittle transition. Results show that the critical chip thickness in silicon for ductile material removal reaches a maximum of 285 nm in the [100] direction and a minimum of 115 nm in the [110] direction, when the depth of cut was 5 mu m. It was found that when a submicrometre depth of cut was applied, microcracks were revealed in the [110] direction, which is the softer direction in silicon. Micro Raman spectroscopy was used to estimate surface residual stress after machining. Compressive residual stress in the range 142 MPa and smooth damage free surface finish was probed in the [100] direction for a depth of cut of 5 mu m...

Estudo da fratura dúctil em chapas de aço médio carbono sob a ótica da teoria da mecânica do dano.; Ductile fracture study of medium carbon steel sheets under the continuum damage mechanics point of view.

Tsiloufas, Stergios Pericles
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 18/09/2012 PT
Relevância na Pesquisa
36.66%
Este trabalho busca avaliar a ductilidade de ligas metálicas utilizando como ferramenta a teoria da mecânica do dano proposta por Kachanov e desenvolvida por Lemaitre, a qual é apresentada desde as hipóteses básicas até as equações que modelam a deterioração de um material em regime de fratura dúctil. Como o enfoque do trabalho é a predição de trincas em processos de conformação mecânica, em especial estampagem de chapas, o mecanismo de formação destes defeitos é revisado, buscando na literatura o entendimento de como os parâmetros microestruturais influenciam na fratura dúctil. Ensaios de tração foram efetuados em corpos de prova retirados de chapas de aço SAE 1050 em duas condições microestruturais, cementita esferoidizada em matriz ferrítica e ferritaperlita, e em duas direções em relação à laminação da chapa original, paralelo e transversal. A evolução do dano foi medida de maneira indireta por meio da variação do módulo elástico e as propriedades mecânicas necessárias para utilização do modelo de Lemaitre foram calculadas. Por meio de difração de raios X, efetuamos o estudo da evolução da textura cristalográfica, apresentado na forma de figuras de distribuição de orientação e análise da intensidade das principais fibras encontradas em aços laminados a quente. Não foi observada influência significativa do tipo de microestrutura e da direção de deformação na evolução da textura. Por fim...

Finite element prediction of ductile fracture in sheet metal forming processes

teixeira, p; santos, ad; pires, fma; de sa, jmac
Fonte: Universidade do Porto Publicador: Universidade do Porto
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.44%
In this contribution, Lemaitres ductile damage model is coupled with Hills orthotropic plasticity criterion. The coupling between damaging and material behaviour is accounted for within the framework of Continuum Damage Mechanics (CDM). The resulting constitutive equations are implemented in the Abaqus/Explicit code, for the prediction of fracture onset in sheet metal forming processes. The damage evolution law takes into account the important effect of micro-crack closure, which dramatically decreases the rate of damage growth under compressive paths. (c) 2006 Elsevier B.V. All rights reserved.

A comparison of shear mechanisms for the prediction of ductile failure under low stress triaxiality

reis, fjp; malcher, l; pires, fma; de sa, jmac
Fonte: Universidade do Porto Publicador: Universidade do Porto
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.59%
Purpose - The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson-Tveegard-Needleman ductile damage constitutive model under low stress triaxiality. Design/methodology/ approach - One of the most widely used ductile damage models is the so-called Gurson-Tveegard-Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro-voids. However, the GTN model does not include void distortion and inter-void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi-static finite element framework and their results critically appraised. Findings - Through the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence. Research limitations/implications - Even though the results obtained with the modified GTN models have shown improvements...

