Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

A set of three-dimensional failure criteria for laminated fiber-reinforced composites, denoted LaRC04, is proposed. The criteria are based on physical models for each failure mode and take into consideration non-linear matrix shear behaviour. The model for matrix compressive failure is based on the Mohr-Coulomb criterion and it predicts the fracture angle. Fiber kinking is triggered by an initial fiber misalignment angle and by the rotation of the fibers during compressive loading. The plane of fiber kinking is predicted by the model. LaRC04 consists of 6 expressions that can be used directly for design purposes. Several applications involving a broad range of load combinations are presented and compared to experimental data and other existing criteria. Predictions using LaRC04 correlate well with the experimental data, arguably better than most existing criteria. The good correlation seems to be attributable to the physical soundness of the underlying failure models.

https://ntrs.nasa.gov/api/citations/20050110223/downloads/20050110223.pdf

Failure Models and Criteria for Frp Under In-Plane or Three-Dimensional Stress States Including Shear Non-Linearity

Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.

/pdf/predicting-low-velocity-impact-damage-and-compression-after-3hwg4r1jq5.pdf

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.

Refined beam theories based on a unified formulation

Recent developments on damage modeling and finite element analysis for composite laminates: A review

https://oatao.univ-toulouse.fr/6769/1/Rivallant_6769.pdf

Low velocity impact modeling in composite laminates capturing permanent indentation

https://oatao.univ-toulouse.fr/2989/1/Bouvet_2989.pdf

Impact and compression after impact experimental study of a composite laminate with a cork thermal shield

In the aeronautical field, sandwich structures are widely used for secondary structures like flaps or landing gear doors. The modeling of low velocity/low energy impact, which can lead to a decrease of the structure strength by 50%, remains a designer’s main problem. Since this type of impact has the same effect as quasi-static indentation, the study focuses on the behavior of honeycomb cores under compression. The crushing phenomenon has been well identified for years but its mechanism is not described explicitly and the model proposed may not satisfy industrial purposes. To understand the crushing mechanism, honeycomb test specimens made of Nomex™, aluminum alloy and paper were tested. During the crushing, a CCD camera showed that the cell walls buckled very quickly. The peak load recorded during tests corresponded to the buckling of the common edge of three honeycomb cells. Further tests on corner structures to simulate only one vertical edge of a honeycomb cell show a similar behavior. The different specimens exhibited similar load/displacement curves and the differences observed were only due to the behavior of the different materials. As a conclusion of this phenomenological study, the hypothesis that loads are mainly taken by the vertical edge can be made. So, a honeycomb core subjected to compression can be modeled by a grid of nonlinear springs. A simple analytical model was then developed and validated by tests on Nomex™ honeycomb core indented by different sized spherical indenters. A good correlation between theory and experiment was found. This result can be used to satisfactorily model using finite elements the indentation on a sandwich structure with a metallic or composite skin and honeycomb core.

Experimental Analysis and Modeling of the Crushing of Honeycomb Cores

https://hal.archives-ouvertes.fr/hal-00499100/document

Modelling of low-energy/low-velocity impact on Nomex honeycomb sandwich structures with metallic skins

https://hal.archives-ouvertes.fr/hal-00933459/document

Jean-Jacques Barrau

Papers

Low velocity impact modeling in composite laminates capturing permanent indentation

Impact and compression after impact experimental study of a composite laminate with a cork thermal shield

Experimental Analysis and Modeling of the Crushing of Honeycomb Cores

Modelling of low-energy/low-velocity impact on Nomex honeycomb sandwich structures with metallic skins

Experimental analysis of CFRP laminates subjected to compression after impact: The role of impact-induced cracks in failure