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Strain engineering is widely used in material science to tune the (opto-)electronic properties of materials and enhance the performance of devices. Two-dimensional atomic crystals are a versatile playground to study the influence of strain,…
In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
Knowledge of the state of plastic deformation in metallic structures is vital to prevent failure. This is why non-destructive acoustic tests based on the measurement of first order elastic constants have been developed and intensively used.…
Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pretty good accuracy since the middle of the previous century. In the classical acoustic measurement method the recalculation of instantaneous…
We analyse a problem of two-dimensional linearised elasticity for a two-component periodic composite, where one of the components consists of disjoint soft inclusions embedded in a rigid framework. We consider the case when the contrast…
A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
Dislocations, as topological defects in crystal lattices, are fundamental to understanding plasticity in materials. Similar periodic structures also arise in continuum field theories, such as chiral soliton lattices (CSLs), which appear in…
The experimental observations of many interaction-driven electronic phases in moir\'e superlattices have stimulated intense theoretical and experimental efforts to understand and engineer these correlated physics. Strain is a powerful tool…
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition…
We investigate the elastic properties of selected zincblende III-V semiconductors. Using hybrid functional density functional theory we calculate the second and third order elastic constants, and first and second-order internal strain…
In this paper, we propose a factorization of a fourth-order harmonic tensor into second-order tensors. We obtain moreover explicit equivariant reconstruction formulas, using second-order covariants, for transverse isotropic and orthotropic…
This paper presents a consistent computational framework for multiscale 1st order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. Based on the principle of multiscale virtual…
A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or…
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…
Many geologic materials have a composite structure, in which macroscopic mechanical behavior is determined by the properties, shape, and heterogeneous distribution of individual constituents. In particular, sedimentary rocks commonly…