Provided are a series of computations which demonstrate the MARS ability to solve fundamental problems of structural mechanics, support design calculations, and provide failure mode assessment.
The plate is modeled using shell elements made of an elasto-plastic material. The plate mesh is initially continuous. Discrete cracks are formed by inserting new nodes at the location where tensile stresses exceed a threshold failure stress. The failure stress varies spatially in a random fashion within a prescribed range to stagger crack formation. A material damping mechanism dissipates the energy released during crack formation. Some of the initial cracks propagate simulating the tearing of the plate.
Concrete was modeled using the K&C concrete model (modified material 16 in DYNA3D). Clusters of concrete elements were adaptively eroded according to a predefined failure criterion. Rebars nodes are tied to the concrete elements using node-to-solid constraints. This makes it possible to mesh rebars and concrete independently.
In this simulation, a detonation pressure load was applied to an interface plate dividing two rooms. The plate is initially continuous and can fracture at certain nodes when the local failure criteria are met. In this example, the plate experiences large strain rates over extended areas. This process generates many micro-cracks that occur almost simultaneously. In this example, the initial cracks did not have enough time to grow in a tearing fashion but rather the extended areas of high strain rates result in the formation of many plate fragments.
A rigid pin is moved down at constant velocity. The lug develops tension stresses which induce micro-cracks. Micro cracks are adaptively introduced in the solid mesh by inserting new nodes and separating the elements so that the mesh is no longer continuous. In this fashion, the cracking process is treated at the structural level rather than within the material constitutive model which assumes material continuity. Initial cracks propagate until the ligament is completely broken. Material damping dissipates locally the energy released during the cracking process preventing a cracking cascade effect.
The model consists of a one-fourth sector of the cylindrical rod. The time sequence of the radial cross section shows progressive fission in the first part of the simulation and fusion as strain rates decay. Notice the relatively undefined area of hydrostatic compression along the axis of the rod. The figure on the right shows an overlap of the final configurations from a static mesh case and a case employing adaptive refinement. The refinement scheme relies on the structure of the solid finite element mesh. The initial mesh is obtained by discretizing the domain with tetrahedral elements and subdividing each of these elements into four, 8-node hexahedra. With this refinement scheme, the mesh remains continuous as it gets refined and no “hanging” nodes are necessary. (“Hanging” nodes are new nodes at the boundary of refined regions which must be tied to the unrefined regions of the mesh.)
The time sequence shows how the mesh, consisting of quadrilateral shells, is progressively refined where the panel bends the most. Again, this h-type refinement scheme makes it possible to refine the mesh avoiding hanging nodes. The QPH shell formulation has been demonstrated to be accurate for elements that are not rectangular in shape.
A blast explosion is located close to the center of the wall. Concrete breaks up under the extreme loading conditions and the reinforcing rebars (shown in red) become exposed. Damaged elements are eroded and converted in spherical particles (fragments) which inherit mass and velocity from the parent solid elements. These concrete fragments are saved in the calculation and can interact with surrounding structure. Their final velocity and trajectory is used to predict further damage to surrounding equipment and personnel.
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