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We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…

Disordered Systems and Neural Networks · Physics 2019-05-22 Paolo Moretti , Jakob Renner , Ali Safari , Michael Zaiser

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…

Soft Condensed Matter · Physics 2022-06-08 Yohai Bar-Sinai , Gabriele Librandi , Katia Bertoldi , Michael Moshe

We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e…

Statistical Mechanics · Physics 2009-11-07 Felipe Barra , H. George E. Hentschel , Anders Levermann , Itamar Procaccia

The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the…

Materials Science · Physics 2015-06-24 D. Sornette

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in…

Materials Science · Physics 2026-04-29 Sarvesh Joshi , Jingye Tan , Craig M. Hamel , Stavros Gaitanaros , Nikolaos Bouklas

We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…

In this paper, a novel hybrid FEM and Peridynamic modeling approach proposed in Ni et al. (2020) is used to predict the dynamic solution of hydro-mechanical coupled problems. A modified staggered solution algorithm is adopted to solve the…

Numerical Analysis · Mathematics 2023-07-24 Tao Ni , Francesco Pesavento , Mirco Zaccariotto , Ugo Galvanetto , Bernhard A. Schrefler

Machine learning techniques have been widely employed as effective tools in addressing various engineering challenges in recent years, particularly for the challenging task of microstructure-informed materials modeling. This work provides a…

Materials Science · Physics 2024-05-29 Xiang-Long Peng , Mozhdeh Fathidoost , Binbin Lin , Yangyiwei Yang , Bai-Xiang Xu

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…

Mathematical Physics · Physics 2015-10-28 Tomas Roubicek , Giuseppe Tomassetti

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…

Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…

Mesoscale and Nanoscale Physics · Physics 2014-03-31 V. I. Yukalov , E. P. Yukalova

Synthesis remains a challenge for advancing materials science. A key focus of this challenge is how to enable selective synthesis, particularly as it pertains to metastable materials. This perspective addresses the question: how can…

Materials Science · Physics 2023-06-14 James R Neilson , Matthew J McDermott , Kristin A Persson

The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive…

Optics · Physics 2024-07-08 P. Lalanne , A. Dmitriev , C. Rockstuhl , A. Sprafke , K. Vynck

Disordered hyperuniform (DHU) materials are an emerging class of exotic heterogeneous material systems characterized by a unique combination of disordered local structures and a hidden long-range order, which endow them with unusual…

Materials Science · Physics 2025-04-11 Liyu Zhong , Sheng Mao , Yang Jiao

Amorphous materials are solids that lack long-range atomic order but possess complex short- and medium-range order. Unlike crystalline materials that can be described by unit cells containing few up to hundreds of atoms, amorphous materials…

Machine Learning · Computer Science 2026-04-01 Yan Lin , Jonas A. Finkler , Tao Du , Jilin Hu , Morten M. Smedskjaer

We use machine learning methods on local structure to identify flow defects - or regions susceptible to rearrangement - in jammed and glassy systems. We apply this method successfully to two disparate systems: a two dimensional experimental…

For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…

Computational Physics · Physics 2026-05-13 Arnaud Vadeboncoeur , Mark Girolami , Kaushik Bhattacharya , Andrew M. Stuart

Quantifying the relationship between geometric descriptors of microstructure and effective properties like permeability is essential for understanding and improving the behavior of porous materials. In this paper, we employ a previously…

Materials Science · Physics 2023-11-27 Matthias Weber , Andreas Grießer , Dennis Mosbach , Erik Glatt , Andreas Wiegmann , Volker Schmidt

This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based…

Computational Engineering, Finance, and Science · Computer Science 2022-09-21 Kai Friebertshäuser , Christian Wieners , Kerstin Weinberg

Dynamic shearing banding and fracturing in unsaturated porous media is a significant problem in engineering and science. This article proposes a multiphase micro-periporomechanics (uPPM) paradigm for modeling dynamic shear banding and…

Numerical Analysis · Mathematics 2024-01-10 Hossein Pashazad , Xiaoyu Song