1,721,070 research outputs found
A phase-field gradient-based energy split for the modeling of brittle fracture under load reversal
No full textIn the phase-field modeling of fracture, the search for a physically reasonable and computationally feasible criterion to split the elastic energy density into fractions that may or may not contribute to crack propagation has been the subject of many recent studies. Within this context, we propose an energy split - or energy decomposition - aimed at accurately representing the evolution of a crack under load reversal. To this purpose, two key assumptions are made. First, the damage gradient direction is interpreted as being representative of the normal-to- crack direction, as already assumed in previous works in the literature. The second assumption consists of considering the sign of the projection of the stress tensor onto the damage gradient direction at a point as an indicator of whether this point should behave as an opening or as a closing crack. We associate the latter case (crack closing) to both (a) a complete recovery of elastic energy density of the intact material (i.e., perfectly rough crack surfaces) and (b) a zero crack driving force at that point. The first case (crack opening) is treated classically as a damageable material point at which damage can increase. The implementation of the proposed approach turns out to be remarkably simple and computationally robust. For the evaluation of the displacements and damage gradients at nodes, the classical Z2 2 technique is used, and a new effective and computationally convenient iterative strategy is implemented to guarantee convergence of the staggered scheme. Four examples are presented in order to assess the suitability of the present model by using both AT1 and AT2 regularization models. Results show the desired effect of limiting crack propagation to prevailing tensile states, as well as of recovering the initial intact stiffness upon load reversal, even when two of the most common energy splits fail
Discussion: “Chaotic Motion of an Elastic-Plastic Beam” (Poddar, B., Moon, F. C., and Mukherjee, S., 1988, ASME J. Appl. Mech., 55, pp. 185–189)
No full textDiscussion on caotic motion of a pinned beam subjected to pulse loadin
A hybrid Lagrangian-Eulerian particle finite element method for free-surface and fluid-structure interaction problems
Full text linkThe dynamics of fluid flows with free surfaces and interacting with highly deformable structures is a complex problem, attracting considerable attention. The Particle Finite Element Method (PFEM) is one of the various numerical methods recently proposed in the literature to simulate this type of problems. It is a mesh-based Lagrangian approach, particularly suited for problems with fast changes in the domain topology, since the fluid boundaries and the Fluid-Structure Interaction (FSI) interface are naturally tracked by the position of the mesh nodes. However, when nonhomogeneous boundary conditions are imposed on velocities or when there are regions where the topology varies moderately, for example, in confined portions of the fluid domain characterized by fixed boundaries, an Eulerian formulation turns out to be more convenient. To exploit the advantages of both formulations, an adaptive hybrid Lagrangian-Eulerian approach is presented in this work. According to the proposed method, nodes on the fluid free-surface and on the FSI interface are treated as Lagrangian, while the remaining nodes can be either Eulerian or Lagrangian. Furthermore, to increase the efficiency of the method, an algorithm to automatically detect runtime the transition zone between the two kinematic descriptions is devised. To validate the proposed approach, several numerical examples are developed and their results are compared to those available in the literature
Variationally consistent self-stabilized Virtual Elements for 2D locking-free elastoplasticity
No full textA variationally consistent numerical approach based on the Virtual Element Method (VEM) is presented for the analysis of 2D elastoplasticity problems. The mixed Hu-Washizu functional of elasticity is extended to incorporate the energy contributions specific to the finite-step elastoplastic problem. It is demonstrated how the governing equations of the discretized elastoplastic problem - including the loading-unloading conditions - emerge naturally as the stationarity conditions of the VEM-discretized functional. Spurious hourglass modes are prevented by formulating a self-stabilized version of Virtual Elements (VEs) that exploits the possibility offered by the mixed approach to define strain and displacement approximations of the same order. The insensitivity of VEs to element distortion and the possibility to use polygonal elements with any shape and number of edges is tested with the analysis of several benchmarks from the literature. It is shown how accurate solutions can be obtained also in the case of non-convex quadrilateral or pentagonal elements. Additionally, the role of internal moment degrees of freedom in preventing elastoplastic locking at the plastic failure limit is elucidated
A small deformations effective stress model of gradient plasticity phase-field fracture
Full text linkA variational formulation of small strain ductile fracture, based on a phase-field modeling of crack propagation, is proposed. The formulation is based on an effective stress description of gradient plasticity, combined with an AT1 phase-field model.
Starting from established variational statements of finite-step elastoplasticity for generalized standard materials, a mixed variational statement is consistently derived, incorporating in a rigorous way a variational finite-step update for both the elastoplastic and the phase-field dissipations. The complex interaction between ductile and brittle dissipation mechanisms is modeled by assuming a plasticity driven crack propagation model. A non-variational function of the equivalent plastic strain is then introduced to modulate the phase-field dissipation based on the developed plastic strains. Particular care has been devoted to the formulation of a consistent Newton–Raphson scheme for the case of Mises plasticity, with a global return mapping and relative tangent matrix, supplemented by a line-search scheme, for the solution of the gradient elastoplasticity problem for fixed phase field. The resulting algorithm has proved to be very robust and computationally effective. Application to several benchmark tests show the robustness and accuracy of the proposed model
Numerical simulation of water waves generated by landslides impact. Application to Vajont disaster
Full text linkSelf-stabilized virtual element modeling of 2D mixed-mode cohesive crack propagation in isotropic elastic solids
Full text linkA comprehensive strategy for the simulation of mixed-mode cohesive crack propagation in a mesh of originally self-stabilized Virtual Elements (VEs) is proposed. Exploiting the VEs substantial insensitivity to mesh distortion, the propagating cohesive crack is accommodated within existing self-stabilized first-order quadrilateral VEs by simply adding new edges separated by a cohesive interface. The added edges make however the VE unstable and a new procedure for the stabilization of initially stable VE is developed. The method is formulated within a recently proposed Hu–Washizu variational framework, allowing for a higher order, independent modeling of stresses. In this way, a more accurate estimate of the stress at the tip of the cohesive process zone can be achieved allowing for a more accurate assessment of crack propagation conditions and direction. The proposed method is validated by application to several benchmark problems
3D simulation of Vajont disaster. Part 2: Multi-failure scenarios
Full text linkPrediction of multi-hazard slope stability events requires an informed and judicious choice of the possible scenarios. An incorrect definition of landslide conditions in terms of expected failure volume, material behavior, or boundary conditions can lead to inaccurate predictions and, in turn, to wrong engineering and risk management decisions. Reduced-scale experiments carried out two years before the Vajont disaster were carried out with a material not representative of the actual rockslide behavior and failed in not considering the simultaneous failure of the whole landslide body. Based on these inappropriate assumptions, the physical models led to wrong estimates of the safety operational level for the Vajont reservoir. This work uses the Particle Finite Element Method (PFEM) to analyze the implications of the wrong hypotheses considered in the pre-event experiments, simulating numerically the Vajont disaster for different sliding volumes and material properties. The use of the PFEM for the accurate assessment of the consequences of landslides impinging in water reservoirs has been already validated in a companion paper. In this work, we demonstrate the capabilities of a robust and reliable numerical modeling approach for the simulation of different scenarios, assessing what could have been a safe operational reservoir level in the case of a landslide generated impulse wave. The three-dimensional analyses were run with a high mesh resolution and demonstrate the suitability and robustness of the PFEM model for large-scale landslide and multi-hazard events simulation
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