Umberto Perego

Numerical aspects of nonlocal damage analyses

ABSTRACT Constitutive models based on nonlocal variables provide an effective and mechanically sound solution to the ill-posedness of the boundary value problem in the presence of damage induced softening. However, the averaging of constitutive variables entails other computational problems like the lack of symmetry of the tangent operator in a finite element approximation. In the present paper, an isotropic local damage model with symmetric tangent matrix is presented. Two alternative nonlocal versions of the same model are comparatively discussed. It is shown how the symmetry of the tangent matrix in the finite element approximation can be preserved formulating the nonlocal model within the context of the thermodynamic nonlocal theory recently proposed by Borirlo et al. The computational implications of the adopted regularization technique are discussed by means of a simple one-dimensional example.

The complete works of Gabrio Piola: Volume I

Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commentedPiolas work and compared it to modern theories in mechanics in order to stress Piolas impact on modern science and proofs that he has set milestones in applied mathematics.This book presents Piolas original Italian text together with ist translations and their comments. It shows impressively that Gabrio Piolas work must still be regarded as a modern theory.

Anisotropic Damage Model for Concrete Affected by Alkali-Aggregate Reaction

An anisotropic two-phase coupled chemo-thermo-damage model is proposed, for the simulation of the behavior of concrete affected by the alkali-aggregate reaction, which may create significant damage in existing concrete structures. The chemical reaction produces a gel expanding in the concrete pores, leading to macroscopic strength and stiffness deterioration in the concrete skeleton. The model is capable to account for the anisotropic damage development and consequent directional degradation of material properties. The model is validated against experimental tests taken from the literature.

A variationally consistent generalized variable formulation for enhanced strain finite elements

The so-called enhanced strain finite elements are based on the enrichment of the standard compatible strain field by the introduction of additional, non-compatible strains. This class of elements can be derived starting from a partial Hu–Washizu variational principle. However, since in the original enhanced strain formulation the stress field is eliminated from the formulation, a separate least-squares procedure had to be implemented for a variational derivation of the stress field. A three-field generalized variable approach incorporating strain enhancement is proposed in the present paper within the context of linear elastic structural problems. It is shown how the original two-field enhanced strain method can be naturally recovered by suitably choosing the strain model. For this case a straightforward, but still variationally consistent stress recovery is proposed. Copyright

Plastic Analysis by Boundary Elements

In the traditional context of small deformation, quasti-static plasticity, we can distinguish the following kinds of problems (for details, see e.g. refs. [1] [2]).

Explicit simulation of forming processes using a novel solid-shell concept based on reduced integration

The contribution deals with the simulation of sheet metal forming processes by means of a recently developed hexahedral solid-shell finite element. In contrast to this earlier work, we pursue here explicit integration. The element formulation has the following features. In order to avoid undesired effects of locking an enhanced assumed strain (EAS) concept using only one EAS degree-of-freedom has been implemented. In addition, by means of the assumed natural strain (ANS) method an excellent performance in bending situations is obtained. A key point of the element formulation is the construction of the hourglass stabilization by means of different Taylor expansions. This procedure leads to the important advantage that the sensitivity of the results with respect to mesh distortion is noticeably reduced. Further the hourglass stabilization is in this way designed that locking is eliminated and numerical stability guaranteed. The finite strain material model for plastic anisotropy and non-linear kinematic and isotropic hardening is motivated by a rheological model including Armstrong-Frederick kinematic hardening. The element formulation has been implemented into the academic code FEAP. Some standard benchmark examples are computed.

Finite element simulation of crack propagation and delamination in layered shells due to blade cutting

This work is focused on some computational issues concerning the simulation of blade cutting of thin walled structures. In comparison to plain crack propagation problems, the presence of the blade brings in additional complexity, mainly due to the interaction between the blade and the material in the crack process zone. The blade sharpness introduces in the problem an extremely small geometrical scale (orders of magnitude smaller than a typical element in-plane size) that is here resolved using the so called directional cohesive elements, recently proposed in [6, 12]. A special feature of this type of problems is that the crack path is driven by the blade trajectory, which is prescribed and hence known in advance. Crack propagation is therefore modeled by adjusting the mesh in such a way that shell element edges are disposed along the expected main crack path and then by interposing directional cohesive elements between the sides of separating elements. The transition from a continuous mesh to a mesh containing a crack with a cohesive interface is well known to be critical for the solution accuracy. Nodal equilibrium is in general violated during the transition, with subsequent generation of spurious stress oscillations that, in view of the non-reversible nature of the problem, can lead to significant deviations in the stress response. This aspect is investigated in this contribution. The effect of the number of introduced directional cohesive elements per opening face is critically assessed and a simple correction, based on an automatic adaptation of the cohesive model, is proposed. Numerical tests taken from the literature are used to validate the proposed approach.

A LAGRANGIAN PFEM APPROACH TO THE NUMERICAL SIMULATION OF 3D LARGE SCALE LANDSLIDES IMPINGING IN WATER RESERVOIRS

Landslides are exceptional natural hazards that can generate extensive damage to structures and infrastructures causing a large number of casualties. A particularly critical condition occurs when the landslide impinges in water reservoirs generating high waves. This work proposes a numerical tool to simulate the macroscopic behavior of a propagating landslide. The Particle Finite Element Method (PFEM) is here used and adapted to the specific case of landslide runout. The Lagrangian Navier-Stokes equations of incompressible fluids are used to describe the macroscopic landslide behavior. A rigid-visco-plastic law with a pressure dependent threshold, typical of a non-Newtonian, Bingham-like fluid, is used to characterize the constitutive behavior of the flowing material. Special attention is devoted to the definition of ad-hoc pressure-dependent slip boundary conditions at the interface between the flowing mass and the basal surface to better represent the real landslide-slope interaction. The proposed approach has been validated against numerical benchmarks and small scale experimental tests, showing a good agreement with the physical measurements. Real case scenarios have also been considered. 3D geometries of critical sites, where landslides have occurred, have been reconstructed allowing for the simulation of large scale real landslide runouts. Results are compared with post-event images and measurements, showing the accuracy and the capability of the method.