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The paper deals with a nonlinear evolution equation describing the dynamics of a non homogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
This paper addresses the dynamics of locally-resonant sandwich beams, where multi-degree-of-freedom viscously-damped resonators are periodically distributed within the core matrix. Using an equivalent single-layer Timoshenko beam model…
Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized…
The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational…
Stress tensors are derived for the multiparticle collision dynamics algorithm, a particle-based mesoscale simulation method for fluctuating fluids, resembling those of atomistic or molecular systems. Systems with periodic boundary…
Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…
We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…
Existing smart composite piezoelectric beam models in the literature mostly ignore the electro-magnetic interactions and adopt the linear elasticity theory. However, these interactions substantially change the controllability and…
This paper develops a general data-driven approach to stochastic elastoplastic modelling that leverages atomistic simulation data directly rather than by fitting parameters. The approach is developed in the context of metallic glasses,…
This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out…
This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…
In the past fifteen years, flow instabilities reminiscent of the Taylor-like instabilities driven by hoop stresses, have been observed in wormlike micelles based on surfactant molecules. In particular, purely elastic instabilities and…
We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…
The elastoplastic behavior of a two-phase stainless steel alloy is explored at the crystal scale for five levels of stress biaxiality. The crystal lattice (elastic) strains were measured with neutron diffraction using tubular samples…
The classical flexure problem of non-linear incompressible elasticity is revisited for elastic materials whose mechanical response is different in tension and compression---the so-called bimodular materials. The flexure problem is chosen to…
We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…
Fluid phase equilibria involving nano-dispersed phases, where at least one of the coexisting phases is confined to a small volume, are investigated by molecular dynamics simulation. Complementing previous studies on nanoscopic droplets,…