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.
This figure depicts the setup of the mixed-mode fracture test in which a double notched prismatic panel was loaded in tension (T) and shear (S). The shear load was applied first up to a shear force close to the force capacity; then the tension was applied under displacement control keeping the shear load constant. The numerical simulation shows the typical curved cracks propagating from the notch tips towards the opposite side of the specimens.
Simulation of mixed mode fracture propagation in concrete panels
This example is relevant to transitional thermal creep tests in which the temperature is changed during the application of sustained load. In addition, the specimen undergoes drying due to an environmental 50% relative humidity. The figure shows the comparison between the experimental and numerical results. The basic creep curve relevant to sealed conditions and constant temperature is also reported for comparison. The difference between the total strain measured under load and the total strain measured on a load-free companion specimen is used as a measure of creep strain. The numerical model correctly predict the increase of creep deformation due to humidity and temperature transient conditions.
creep strain versus time under temeperature and humidity variation
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