Ductile connection characterization regarding seismic retrofitting of masonry buildings

Carles, Tristan Hamilton
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Dissertação de Mestrado
Publicado em //2012 ENG
Relevância na Pesquisa
36.58%
Dissertação de mestrado em Structural Analysis of Monuments and Historical Constructions; Anthropological reasons apart, earthquakes are one of the most devastating causes of damage to monuments and historical constructions, and, as a consequence, lead to significant cultural, human, and economical losses. Protection of such structures against seismic excitations is thus an important factor regarding life safety and the conservation of our historical heritage. Efficient connections between structural elements can highly reduce the seismic vulnerability of masonry buildings by enhancing the out of plane behaviour of the walls regarding lateral loads which are presented as the principal cause of failure in this type of structure. In spite of the importance of structural connections regarding the global behaviour of historical constructions under seismic actions, research in this field is almost nonexistent and needs to be developed. The objective of this thesis is to study the seismic response to a ductile connection used to connect tie-rods to masonry walls in the scope of seismic retrofitting of historical constructions and to analyse its behaviour in comparison to the behaviour of the other structural elements. In seismic vulnerability assessment...

A damage model for ductile crack initiation and propagation

Areias, Pedro; Van Goethem, Nicolas; Borges Pires, Eduardo
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
POR
Relevância na Pesquisa
36.52%
Damage-induced ductile crack initiation and propagation is modeled using a constitutive law with asymmetrical contraction of the yield surface and tip remeshing combined with a nonlocal strain technique. In practice, this means that the void fraction depends on a nonlocal strain. Finite strain plasticity is used with smoothing of the complementarity condition. The prototype constitutive laws take into account pressure sensitivity and the Lode angle effect in the fracture strain. Two plane idealizations are tested: plane stress and plane strain. Thickness variation in the former is included by imposing a null out-of-plane normal stress component. In plane strain, pressure unknowns and bubble enrichment are adopted to avoid locking and ensure stability of the equilibrium equations. This approach allows the representation of some 3D effects, such as necking. The nonlocal approach is applied to the strains so that the void fraction value evolves up to one and this is verified numerically. Three verification examples are proposed and one validation example is shown, illustrating the excellent results of the proposed method. One of the verification examples includes both crack propagation in the continuum and rigid particle decohesion based on the same model.

Numerical investigation of constraint effects on ductile fracture in tensile specimens

Ruggieri,C.
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2004 EN
Relevância na Pesquisa
36.69%
This study explores the capabilities of a computational cell framework into a 3-D setting to model ductile fracture behavior in tensile specimens. The cell methodology provides a convenient approach for ductile crack extension suitable for large scale numerical analyses which includes a damage criterion and a microstructural length scale over which damage occurs. Laboratory testing of a high strength structural steel provides the experimental stress-strain data for round bar and circumferentially notched tensile specimens to calibrate the cell model parameters for the material. The present work applies the cell methodology using two damage criterion to describe ductile fracture in tensile specimens: (1) the Gurson-Tvergaard (GT) constitutive model for the softening of material and (2) the stress-modified, critical strain (SMCS) criterion for void coalescence. The present work first applies the cell methodology to investigate effects of constraint (stress triaxiality) on ductile crack initiation of notched tensile specimens. An application also follows to determine the dependence of ductility on stress triaxiality for the tested steel. These exploratory 3-D studies using computational cells clearly demonstrate its capability to predict the strong effects of constraint on measured stress-strain response for tensile specimens.

Evaluation of Varying Ductile Fracture Criteria for 42CrMo Steel by Compressions at Different Temperatures and Strain Rates

Quan, Guo-zheng; Luo, Gui-chang; Mao, An; Liang, Jian-ting; Wu, Dong-sen
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
Publicado em 30/01/2014 EN
Relevância na Pesquisa
36.73%
Fracturing by ductile damage occurs quite naturally in metal forming processes, and ductile fracture of strain-softening alloy, here 42CrMo steel, cannot be evaluated through simple procedures such as tension testing. Under these circumstances, it is very significant and economical to find a way to evaluate the ductile fracture criteria (DFC) and identify the relationships between damage evolution and deformation conditions. Under the guidance of the Cockcroft-Latham fracture criteria, an innovative approach involving hot compression tests, numerical simulations, and mathematic computations provides mutual support to evaluate ductile damage cumulating process and DFC diagram along with deformation conditions, which has not been expounded by Cockcroft and Latham. The results show that the maximum damage value appears in the region of upsetting drum, while the minimal value appears in the middle region. Furthermore, DFC of 42CrMo steel at temperature range of 1123~1348 K and strain rate of 0.01~10 s−1 are not constant but change in a range of 0.160~0.226; thus, they have been defined as varying ductile fracture criteria (VDFC) and characterized by a function of temperature and strain rate. In bulk forming operations, VDFC help technicians to choose suitable process parameters and avoid the occurrence of fracture.

