Strength properties of nanoporous materials: molecular dynamics computations and theoretical analysis

Since the recent arising of advanced nano-technologies, as well as of innovative engineering design approaches, nanoporous materials have been extensively studied in the last two decades, leading to a considerable worldwide research interest in both industrial and academic domains. Generally characterised by high specific surface area, uniform pore size and rich surface chemistry, nanoporous materials have allowed for the development of challenging ultra-high performance devices with tailorable properties, finding widespread application in several technical fields, including civil and environmental engineering, petroleum and chemical industries, biomechanics, molecular sieving and sensoring. In order to fulfil to these promising applications, one of the most fundamental research aspect consists in characterising and predicting the strength properties of these materials, as dependent on the size of voids. Since the current lack of an exhaustive benchmarking evidence, as well as of a comprehensive theoretical modelling, the central purpose of the present paper consists in: -) investigating strength properties of an in-silico nanoporous sample via Molecular Dynamics computations. In detail, a parametric analysis with respect to the void radius and for different porosity levels has been carried out, by considering different loading paths with a wide range of triaxiality scenarios. As a result, the influence of void-size effects on the computed strength properties has been clearly quantified, also highlighting the dependence of the predicted material strength domain on the three stress invariants; -) establishing an engineering-oriented theoretical model able to predict macroscopic strength properties of nanoporous materials, by properly accounting for void-size effects. To this end, a homogenization procedure based on a kinematic limit-analysis is performed addressing a hollow-sphere model comprising a rigid-ideal-plastic solid matrix and undergoing axisymmetric strain-rate boundary conditions. Void-size effects are accounted for by introducing an imperfect-coherent interface at the cavity boundary. Both the interface and the solid matrix are assumed to obey to a simplified form of the general yield function proposed by Bigoni and Piccolroaz [Int J Solids Struct; 41: 2855-2878], thereby allowing for an extreme flexibility in describing triaxiality and Lode-angle effects. A parametric closed-form relationship for the macroscopic strength criterion is obtained as the unique physically-consistent solution of an inequality-constrained minimization problem, the latter being faced via the Lagrangian method combined with Karush-Kuhn-Tucker conditions. Any possible choice of local-yield-function parameters is carefully addressed, by clearly highlighting the effects of a specific local plastic behaviour on the material macroscopic response. Finally, several comparative illustrations are provided, showing the influence of model parameters on the proposed yield function, as well as the model capability to describe the macroscopic strengthening, typical of nanoporous materials, induced by a void-size reduction for a fixed porosity level

Limit analysis and homogenization of nanoporous materials with a general isotropic plastic matrix

In this paper, a closed-form expression of a macroscopic strength criterion for ductile nanoporous materials is established, by considering the local plastic behavior as dependent on all the three isotropic stress invariants and by referring to the case of axisymmetric strain-rate boundary conditions. The proposed criterion also predicts void-size effects on macroscopic strength prop- erties. A homogenization procedure based on a kinematic limit-analysis is performed by addressing a hollow-sphere model comprising a rigid-ideal-plastic solid matrix. Void-size effects are accounted for by introducing an imperfect-coherent interface at the cavity boundary. Both the interface and the solid matrix are assumed to obey to a general isotropic yield function, whose parametric form allows for a significant flexibility in describing effects induced by both stress triaxiality and stress Lode angle. Taking advantage of analytical expressions recently provided by Brach et al. [Int J Plasticity 2017; 89: 1–28] for the corresponding support function and for the exact velocity field under isotropic loadings, a parametric closed-form relationship for the mac- roscopic strength criterion is obtained as the solution of an inequality-constrained minimization problem, the latter being faced via the Lagrangian method combined with Karush-Kuhn-Tucker conditions. Finally, several comparative illustrations are provided, showing the influence of local-yield-function parameters on the established criterion, as well as the model capability to describe the macroscopic strengthening, typical of nanoporous materials, induced by a void-size reduction for a fixed porosity level

Limit analysis and homogenization of nanoporous materials with a general isotropic plastic matrix

In this paper, a closed-form expression of a macroscopic strength criterion for ductile nanoporous materials is established, by considering the local plastic behavior as dependent on all the three isotropic stress invariants and by referring to the case of axisymmetric strain-rate boundary conditions. The proposed criterion also predicts void-size effects on macroscopic strength prop- erties. A homogenization procedure based on a kinematic limit-analysis is performed by addressing a hollow-sphere model comprising a rigid-ideal-plastic solid matrix. Void-size effects are accounted for by introducing an imperfect-coherent interface at the cavity boundary. Both the interface and the solid matrix are assumed to obey to a general isotropic yield function, whose parametric form allows for a significant flexibility in describing effects induced by both stress triaxiality and stress Lode angle. Taking advantage of analytical expressions recently provided by Brach et al. [Int J Plasticity 2017; 89: 1–28] for the corresponding support function and for the exact velocity field under isotropic loadings, a parametric closed-form relationship for the mac- roscopic strength criterion is obtained as the solution of an inequality-constrained minimization problem, the latter being faced via the Lagrangian method combined with Karush-Kuhn-Tucker conditions. Finally, several comparative illustrations are provided, showing the influence of local-yield-function parameters on the established criterion, as well as the model capability to describe the macroscopic strengthening, typical of nanoporous materials, induced by a void-size reduction for a fixed porosity level

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part II: Numerical bounds and assessment of the theoretical model

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Random distribution of polydisperse ellipsoidal inclusions and homogenization estimates for porous elastic materials

International audienceThis work proposes an extension of the well-known random sequential adsorption (RSA) method in the context of non-overlapping random mono-and polydisperse ellipsoidal inclusions. The algorithm is general and can deal with inclusions of different size, shape and orientation with or without periodic geometrical constraints. Specifically, polydisperse inclusions, which can be in terms of different size, shape, orientation or even material properties, allow for larger volume fractions without the need of additional changes in the main algorithm. Unit-cell computations are performed by using either the fast Fourier transformed-based numerical scheme (FFT) or the finite element method (FEM) to estimate the effective elastic properties of voided particulate microstructures. We observe that an isotropic overall response is very difficult to obtain for random distributions of spheroidal inclusions with high aspect ratio. In particular, a substantial increase (or decrease) of the aspect ratio of the voids leads to a markedly anisotropic response of the porous material, which is intrinsic of the RSA construction. The numerical estimates are probed by analytical Hashin-Shtrikman-Willis (HSW) estimates and bounds