A two-level macroscale continuum description with embedded discontinuities for nonlinear analysis of brick/block masonry

A great proportion of the existing architectural heritage, including historical and monumental constructions, is made of brick/block masonry. This material shows a strong anisotropic behaviour resulting from the specific arrangement of units and mortar joints, which renders the accurate simulation of the masonry response a complex task. In general, mesoscale modelling approaches provide realistic predictions due to the explicit representation of the masonry bond characteristics. However, these detailed models are very computationally demanding and mostly unsuitable for practical assessment of large structures. Macroscale models are more efficient, but they require complex calibration procedures to evaluate model material parameters. This paper presents an advanced continuum macroscale model based on a two-scale nonlinear description for masonry material which requires only simple calibration at structural scale. A continuum strain field is considered at the macroscale level, while a 3D distribution of embedded internal layers allows for the anisotropic mesoscale features at the local level. A damage-plasticity constitutive model is employed to mechanically characterise each internal layer using different material properties along the two main directions on the plane of the masonry panel and along its thickness. The accuracy of the proposed macroscale model is assessed considering the response of structural walls previously tested under in-plane and out-of-plane loading and modelled using the more refined mesoscale strategy. The results achieved confirm the significant potential and the ability of the proposed macroscale description for brick/block masonry to provide accurate and efficient response predictions under different monotonic and cyclic loading conditions.

Comment on “Free surface tension in incompressible smoothed particle hydrodynamics (ISPH)” [Comput. Mech. 2020, 65, 487–502]

We comment on a recent article [Comput. Mech. 2020, 65, 487–502] about surface-tension modeling for free-surface flows with Smoothed Particle Hydrodynamics. The authors motivate part of their work related to a novel principal curvature approximation by the wrong claim that the classical curvature formulation in SPH overestimates the curvature in 3D by a factor of 2. In this note we confirm the correctness of the classical formulation and point out the misconception of the commented article.

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.

Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities

This work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.

A mixed u–p edge-based smoothed particle finite element formulation for viscous flow simulations

A mixed u–p edge-based smoothed particle finite element formulation is proposed for computational simulations of viscous flow. In order to improve the accuracy of the standard particle finite element method, edge-based and face-based smoothing operations on the displacement gradient are proposed for 2D and 3D analyses, respectively. Consequently, spatial integration involving the smoothing operator is performed on smoothing domains. The constitutive model is based on an elasto-viscoplastic formulation allowing for simulations of viscous fluid or fluid-like solid materials. The viscous response is modeled using an overstress function. The performance of the proposed edge-based smoothed particle finite element method (ES-PFEM) is demonstrated by several numerical benchmark studies, showing an excellent agreement with analytical and reference solutions and an improved accuracy and computational efficiency in comparison with results from the standard PFEM model. Finally, a numerical application of the ES-PFEM to the computational simulation of the extrusion process during 3D-concrete-printing is discussed.