Computational Mechanics

A new computational framework is introduced for the automated finite element (FE) modeling of fiber reinforced composites and simulating their micromechanical behavior. The proposed methodology relies on a new microstructure reconstruction algorithm that implements the centroidal Voronoi tessellation (CVT) to generate an initial uniform distribution of fibers with desired volume fraction and size distribution in a repeating unit cell of the composite. The genetic algorithm (GA) is then employed to optimize locations of fibers such that they replicate the target spatial arrangement. We also use a non-iterative mesh generation algorithm, named conforming to interface structured adaptive mesh refinement (CISAMR), to create FE models of the CFRPC. The CVT–GA–CISAMR framework is then employed to investigate the appropriate size of the composite’s representative volume element. We also study the strength and failure mechanisms in the CFRPC subject to varying uniaxial and mixed-mode loadings.

Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification.This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial neural network (ANN) for reliable and fast computation of poroelastic model parameters. Based on the strong-form governing equations for the poroelastic problem derived from asymptotic homogenisation, the weighted residuals formulation of the cell problem is obtained. Approximate solution of the resulting linear variational boundary value problem is achieved by means of the finite element method. The advantages and downsides of macroscale properties identification via asymptotic homogenisation and the application of ANN to overcome parameter characterisation challenges caused by the costly solution of cell problems are presented. Numerical examples, in this study, include spatially dependent porosity and solid matrix Poisson ratio for a generic model problem, application in tumour modelling, and utilisation in soil mechanics context which demonstrate the feasibility of the presented framework.

We derive a generalized version of the known system of two simultaneous second order differential equations for the problem of axi-symmetric torsionless deformations of elastic shells of revolution, for finite deformations and including transverse shear deformations and membrane drilling moments. Our generalization, which involves the introduction of a semicomplementary energy density, comes out in a particularly simple and compact form. We furthermore consider the effect of transverse normal stress deformations and discover the possibility of reducing this problem to a system of three simultaneous second order equations, with the supplementary third equation harmoniously adding itself to the two equations without consideration of transverse normal stress deformation effects.

We aim to enhance the stability of finite element models of dynamic structural contact with multiphase granular soils which are described by advanced soil plasticity models that can simulate monotonic and cyclic behaviour of multiphase soils. Often, numerical oscillations cannot be avoided in these contact models and can cause advanced soil models to significantly overshoot stress, leading to unrealistic discontinuities in the stress paths. This situation can challenge the stability of the stress integration scheme and the global finite element solver and lead to the early termination of the analysis. We specifically address the issue of stress overshooting by presenting novel solutions and the corresponding stress integration schemes for a representative soil model for unsaturated granular soils. Also, several examples are provided to evaluate the integration scheme and show the advantages and limitations of the proposed overshooting solutions in solving a contact-impact problem involving unsaturated granular soils.

One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to $$ H ^1$$ , such that standard nodal $$ H ^1$$ -finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces $$ H ^1$$ and $$ H (\mathrm {curl})$$ , demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates.

A temporal multiscale modelling applied to fatigue damage evolution in cortical bone is presented. Microdamage accumulation in cortical bone, ensued from daily activities, leads to impaired mechanical properties, in particular by reducing the bone stiffness and inducing fatigue. However, bone damage is also known as a stimulus to bone remodelling, whose aim is to repair and generate new bone, adapted to its environment. This biological process by removing fatigue damage seems essential to the skeleton lifetime. As daily activities induce high frequency cycles (about 10,000 cycles a day), identifying two-time scale is very fruitful: a fast one connected with the high frequency cyclic loading and a slow one related to a quasi-static loading. A scaling parameter is defined between the intrinsic time (bone lifetime of several years) and the high frequency loading (few seconds). An asymptotic approach allows to decouple the two scales and to take into account history effects (Guennouni and Aubry in CR Acad Sci Paris Ser II 20:1765–1767, 1986). The method is here applied to a simple case of fatigue damage and a real cortical bone microstructure. A significant reduction in the amount of computation time in addition to a small computational error between time homogenized and non homogenized models are obtained. This method seems thus to give new perspectives to assess fatigue damage and, with regard to bone, to give a better understanding of bone remodelling.