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In this work, the Theory of Porous Media (TPM) is employed to model percutaneous vertebroplasty, a medical procedure in which acrylic cement is injected into cancellous vertebral bone. Previously, isothermal macroscale models have been…

Fluid Dynamics · Physics 2026-03-10 Jan-Sören L. Völter , Zubin Trivedi , Andreas Boger , Tim Ricken , Oliver Röhrle

In this paper, we introduce a novel bond-based peridynamic model that utilizes a Gaussian kernel function. Previous peridynamic models, when directly discretized, have exhibited a lack of asymptotically compatibility with their…

Mathematical Physics · Physics 2025-12-15 Chenguang Liu , Hao Tian , Jinlong Shao

Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to…

Analysis of PDEs · Mathematics 2020-01-10 J. C. Bellido , J. Cueto , C. Mora-Corral

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…

Materials Science · Physics 2021-07-21 Carlos J. G. Rojas , Marco L. Bitterncourt , José L. Boldrini

While cracks in isotropic homogeneous materials propagate straight, perpendicularly to the tensile axis, cracks in natural and synthetic composites deflect from a straight path, often increasing the toughness of the material. Here we…

Materials Science · Physics 2020-08-05 Ataollah Mesgarnejad , Chunzhou Pan , Randall M. Erb , Sandra J. Shefelbine , Alain Karma

In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Fei Han , Zhibin Li

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…

Computational Engineering, Finance, and Science · Computer Science 2019-03-01 Jacinto Ulloa , Patricio Rodríguez , Cristóbal Samaniego , Esteban Samaniego

Spatial ordering of matter elicits exotic properties sometimes absent from a material's constituents. A few highly mineralised natural materials achieve high toughness through delocalised damage, whereas synthetic particulate composites…

Materials Science · Physics 2024-01-23 Victoria Vilchez , Shitong Zhou , Florian Bouville

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…

Numerical Analysis · Mathematics 2016-12-21 Hisham Assi , Richard S. C. Cobbold

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities, and multi-physics…

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…

Materials Science · Physics 2015-05-18 R. Spatschek , E. Brener , A. Karma

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures…

Computational Physics · Physics 2015-08-04 Shubhankar Roy Chowdhury , Pranesh Roy , Debasish Roy , J. N. Reddy

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…

Applied Physics · Physics 2024-07-31 Samuel P. Wallen , Michael R. Haberman , Washington DeLima

The endochronic theory, developed in the early 70s, allows the plastic behavior of materials to be represented by introducing the notion of intrinsic time. With different viewpoints, several authors discussed the relationship between this…

Classical Physics · Physics 2009-01-13 Silvano Erlicher , Nelly Point

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact,…

We investigate the emergence of non-linear diffusivity in kinetically constrained, one-dimensional symmetric exclusion processes satisfying the gradient condition. Recent developments introduced new gradient dynamics based on the Bernstein…

Probability · Mathematics 2025-04-18 G. S. Nahum

Understanding crack propagation in structures subjected to fluid loads is crucial in various engineering applications, ranging from underwater pipelines to aircraft components. This study investigates the dynamic response of structures,…

Computational Engineering, Finance, and Science · Computer Science 2023-10-06 Md Rushdie Ibne Islam

This work presents a comprehensive phase-field framework for modeling anisotropic viscoelastic-viscoplastic fracture in short fiber-reinforced polymer (SFRP) composites under hygrothermal environments at finite deformation. The constitutive…

Computational Engineering, Finance, and Science · Computer Science 2026-03-04 Behrouz Arash , Shadab Zakavati , Timon Rabczuk

Many geologic materials have a composite structure, in which macroscopic mechanical behavior is determined by the properties, shape, and heterogeneous distribution of individual constituents. In particular, sedimentary rocks commonly…

Geophysics · Physics 2020-08-26 Shabnam J. Semnani , Joshua A. White

This paper addresses the numerical simulation of self-piercing rivetting processes to join fibre reinforced polymers and sheet metals. Special emphasis is placed on the modelling of the deformation and failure behaviour of the composite…