Gianluca Cusatis, Ph.D. - Assistant Professor - Department Of Civil And Environmental Engineering - School Of Engineering - Rensselaer Polytechnic Institute - Troy, NY 12180 - 3590
This simulation consists of a metallic rod impacting a quasi-brittle brick at various velocities. The objective of this study is to demonstrate the ability of the Lattice Discrete Particle Model to simulate impact induced fragmentation. The image shows the failure patterns associated with four different velocities, ranging from 400 in/s to 1600 in/s. For the lowest velocity, the brick splits essentially in two fragments. At 800 in/s, there are four major fragments with some debris in between. At higher velocities the number of fragments increases up to the complete fragmentation of the brick.
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This post discusses the numerical simulations of tension testes on fiber reinforced concrete specimens. Figure (a) below shows experimental and numerical stress versus displacement curves for four different fiber volume fractions (Vf ): 0% (plain concrete), 2%, 3%, and 6%. The lattice discrete particle model is able to predict the increased strength and ductility due to the effect of fibers. The behavior gradually transitions from softening for plain concrete and low Vf , to hardening for high Vf . The numerical results are further investigated in Fig. (b), where contours of the mesoscale crack opening at the end of the simulations are reported for three fiber volume fractions. For plain concrete, the crack pattern is characterized by one localized crack that propagates from one side of the specimen towards the other. As fracture propagates, material outsidethe crack unloads as the overall load applied tothe specimen tends to zero. For the 2% Vf , there is still one main crack propagation, but the entire specimen features diffuse cracking and no unloading occurs. Absence of unloading outside the main crack is due to the fact that even though the overall behavior is softening, the stress versus displacement curve shows a non-zero residual stress associated with the fiber crack bridging effect. Finally, for the 6% Vf , the crack pattern is characterized by several branched cracks whose propagation is arrested by the effect of the fibers. No unloading occurs outside the main cracks since the overall behavior is strain-hardening and, up to a displacement of 0.5 mm (average nominal strain of 0.5 mm / 120 mm 0.42%), no reduction of the load carrying capacity can be observed.
Stress versus strain curves and fracture patterns for fiber reinforced concrete specimens
This post deals the results of three-point bending test simulations on notched specimens. Only the central part of the specimen is simulated through the accurate lattice discrete particle model while the two lateral parts are modeled used elastic finite elements. This is reasonable because the presence of the notch ensures that damage localizes ahead of the notch tip. The figures below the meso-scale crack openings (blue=0.0005 mm, red=0.66 mm and above) for plain concrete (top) and fiber reinforced concrete (bottom) with a 0.45% volume fraction. As one can see for the fiber reinforced case fracture are less localized compared to the plain concrete case.
Meso scale racture distribution for plain concrete (top) and fiber reinforced concrete (bottom).
In this figure the results of biaxial quasi-static tests on plain concrete panels are reported. In the center of the picture one can see the comparison between the numerical (solid curves) and experimental (circles) failure domains normalized with the compressive strength. The top left of the figure shows classical shear band failure characterizing uniaxial unconfined compression tests. The top right shows the failure mode under uniaxial tension. The bottom left is relevant to equi-biaxial tension characterized by a 45 deg fracture. The bottom right reports the failure mode obtained while applying compression in the vertical direction and transverse tension.
The simulation of damage induced by a blast on a reinforced concrete wall is reported in this figure. The top of the figure shows the geometry of the wall as well as the position of the charge. The bottom of the figures reports the damage evolution at three time instants during the simulation. At the beginning the wall shows a failure that resembles the effect of a concentrate load with several radial cracks emanating for the center of the wall. Later damage concentrates at the bottom (where the wall is clamped) and the final failure mode is characterized by the complete shearing of the wall base.