Calibration Procedures for a Computational Model of Ductile Fracture

Xue, Z; Pontin, M. G.; Zok, F. W.; Hutchinson, John W.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
36.52%
A recent extension of the Gurson constitutive model of damage and failure of ductile structural alloys accounts for localization and crack formation under shearing as well as tension. When properly calibrated against a basic set of experiments, this model has the potential to predict the emergence and propagation of cracks over a wide range of stress states. This paper addresses procedures for calibrating the damage parameters of the extended constitutive model. The procedures are demonstrated for DH36 steel using data from three tests: (i) tension of a round bar, (ii) mode I cracking in a compact tension specimen, and (iii) shear localization and mode II cracking in a shear-off specimen. The computational model is then used to study the emergence of the cup-cone fracture mode in the neck of a round tensile bar. Ductility of a notched round bar provides additional validation.; Engineering and Applied Sciences

Cohesive Traction-Separation Laws for Tearing of Ductile Metal Plates

Hutchinson, John W.; Nielsen, K. L.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
36.46%
The failure process ahead of a mode I crack advancing in a ductile thin metal plate or sheet produces plastic dissipation through a sequence of deformation steps that include necking well ahead of the crack tip and shear localization followed by a slant fracture in the necked region somewhat closer to the tip. The objective of this paper is to analyze this sequential process to characterize the traction–separation behavior and the associated effective cohesive fracture energy of the entire failure process. The emphasis is on what is often described as plane stress behavior taking place after the crack tip has advanced a distance of one or two plate thicknesses. Traction–separation laws are an essential component of finite element methods currently under development for analyzing fracture of large scale plate or shell structures. The present study resolves the sequence of failure details using the Gurson constitutive law based on the micromechanics of the ductile fracture process, including a recent extension that accounts for damage growth in shear. The fracture process in front of an advancing crack, subject to overall mode I loading, is approximated by a 2D plane strain finite element model, which allows for an intensive study of the parameters influencing local necking...

Tension–Torsion Fracture Experiments – Part II: Simulations with the Extended Gurson Model and a Ductile Fracture Criterion Based on Plastic Strain

Xue, Zhenyu; Faleskog, Jonas; Hutchinson, John W.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
36.64%
An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension-torsion test fracture data presented in Faleskog and Barsoum (2012) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension-torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing.; Engineering and Applied Sciences

Simulations of Ductile Fracture in an Idealized Ship Grounding Scenario Using Phenomenological Damage and Cohesive Zone Models

Woelke, Pawel B.; Shields, Michael D.; Abboud, Najib N.; Hutchinson, John W.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
36.77%
Two complementary simulation methodologies for ductile fracture in large sheet metal components are presented and evaluated in this paper. The first approach is based on the phenomenological dilatational plasticity-damage model developed by Woelke and Abboud [68], which accounts for pressure-dependent volumetric damage growth through a scalar damage variable. The damage function represents phenomenologically micromechanical changes the material undergoes during the process of necking. Secondly, the cohesive zone model with an opening mode traction-separation law is employed to simulate the same ductile fracture problems accounting for significant variation of the multiaxial stress state along the crack path. Both methods are examined as to their capabilities to reproduce and predict the outcome of large scale experimental fracture tests of welded and unwelded ductile plates subjected to large-scale penetration, simulating an idealized ship grounding (Alsos and Amdahl, [1, 2]). The results of the current study indicate that, with appropriate calibration, both approaches can be successfully employed to simulate ductile fracture in structural components under multiaxial stress. The advantages and shortcomings of each approach is discussed from the point of view of post-test numerical investigation as well as its predictive capabilities as an engineering tool.; Engineering and Applied Sciences

