arXiv subjects

Jorge San Martín

Publications and source records attributed to Jorge San Martín.

3 recordsLinked to original sources

arXiv2020

A shear-compression damage model for the simulation of underground mining by block caving

Block caving is an ore extraction technique used in the copper mines of Chile. It uses gravity to ease the breaking of rocks, and to facilitate the extraction from the mine of the resulting mixture of ore and waste. To simulate this extraction process numerically and better understand its impact on the mine environment, we study 3 variational models for damage, based on the gradient damage model of Pham and Marigo (2010). In these models, the damage criterion may exhibit an anisotropic dependence on the spherical and deviatoric parts of the stress tensor. We report simulations that satisfactorily represent the expected evolution of the stress field in a block caving operation.

math.OC↗

arXiv2016

Bloch wave spectral analysis in the class of generalized Hashin-Shtrikman micro-structures

In this paper, we use spectral methods by introducing the Bloch waves to study the homogenization process in the non-periodic class of generalized Hashin-Shtrikman micro-structures \cite[page no. 281]{T}, which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result with providing the spectral representation of the homogenized coefficients. It offers a new lead towards extending the Bloch spectral analysis in the non-periodic, non-commutative class of micro-structures.

math.AP↗

arXiv2016

Dispersion tensor and its unique minimizer in Hashin-Shtrikman micro-structures

In this paper, we introduce the macroscopic quantity, namely the dispersion tensor or the \textit{Burnett coefficient}s in the class of generalized Hashin-Shtrikman micro-structures \cite[page no. 281]{T}. In the case of two-phase materials associated with the periodic Hashin-Shtrikman structures, we settle the issue that the dispersion tensor has an unique minimizer, which is so called Apollonian-Hashin-Shtrikman micro-structure.

math.AP↗