Simulation of blast effects on a reinforced concrete wall
This simulation consists of a metallic rod impacting a quasi-brittle brick at various velocities. The objective of this study is to demonstrate the ability of the Lattice Discrete Particle Model to simulate impact induced fragmentation. The image shows the failure patterns associated with four different velocities, ranging from 400 in/s to 1600 in/s. For the lowest velocity (top left), the brick splits essentially in two fragments. At 800 in/s (top right), there are four major fragments with some debris in between. At higher velocities (bottom left and right) the number of fragments increases up to the complete fragmentation of the brick.
Simulation of fragmentation caused by a steel rod impacting a brick of quasi-brittle material
This figure shows the simulation of a steel projectile penetration through a reinforced concrete slab. Concrete, rebars, and projectile are modeled by LDPM, elasto-platic beam elements, and elasto-plastic brick elements, respectively (top left and top right). The striking velocity is 1060 m/s. The the projectile velocity history during the penetration is reported in the bottom left of the figure. Initially, the projectile velocity decreases linearly with time. About 0.18 ms after the impact the front face scabbing initiates and the projectile deceleration is greatly reduced. After 0.35 ms the projectile achieved complete penetration with an exit velocity of about 960 m/s. The damage distribution after the penetration event is shown in the bottom right of the figure.
Simulation of a steel projectile penetration into a reinforced concrete slab.
Institution: Rensselaer Polytechnic Institute, Troy (NY), USA.
Terms: Spring 2006; Spring 2008; Spring 2010
Number of students:14; 41; 48
Course Objective:The objective of this course is to develop a working knowledge on matrix analysis of elastic structures, plastic behavior of structures, buckling of elastic structures. Students will do this by building on the knowledge gained through IEA (ENGR 1100) and introduction to structural engineering (CIVL 2670). Upon successful completion of the course, students will have an adequate insight of elastic, plastic, and bucking behavior of structures as well as specific structural analysis tools needed in the professional practice of modern structural engineers.
Course Outcomes: After successfully completing this course students will be able to:
Solve statically indeterminate elastic trusses, beams, and frames by the stiffness method.
Perform the incremental analysis of elastic-plastic trusses, beams, and frames.
Calculate the buckling load for elastic columns and frames.
Institution: Rensselaer Polytechnic Institute, Troy (NY), USA.
Terms: Spring 2007; Spring 2009; Spring 2010;
Number of students:60; 68; 64;
Course Objective: The objective of this course is to develop a working knowledge of the principles of reinforced concrete design as applied to structural systems. Students will do this by building on the knowledge gained through their courses in statics, mechanics of materials, and structural analysis/design. Upon successful completion of the course, students will have an understanding of how reinforced concrete is used as a building material, how reinforced concrete structural components (e.g., beams, columns, and footings) are designed, and how to use the ACI building code document. Having successfully completed this course, you will have the necessary skills to perform basic reinforced concrete design and to take graduate courses in advanced concrete design.
Course Outcomes: After successfully completing this course students will be able to:
Analyze and report experimental data relevant to uniaxial compression tests.
Design reinforced concrete column under pure compression.
Design longitudinal reinforcement in beams.
Design transverse reinforcement in beams.
Design reinforced concrete column under compression and bending.
Institution: Rensselaer Polytechnic Institute, Troy (NY), USA.
Terms: Fall 2008;
Number of students: 21;
Course Objective: The objective of this course is to introduce graduate and senior undergraduate students to advanced topics on the mechanics of concrete behavior. Students will do this by building on the knowledge gained through all mechanics related courses of the undergraduate curriculum (statics, mechanics of materials, concrete design, etc.). Upon successful completion of the course, students will have an advanced understanding of concrete behavior as well as knowledge of specific modeling theories that can be used for the numerical simulation of concrete structures. Having successfully completed this course, students will have the necessary skills to conduct concrete research as well as to solve advanced concrete design problems.
Course Outcomes: After successfully completing this course students will be able to:
Perform experimental tests in compression;
Perform experimental tests in tension (direct and indirect);
Analyze and report experimental results;
Use advanced constitutive models for concrete to compute the response of structures;
Use linear elastic fracture mechanics to predict the maximum capacity of brittle materials;
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