THE RELATIONSHIP BETWEEN MICROSTRUCTURE AND DAMAGE EVOLUTION IN HOT-ROLLED COMPLEX-PHASE STEEL SHEET

Bell, Grant
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado
EN; EN
Relevância na Pesquisa
36.51%
Complex-phase (CP) steels are employed in applications that require high-strength and good edge formability. These steels derive their strength from a fine-grained bainite-ferrite microstructure, and alloying to provide solid-solution and precipitation strengthening. CP steels are produced industrially through a process of controlled rolling and cooling to produce desirable microstructures. Hole-expansion tests are typically used as a measure of edge formability for applications such as stretch-flanges. It has been shown that CP microstructures are susceptible to large fluctuations in hole-expansion performance with little change in processing or resulting tensile properties. The steel’s characteristics of damage evolution are critical to the hole-expansion performance. This study investigates the role of microstructure in the development of damage in CP microstructural variants. Two variant pairs of different thicknesses were produced from the leading and trailing edge of industrially produced hot-rolled sheet. Each pair consisted of a variant with poor hole-expansion performance, and a variant with good hole-expansion performance. Each variant was tested via interrupted double-notched uniaxial tension testing to induce damage. Damage evolution in each variant was quantified by X-ray micro-computed tomography (XµCT)...

Experimental characterization and numerical modeling of micromechanical damage under different stress states

ACHOURI, Mohamed; GERMAIN, Guénaël; DAL SANTO, Philippe; SAIDANE, Delphine
Fonte: ELSEVIER Publicador: ELSEVIER
EN_US
Relevância na Pesquisa
46.46%
The use of HSLA steels for the manufacture of automotive components is interesting from an engineering point of view. This family of steels, while possessing high strength, also has good formability and can be used in forming manufacturing processes. In some forming processes such as blanking, shear strain localization occurs, which causes damage and results in the final fracture of the material. This paper presents an experimental study based on in situ tests to understand and identify the physical mechanisms of ductile damage under two stress states: tension and shear. Different macroscopic tests were performed to calibrate a damage model based on a micromechanical approach. This damage model is based on the Gurson–Tvergaard–Needleman theory and presents recent improvements proposed by Nahshon and Hutchinson and by Nielsen and Tvergaard so as to better predict fracture under a wide range of stress states, especially with low levels of stress triaxiality. These extensions have made the identification of the material parameter more complicated. In this work an identification strategy has been proposed using tests on specimens with different shapes. The identified parameter values are validated and the fracture model show good predictive capability over a wide stress state range.

Numerical integration of an advanced Gurson model for shear loading: Application to the blanking process

ACHOURI, Mohamed; GERMAIN, Guénaël; DAL SANTO, Philippe; SAIDANE, Delphine
Fonte: ELSEVIER Publicador: ELSEVIER
EN
Relevância na Pesquisa
36.56%
A new extension of the Gurson damage model has been proposed recently to predict ductile fracture under shear dominated loads. The aim of this work is to verify the ability of this approach to simulate, in an accurate way, the damage evolution in shearing processes. An implicit stress integration algorithm is then developed to implement the new model in a finite element code. The numerical procedure is checked through simulations of shear and uniaxial tension tests on a single elements. The extended Gurson damage model is tested and applied to the punching process to compare its predictive ability with the original approach. The obtained numerical results are in good agreement with experimental results of the punching process, showing better ductile fracture predictions compared to the original Gurson model.

