arXiv subjects

Renald Brenner

Publications and source records attributed to Renald Brenner.

3 recordsLinked to original sources

arXiv2026

Symmetries of (quasi)periodic materials: Superposability vs. Indistinguishability

This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and is defined in terms of the spatial autocorrelation functions of the material under consideration. By using the representation of these autocorrelation functions in Fourier space, the space groups of both periodic and quasiperiodic materials can be obtained. In this context, an image processing methodology is proposed to identify the key characteristics of a material's space group (i.e its point group and its symmorphism) directly from the Fourier transform of the mesostructure. The method is validated on synthetic two-dimensional images of (quasi)periodic architectured materials and it is pointed out, as an illustrative example, that the rotational symmetry of the classical Penrose tiling is of order ten.

math-ph↗

arXiv2025

Evolution of the contact between rough viscoelastic solids after decreasing loads: memory erasure and monotonic increase

The real area of contact governs, in part, the magnitude of the friction force, yet its time evolution in rough viscoelastic interfaces remains incompletely understood. In experiments of contact between polymethylmethacrylate blocks under decreasing normal loads, Dillavou and Rubinstein have shown that the true contact area exhibits, after unloading, a decreasing phase and long-term memory of the contact state prior to unloading. It is however unclear what modeling ingredients are necessary to reproduce these two features. Here, we investigate these effects using fractional viscoelastic rough contact models. By adapting existing contact theories and numerical simulation methods to fractional viscoelasticity, which induces a wide relaxation spectrum, we reproduce logarithmic aging under constant load, but show that memory of the contact state is erased upon unloading. Indeed, the contact area behaves as if it had always experienced the reduced load, even on short time-scales, contrasting with the response of a standard linear solid. Moreover, none of our results show a decreasing regime of the contact area after unload: we ultimately prove that this is the case for all linear viscoelastic models -- despite capturing logarithmic aging -- leading to the conclusion that additional local internal variables are required to explain both long-term contact memory and contact area reduction after unloading.

cond-mat.soft↗

arXiv2019

Numerical simulation of model problems in plasticity based on field dislocation mechanics

The aim of this paper is to investigate the numerical implementation of the Field Dislocation Mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al., 2014). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.

cs.CE↗