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The impulse imparted by a blast wave to a freestanding solid plate is studied analytically and numerically focusing on the case in which nonlinear compressibility effects in the fluid are important, as is the case for explosions in air. The analysis furnishes, in effect, an extension of Taylor’s pioneering contribution to the understanding of the influence of fluid-structure interaction (FSI) on the blast loading of structures [The Scientific Papers of Sir Geoffrey Ingram Taylor, edited by G. K. Batchelor (Cambridge University Press, Cambridge, 1963), Vol. III, pp. 287–303] to the nonlinear range. The limiting cases of extremely heavy and extremely light plates are explored analytically for arbitrary blast intensity, from where it is concluded that a modified nondimensional parameter representing the mass of compressed fluid relative to the mass of the plate governs the FSI. The intermediate asymptotic FSI regime is studied using a numerical method based on a Lagrangian formulation of the Euler equations of compressible flow and conventional shock-capturing techniques. Based on the analytical and numerical results, an approximate formula describing the entire range of relevant FSI conditions is proposed. The main conclusion of this work is that nonlinear fluid compressibility further enhances the beneficial effects of FSI in reducing the impulse transmitted to the structure. More specifically, it is found that transmitted impulse reductions due to FSI when compared to those obtained ignoring FSI effects are more significant than in the acoustic limit. This result can be advantageously exploited in the design and optimization of structures with increased blast resistance.

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires the identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of matching mesh condition on opposite RVE boundaries.

A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discontinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the reinstatement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces.The main advantage of the method is that it avoids the need to propagate topological changes in the mesh as cracks and fragments develop, which enables the Preprint submitted to Elsevier Science 16 August 2010indistinctive treatment of crack propagation across processor boundaries and, thus, the scalability in parallel computations. Another advantage of the method is that it preserves consistency and stability in the uncracked interfaces, thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches.A simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process. We also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries.

SUMMARYA discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non-linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided.

This paper presents an incremental secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to define the Linear-Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.

SUMMARYAn explicit-dynamics spatially discontinuous Galerkin (DG) formulation for non-linear solid dynamics is proposed and implemented for parallel computation. DG methods have particular appeal in problems involving complex material response, e.g. non-local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi-discrete system of ordinary differential equations is integrated in time using a conventional second-order central-difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress-wave propagation and large plastic deformations.

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