Development of a microscopic damage model for low stress triaxiality

ACHOURI, Mohamed; GERMAIN, Guénaël; DAL SANTO, Philippe; LEBRUN, Jean-Lou; SAIDANE, Delphine
Fonte: Scientific.Net Publicador: Scientific.Net
EN_US
Relevância na Pesquisa
56.44%
Sheet Metal 2011; This work deals a contribution to ductile damage of High-Strength Low-Alloy (HSLA) steel steels under low stress triaxiality. This work is based on micrographics observations and in situ shear tests to examine the evolution of microstructure in this kind of loading and to identify the damage process associated. Numerical simulations by finites elements has been performed to simulate the material behavior of nucleation mechanism and the interaction between cavities during the coalescence phase, as well as the effect of the relative position of the inclusions in the shear plane. The model used as a reference in this work is the Gurson-Tvergaard- Needleman (GTN) model. It has been recently improved in order to take into account the effects of low triaxiality during shearing. The implementation of this model in a finite element code is in progress.; Devillé SA

A Finite Element Implementation of a Ductile Damage Model for Small Strains

Gates, Robert Lee
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/02/2013
Relevância na Pesquisa
46.4%
Lemaitre's ductile damage model and a simplified variant excluding kinematic hardening were studied and implemented into computer code. For purposes of verifying the model, results from computations with the finite element method are compared to literature. It is found that the behavior expected from theory is modeled by both implementations. Quadratic levels of convergence were observed for the simplified model, while results show that convergence of the kinematic hardening implementation deteriorates with damage. It is concluded that further examination is needed to verify the correct implementation of the kinematic hardening model.; Comment: Bachelor thesis, grade 1.0 (excellent), 69 pages, including 14 pages of source code, 38 references, 24 figures, 1 table

Ductile damage model for metal forming simulations including refined description of void nucleation

Shutov, A. V.; Silbermann, C. B.; Ihlemann, J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.48%
We address the prediction of ductile damage and material anisotropy accumulated during plastic deformation of metals. A new model of phenomenological metal plasticity is proposed which is suitable for applications involving large deformations of workpiece material. The model takes combined nonlinear isotropic/kinematic hardening, strain-driven damage and rate-dependence of the stress response into account. Within this model, the work hardening and the damage evolution are fully coupled. The description of the kinematics is based on the double multiplicative decomposition of the deformation gradient proposed by Lion. An additional multiplicative decomposition is introduced in order to account for the damage-induced volume increase of the material. The model is formulated in a thermodynamically admissible manner. Within a simple example of the proposed framework, the material porosity is adopted as a rough measure of damage. A new simple void nucleation rule is formulated based on the consideration of various nucleation mechanisms. In particular, this rule is suitable for materials which exhibit a higher void nucleation rate under torsion than in case of tension. The material model is implemented into the FEM code Abaqus and a simulation of a deep drawing process is presented. The robustness of the algorithm and the performance of the formulation is demonstrated.; Comment: 35 pages...

Fragility curves for non-ductile reinforced concrete frames that exhibit different component response mechanisms

Jeon, Jong-Su; Lowes, Laura N.; DesRoches, Reginald; Brilakis, Ioannis
Fonte: Elsevier Publicador: Elsevier
Tipo: Article; accepted version
EN
Relevância na Pesquisa
36.49%
This is the accepted manuscript of a paper published in Engineering Structures (J-S Jeon, LN Lowes, R DesRoches, I Brilakis, Engineering Structures 2015, 85, 127?143); Around the world, a large percentage of buildings in regions of high seismicity are older, non-ductile reinforced concrete. To assess the risk posed by these buildings, fragility functions are required to define the likelihood that these buildings will sustain damage and collapse under earthquake loading. This paper presents the initial phase of a research effort to develop fragility functions for non-ductile concrete frames using numerical simulation; the research presented in this paper focuses on development of the numerical model and application of the model to develop fragility functions for a prototype non-ductile concrete frame. To enable numerical simulation of concrete frame buildings, response models for beam?column joints and columns are developed to provide (1) appropriate simulation of component response and, thereby, reliable assessment of risk and (2) computational efficiency and robustness. These new models are developed using existing experimental data, build on response models proposed by others, and employ component and material models available in the OpenSees analysis platform (http://opensees.berkeley.edu). A new beam?column joint model combines a new expression for joint strength and newly developed cyclic response parameters; a new column response model includes a new shear-strength model and newly developed cyclic response parameters. Numerical models of a prototype non-ductile concrete frame are developed that include simulation of one or more of the following characteristics: (1) rigid beam?column joint...