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This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
The application of hybrid composites in lightweight engineering enables the combination of material-specific advantages of fiber-reinforced polymers and classical metals. The interface between the connected materials is of particular…
The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of…
In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…
We investigate numerically the yielding transition of a two dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, that we derive from the full (tensorial) description of…
The mechanical properties of metal matrix fiber-reinforced composites depend on many aspects of their structure in a complicated way. In this paper, we propose a \emph{minimalistic} approach to study interface debonding, matrix cracking,…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to…
In this study, we present a finite element solver for a thermodynamically consistent electrolyte model that accurately captures multicomponent ionic transport by incorporating key physical phenomena such as steric effects, solvation, and…
Open boundary conditions are always used in investigating the effective properties of composites. In this paper, Eshelby's transformation field method is developed to deal with the effective response of unidirectional periodic composites…
We investigate linear theories of incompatible micromorphic elasticity, incompatible microstretch elasticity, incompatible micropolar elasticity and the incompatible dilatation theory of elasticity (elasticity with voids). The…
In this article, convex optimization is introduced as a promising tool to study Eshelby based inverse micromechanics problems. The focus is on inverse micromechanics using the Eshelby-Mori-Tanaka model given the dielectric constants of the…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
A primitive problem of predicting the effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method is developed to solve the open boundary problem of two-phase composites having…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…