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Modeling complex material failure with competing mechanisms is a difficult task that often leads to mathematical and numerical challenges. This work contributes to the study of localized failure mechanisms by means of phase fields in a variational framework: in addition to the treatment of brittle and ductile fracture, done in previous work, we consider the case of shear band formation followed by ductile fracture. To achieve this, a new degradation function is introduced, which distinguishes between two successive failure mechanisms: (i) plastic strain localization and (ii) ductile fracture. Specifically, the onset of elastic damage is delayed to allow for the formation of shear bands driven by plastic deformations, thus accounting for the mechanisms that precede the coalescence of voids and microcracks into macroscopic ductile fractures. Once a critical degradation value has been reached, a phase-field model is introduced to capture the (regularized) kinematics of macroscopic cracks. To tackle the issue of potentially high computational cost, we propose a parallel implementation of the phase-field approach based on an iterative algorithm. The algorithm was implemented within the Alya system, a high performance computational mechanics code. Several examples show the capabilities of our implementation. We pay special attention to the ability to capture different failure mechanisms

Strain localization is one of the most challenging phenomena in solid mechanics. It occurs when strains concentrate in very narrow bands within a solid, typically referred to as localization bands. This behaviour is related to different types of failure mechanisms: fracture, shear bands and slip lines. Being a dissipative process, the modelling of strain localization could seem to preclude the use of variational methods. However, a sound framework to deal with this issue has been developed in the last few decades. In this contribution, we review the modelling of strain localization by means of variational methods systematically, presenting the main underlying theoretical concepts. The issue of irreversibility is approached by means of the theory of generalized standard materials, which constitutes the basis for the variational approach. Then, typical problems occurring in the modelling of strain localization are analyzed: the tendency to localize in a band of zero thickness with no dissipation, the determination of the geometry of the localization band, and the orientation bias of such band with respect to mesh alignment in finite element discretizations. We discuss solutions for these problems, focusing on the approach that tackles the description of the localization band using phase fields. © 2020, CIMNE, Barcelona, Spain.

The modeling of the post-critical behavior of materials is still a scientific challenge. This is especially true when dealing with materials that undergo complex behavior, in which several mechanisms are combined. This physical complexity is reflected in the mathematics and the numerics of this kind of problems. In this work, we study the modeling of brittle and ductile fracture. We adopt regularized kinematics based on a phase field description of the fracture topology. In order to ensure mathematical soundness, we use a rigorous variational framework for dissipative rate-independent materials. This framework allows to introduce several dissipative mechanisms in a straightforward and clear manner. For instance, gradients for both damage and plasticity are introduced. This implies the existence of two internal length scales that control the degree of ductility of the macroscopic fracture mechanism. A finite element discretization allows to test the possibilities of the proposed model to describe different fracture behaviors with several benchmark numerical experiments. In addition, the variational framework naturally leads to a robust staggered algorithm. Despite the simplicity of the numerical solution, different types of fracture processes can be described as particular cases: quasi-brittle, elasto-plastic brittle, and ductile.

The implementations of an updated body-fitted and a non body-fitted method to deal with the interaction of a fluid and a rigid body are described. The physics of the fluid is modeled by the incompressible Navier-Stokes equations. A parallel fluid solver based on the VMS (Variational Multiscale) Finite Element method serves as the basis for the implementation. For the rigid body movement, the Newton-Euler equations are solved numerically. To account for the interaction, the force that the fluid exerts on the rigid body is determined, on the one hand. On the other hand, the velocity of the rigid body is imposed as a Dirichlet boundary condition on the fluid. A fixed Eulerian mesh discretizes the fluid domain, except for nodes in the vicinity of the rigid body boundary for the case of the updated body-fitted approach. The wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh. It is a distinctive characteristic of the updated body-fitted strategy that, in order to impose velocities on the interface, some of the nodes near the body surface are moved by using a local r-adaptivity algorithm to conform with this surface. By contrast, the non body-fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface. Given that fluid nodes can become solid nodes and viceversa due to the rigid body movement, we have adopted the FMALE approach, a variation of the ALE method to keep the fluid mesh fixed. Algorithms to ensure high performance, like skd-trees to determine if a given spatial point is currently inside the solid, are also used. All these ingredients constitute two approaches that are both computationally efficient and accurate. Numerical experiments are presented to assess their performance comparatively., We would like to especially thank Oscar Peredo for his idea and support in introducing a more technical notation and terminology for the data-structures described in this work., Peer Reviewed, Postprint (author's final draft)

One of the main difficulties using multi-point statistical (MPS) simulation based on annealing techniques or genetic algorithms concerns the excessive amount of time and memory that must be spent in order to achieve convergence. In this work we propose code optimizations and parallelization schemes over a genetic-based MPS code with the aim of speeding up the execution time. The code optimizations involve the reduction of cache misses in the array accesses, avoid branching instructions and increase the locality of the accessed data. The hybrid parallelization scheme involves a fine-grain parallelization of loops using a shared-memory programming model (OpenMP) and a coarse-grain distribution of load among several computational nodes using a distributed-memory programming model (MPI). Convergence, execution time and speed-up results are presented using 2D training images of sizes 100 × 100 × 1 and 1000 × 1000 × 1 on a distributed-shared memory supercomputing facility., Peer Reviewed, Postprint (author's final draft)

While solid mechanics codes are now conventional tools both in industry and research, the increasingly more exigent requirements of both sectors are fuelling the need for more computational power and more advanced algorithms. For obvious reasons, commercial codes are lagging behind academic codes often dedicated either to the implementation of one new technique, or the upscaling of current conventional codes to tackle massively large scale computational problems. Only in a few cases, both approaches have been followed simultaneously. In this article, a solid mechanics simulation strategy for parallel supercomputers based on a hybrid approach is presented. Hybrid parallelization exploits the thread-level parallelism of multicore architectures, combining MPI tasks with OpenMP threads. This paper describes the proposed strategy, programmed in Alya, a parallel multi-physics code. Hybrid parallelization is specially well suited for the current trend of supercomputers, namely large clusters of multicores. The strategy is assessed through transient non-linear solid mechanics problems, both for explicit and implicit schemes, running on thousands of cores. In order to demonstrate the flexibility of the proposed strategy under advance algorithmic evolution of computational mechanics, a non-local parallel overset meshes method (Chimera-like) is implemented and the conservation of the scalability is demonstrated., D.D.T and A.J acknowledge funding through SIMUCOMP and ERA-NET MATERA+ project financed by the Consejería de Educación y Empleo of the Comunidad de Madrid and by the European Union’s Seventh Framework Programme (FP7/2007-2013). Thisworkwas partially supported by the grant SEV-2011-00067, Severo Ochoa Program, awarded by the Spanish Government. The authors’ would like to acknowledge PRACE infrastructure support., Peer Reviewed, Postprint (published version)