A formal hierarchy of exact evolution equations are derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to expose the intractable complexity of such systems of nonlinear partial differential equations that, furthermore, remain `non-closed,' and therefore subject to phenomenological

The model-free distance-minimizing data-driven computational method has recently become a novel paradigm for solving various mechanics problems. However, the paradigm may suffer from low efficiency since tremendous iterative searches of key data points in the material dataset are needed during the solution process. A fast data-driven solver is therefore proposed here for the accurate and efficient

The present work investigates the thermodynamic inconsistencies in the definition of compatibility conditions on stress for constant and non-constant material functions in one-dimensional modelling of shape-memory alloys based on the first principles. In this part II of the work simplifications are provided validating inconsistencies in the earlier proposed non-constant material functions used to satisfy

A general method, based on a multi-scale approach, is proposed to derive the effective elastic shear modulus of a rubber with 14\% of carbon black fillers from finite element (FE) and fast Fourier transform (FFT) methods. The complex multi-scale microstructure of such material was generated numerically from a mathematical model of its morphology which was identified from statistical moments out of

In the field of nanomedicine, there is a pressing need for predictive, quantitative tools to rationally design and optimize carriers for therapeutic and imaging applications. Current nano/microfabrication technologies allow us to control a large number of parameters, including the size, shape surface properties, and mechanical stiffness. These design parameters affect the biophysical behavior of nanomedicines

Heterogeneous media with several spatial scales are often found in heat transfer applications. For instance, two-phase nanofluids made of nanoparticles immersed in a fluid containing both individual particles and clusters, which exhibit at least three structural scales, have shown improved thermal conductivity over the individual constituents. In this work, a problem for the Fourier heat equation with

Microtomography images allow obtaining fully detailed microstructural descriptions of heterogeneous materials and structures. To evaluate the effects of local gradients induced by the boundary conditions, it might be of interest to perform direct numerical simulations (DNS) of such structures. In this paper, a multiscale method is developed to perform DNS on large, nonperiodic linear heterogeneous

We write to introduce our novel group formed to confront some of the issues raised by the COVID-19 pandemic. Information about the group, which we named "cure COVid for Ever and for All" (RxCOVEA), its dynamic membership (changing regularly), and some of its activities−described in more technical detail for expert perusal and commentary−are available upon request.

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify