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The material characterization of ultra-thin solid sheets, including two-dimensional materials like graphene, is often performed through indentation tests on a flake suspended over a hole in a substrate. While this `suspended indentation' is…
We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evolution, as the size of the layers vanishes. The limit…
A crucial challenge in engineering modern, integrated systems is to produce robust designs. Ensuring robust design is difficult because subsystem couplings produce unpredictable response to changes in whole system specifications. Here, we…
In this paper, we investigate some micromechanical aspects of elasto-plasticity in heterogeneous geomaterials. The aim is to upscale the elasto-plastic behavior for a representative volume of the material which is indeed a very challenging…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
The paper deals with the inverse problem of determining a polyhedral inclusion compactly contained in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and…
We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and…
Contact involving soft materials often combines dry adhesion, sliding friction, and large deformations. At the local level, these three aspects are rarely captured simultaneously, but included in the theoretical models by Mergel et al.…
Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We…
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…
Theoretical calculations of the elastic response of carbon composites and amorphous carbon are reported. The studied composites consist of crystalline nanoinclusions, either spherical diamonds or carbon nanotubes, embedded in amorphous…
An elastic cloak hides a hole or an inhomogeneity from elastic fields. In this paper, a formulation of the optimal design of elastic cloaks based on the adjoint state method, in which the balance of linear momentum is enforced as a…
Living organisms intertwine soft (e.g., muscle) and hard (e.g., bones) materials, giving them an intrinsic flexibility and resiliency often lacking in conventional rigid robots. The emerging field of soft robotics seeks to harness these…
The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. While the influence of…
The problem of the observable equilibrium domain structure in pure antiferromagnets (and other thermoelastics) is investigated with the use of continuous elasticity theory. It is shown that completely rigid surface produces the imaginary…
We propose an effective permittivity model to homogenize an array of long thin epsilon-negative rods arranged in a periodic lattice. It is proved that the effect of spatial dispersion in this electromagnetic crystal cannot be neglected, and…
In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of…
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance…
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…
An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by…