Tootfinder

A continued fraction approximation for the effective elasticity tensor of two-dimensional polycrystals as a function of the crystal elasticity tensor
Graeme W. Milton
https://arxiv.org/abs/2510.10297

A continued fraction approximation for the effective elasticity tensor of two-dimensional polycrystals as a function of the crystal elasticity tensor
For two-dimensional polycrystals the effective elasticity tensor $C_*$ as a function $C_*(C_0)$ of the elasticity tensor $C_0$ of the constituent crystal is considered. It is shown that this function can be approximated by one with a continued fraction expansion resembling that associated with a class of microstructure known as sequential laminates. These are hierarchical microstructures defined inductively. Rank 0 sequential laminates are simply rotations of the pure crystal. Rank $j$ sequenti…

Mathematical Modeling of Networks in Strength of Materials
Ioannis Dassios
https://arxiv.org/abs/2510.10132 https://arxiv.org/pdf/2510.10132

Mathematical Modeling of Networks in Strength of Materials
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity, plasticity, and possibly cracking. The goal is to solve this system and understand how the material responds. Students are asked to start with a simple triangle example and then apply the method to larger structures. The final aim is to solve the full system an…

Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
Cunyuan Jiang
https://arxiv.org/abs/2510.10928 htt…

Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
Interpreting the vibrational properties of amorphous solids beyond Debye's theory is challenging due to the presence of inhomogeneity on the mesoscopic scale. In this work, we model this inhomogeneity by real-space fluctuating elasticity with a spatially correlated distribution and calculate the dynamical properties using an exact real-space field theoretical approach. Our results clarify that the excess low-frequency density of states (DOS) originates from a selective scattering effect (strong…

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths
Angela Maria Fajardo Lacave, Francesco Vicentini, Fabian Welschinger, Laura De Lorenzis
https://arxiv.org/abs/2510.11309

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths
We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while avoiding the introduction of multiple damage variables. In addition to the classical components of anisotropic phase-field models based on a single damage variable -- namely, anisotropic elasticity and the extension of the fracture energy density via a second-orde…

Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
Isaac Bermudez, Bryan Gomez-Vargas, Andres E. Rubiano, Ricardo Ruiz-Baier
https://arxiv.org/abs/2510.12307

Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner principle). A novelty of this work is that we introduce a less restrictive assumption on the stress-assisted diffusion coefficient, requiring an analysis of the perturbed diffusion equation using Banach spaces. The solvability of the continuous and discrete …