Savvas P. Triantafyllou

A novel Material Point Method (MPM) is introduced for addressing contact problems. In contrast to the standard multi‐velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised boundaries of their respective physical domains. This enhances simulation fidelity by accurately considering the deformability of the contact surface and preventing fictitious gaps between bodies in contact. Additionally, the method utilises the Extended B‐Splines (EBSs) domain approximation, providing two key advantages. First, EBSs robustly mitigate grid cell‐crossing errors by offering continuous gradients of the basis functions on the interface between adjacent grid cells. Second, numerical integration errors are minimised, even with small physical domains in occupied grid cells. The proposed method's robustness and accuracy are evaluated through benchmarks, including comparisons with analytical solutions, other state‐of‐the‐art MPM‐based contact algorithms, and experimental observations from the literature. Notably, the method demonstrates effective mitigation of stress errors inherent in contact simulations.

An approximate efficient stochastic dynamics technique is developed for determining response statistics of linear systems with frequency-dependent parameters, which are used for modeling wave propagation through rigid porous media subject to stochastic excitation. This is done in conjunction with a filter approximation of the system frequency response function. The technique exhibits the following advantages compared to alternative solution treatments in the literature. First, relying on an input–output relationship in the frequency domain, the response power spectrum matrix is integrated analytically for determining the stationary response covariance matrix, at zero computational cost. Second, the proposed filter approximation facilitates a state-variable formulation of the governing stochastic differential equations in the time domain. This yields a coupled system of deterministic differential equations to be solved numerically for the response covariance matrix. Thus, the nonstationary (transient) response covariance can be computed in the time domain at a relatively low computational cost. Various numerical examples are considered for demonstrating the accuracy and computational efficiency of the herein developed technique. Comparisons with pertinent Monte Carlo simulation (MCS) data are included as well.

The effectiveness of textile-reinforced mortar (TRM) strengthening of masonry walls largely depends on the bond between the constituent materials. Finite element analysis (FEA) can provide valuable insights on the effect of the parameters affecting the bond; however, detailed FEA is computationally intensive. To alleviate this, we develop novel empirical equations to estimate effective textile fibre properties, thus implicitly accounting for yarn and mortar debonding. As a result, 3D finite element simulations of strengthened wall specimens are simplified and accelerated. The proposed scheme is calibrated using load–displacement paths derived from experimental data, and the simulated failure modes are compared against the experimental ones demonstrating perfect agreement. A parametric analysis is conducted, exploring the impact of the mechanical ratio of TRM reinforcement and the axial wall load on the effectiveness of TRM strengthening. We demonstrate that low values of mechanical reinforcement, corresponding to natural fibres, give rise to an 8-fold increase in the capacity of unreinforced walls. The findings draw conclusions about the efficacy of TRM strengthening in masonry structures, and provide valuable insights for optimising TRM reinforcement, considering different fibre materials and axial loads in masonry structures.

We introduce a novel heterogeneous multi‐scale method for the frequency response analysis of waves propagating in porous domains with a complex micro‐structure. In this, the domain is decomposed onto polygonal coarse elements each clustering its local micro‐structure. The micro‐structure is resolved using the virtual element method hence providing ample flexibility into capturing fine scale heterogeneities of arbitrary polygonal shapes. The upscaling is performed through a set of numerically evaluated multi‐scale basis functions. Rather than evaluating the basis for a broad band set of frequencies, a reduced order modeling approach is opted for. In this, the basis is evaluated for a select subset of frequencies, that is used as a basis for the evaluation of the remaining set through a proper orthogonal decomposition procedure. The solution of the coupled governing equations is then performed at the coarse‐scale at a reduced computational cost. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples for poro‐elastic materials with heterogeneities of various shapes.