arXiv subjects

Mohammad Sarhil

Publications and source records attributed to Mohammad Sarhil.

6 recordsLinked to original sources

arXiv2026

Breaking Scale Separation in Metamaterials' homogenization: Interface-Inertia-Enhanced Relaxed Micromorphic Model

Homogenized continuum models are widely used to describe wave propagation and band-gap behavior in mechanical metamaterials without explicitly resolving their microstructure. Their validity, however, typically relies on the classical separation of scales assumption, according to which the wavelength of the propagating disturbance is much larger than the characteristic size of the unit cell. In finite-size metamaterial samples and at higher frequencies, this assumption progressively breaks down, and the dynamic response becomes strongly influenced by the way the microstructure is truncated at the external boundaries. In this work we introduce a fundamentally new concept in the homogenized description of mechanical metamaterials: the inertial contribution of macroscopic interfaces. We show that different truncations of the same lattice generate boundaries with distinct mass distributions, which lead to measurable differences in the dynamic response of finite-sized specimens. To capture this complex mechanism in a homogenized framework, we extend the relaxed micromorphic model by introducing a kinetic surface energy defined on the boundary of the considered body. This generates an additional inertial term in the boundary conditions that can be seen as the homogenized counterpart of the interface inertia produced by the truncation of the microstructure. As a result, the homogenized model can now distinguish between finite-sized specimens that share identical bulk properties but differ only in the configuration of their interfaces. The proposed formulation preserves the variational structure of the relaxed micromorphic model while enabling the continuum to reproduce boundary-dependent responses observed in fully resolved simulations, particularly in frequency regimes ....... See the PDF for the full abstract.

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arXiv2025

Static size-effects meet the dynamic scattering properties of finite-sized mechanical metamaterials: a relaxed micromorphic study with parameter identification via two-stage static-dynamic optimization

Mechanical metamaterials exhibit size-effects when a few unit-cells are subjected to static loading because no clear micro-macro scale separation holds and the characteristic length of the deformation becomes comparable to the unit-cell size. These size-effects typically manifest themselves as a strengthening of the response in a form summarized as "smaller is stiffer". Moreover, the dynamical behavior of mechanical metamaterials is very remarkable, featuring unique phenomena such as dispersive behavior and band-gaps where elastic waves cannot propagate over specific frequency ranges. In these frequency ranges, the wavelength becomes gradually comparable to the unit-cell size, giving rise to microstructure related phenomena which become particularly visible in the reflection/transmission patterns where an incident wave hits the metamaterial's interfaces. This raises the question of whether the static size-effects and dynamic reflection/transmission patterns are correlated. In this work, we investigate the interaction of the static size-effects and the dynamic scattering response of mechanical metamaterials by employing the relaxed micromorphic model. We introduce a two-stage optimization procedure to identify the material parameters. In the first stage, the static material parameters are identified by exploiting the static size-effects through a least squares fitting procedure based on the total energy. The dynamic parameters are determined in the second stage by fitting the dispersion curves of the relaxed micromorphic model to those of the fully discretized microstructure. At this second stage, we assess the results obtained by fitting the dispersion curves in one and in two propagation directions, for both the relaxed micromorphic model (RMM) with curvature and its reduced counterpart (RRMM) without curvature. The full abstract is presented in the paper.

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arXiv2025

Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces

To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in obtaining the mechanical driving forces of phase-field evolution. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields associated to their pairwise normals, except in the dual-phase-field regions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces as a function of pairwise strains. These ad hoc pairwise definitions enable us to satisfy the static equilibrium and kinematic compatibility conditions between all the locally-active phase-fields. Different numerical examples are presented, which compare the developed model against the equal-strain and equal-stress limiting cases.

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arXiv2024

A computational approach to identify the material parameters of the relaxed micromorphic model

We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squares fitting of the total energy of the relaxed micromorphic homogeneous continuum to the total energy of the fully-resolved heterogeneous microstructure, governed by classical linear elasticity. The relaxed micromorphic model is a generalized continuum that utilizes the $\Curl$ of a micro-distortion field instead of its full gradient as in the classical micromorphic theory, leading to several advantages and differences. The most crucial advantage is that it operates between two well-defined scales. These scales are determined by linear elasticity with microscopic and macroscopic elasticity tensors, which respectively bound the stiffness of the relaxed micromorphic continuum from above and below. While the macroscopic elasticity tensor is established a priori through standard periodic first-order homogenization, the microscopic elasticity tensor remains to be determined. Additionally, the characteristic length parameter, associated with curvature measurement, controls the transition between the micro- and macro-scales. Both the microscopic elasticity tensor and the characteristic length parameter are here determined using a computational approach based on the least squares fitting of energies. This process involves the consideration of an adequate number of quadratic deformation modes and different specimen sizes. We conduct a comparative analysis between the least square fitting results of the relaxed micromorphic model, the fitting of a skew-symmetric micro-distortion field (Cosserat-micropolar model), and the fitting of the classical micromorphic model with two different formulations for the curvature...

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arXiv2023

Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model

In this paper we model the size-effects of metamaterial beams under bending with the aid of the relaxed micromorphic continuum. We analyze first the size-dependent bending stiffness of heterogeneous fully discretized metamaterial beams subjected to pure bending loads. Two equivalent loading schemes are introduced which lead to a constant moment along the beam length with no shear force. The relaxed micromorphic model is employed then to retrieve the size-effects. We present a procedure for the determination of the material parameters of the relaxed micromorphic model based on the fact that the model operates between two well-defined scales. These scales are given by linear elasticity with micro and macro elasticity tensors which bound the relaxed micromorphic continuum from above and below, respectively. The micro elasticity tensor is specified as the maximum possible stiffness that is exhibited by the assumed metamaterial while the macro elasticity tensor is given by standard periodic first-order homogenization. For the identification of the micro elasticity tensor, two different approaches are shown which rely on affine and non-affine Dirichlet boundary conditions of candidate unit cell variants with the possible stiffest response. The consistent coupling condition is shown to allow the model to act on the whole intended range between macro and micro elasticity tensors for both loading cases. We fit the relaxed micromorphic model against the fully resolved metamaterial solution by controlling the curvature magnitude after linking it with the specimen's size. The obtained parameters of the relaxed micromorphic model are tested for two additional loading scenarios.

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arXiv2021

Lagrange and $H(\operatorname{curl},{\cal B})$ based Finite Element formulations for the relaxed micromorphic model

Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model has shown many advantages in this field. In this contribution, we present the significant aspects related to the relaxed micromorphic model realization with the finite element method. The variational problem is derived and different FEM-formulations for the two-dimensional case are presented. These are a nodal standard formulation $H^1({\cal B}) \times H^1({\cal B})$ and a nodal-edge formulation $H^1({\cal B}) \times H(\operatorname{curl}, {\cal B})$, where the latter employs the Nédélec space. However, the implementation of higher-order Nédélec elements is not trivial and requires some technicalities which are demonstrated. We discuss the convergence behavior of Lagrange-type and tangential-conforming finite element discretizations. Moreover, we analyze the characteristic length effect on the different components of the model and reveal how the size-effect property is captured via this characteristic length.

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