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A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…

Predicting material properties of disordered systems remains a long-standing and formidable challenge in rational materials design. To address this issue, we introduce an automated software framework capable of modeling partial occupation…

Materials, at their essence, are networks defined by homogeneity: uniform bonds, fixed thicknesses, and discrete length scales. Mechanical metamaterials, while representing structurally more diverse microstructures, remain defined by the…

Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature; diverse biological materials, such as bone, cellulose, and muscle, have as many as ten hierarchical levels. Structural…

In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are…

Interest in layered two dimensional materials, particularly stacked heterostructures of transition metal dichalcogenides, has led to the need for a better understanding of the structural and electronic changes induced by stacking. Here, we…

A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…

Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…

Both the shape of individual particles and their surface properties contribute to the strength of a granular material under shear. Here we show the degree to which these two aspects can be intertwined. In experiments on assemblies of 3D…

Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…

Subjected to compressive stresses, soft polymers with stiffness gradients can display various buckling patterns. These compressive stresses can have different origins, like mechanical forces, temperature changes, or, for hydrogel materials,…

A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape…

Human softness perception in haptics has mainly been studied using mechanically homogeneous objects, despite the fact that many real-world objects exhibit heterogeneous layered structures with nonuniform stiffness. This study examined how…

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…

Prediction of hydrogen embrittlement requires a robust modelling approach and this will foster the safe adoption of hydrogen as a clean energy vector. A generalised computational model for hydrogen embrittlement is here presented, based on…

Growth-induced pattern formations in curved film-substrate structures have attracted extensive attentions recently. In most existing literature, the growth tensor is assumed to be homogeneous or piecewise homogeneous. In this paper, we aim…

This paper investigates the effective categoricity of ultrahomogeneous structures. It is shown that any computable ultrahomogeneous structure is $\Delta^0_2$ categorical. A structure A is said to be weakly ultrahomogeneous if there is a…

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is…