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This paper introduces a new formulation for material homogenization of thin-shell microstructures. It addresses important challenges that limit the quality of previous approaches: methods that fit the energy response neglect visual impact,…

Computational Physics · Physics 2025-05-06 Antoine Chan-Lock , Miguel Otaduy

Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer…

Optimization and Control · Mathematics 2020-04-14 M. N. Dao , J. Gwinner , D. Noll , N. Ovcharova

We present a computational framework to explore the effect of microstructure and constituent properties upon the fracture toughness of fibre-reinforced polymer composites. To capture microscopic matrix cracking and fibre-matrix debonding,…

Applied Physics · Physics 2020-11-03 Wei Tan , Emilio Martínez-Pañeda

The application of hybrid composites in lightweight engineering enables the combination of material-specific advantages of fiber-reinforced polymers and classical metals. The interface between the connected materials is of particular…

Applied Physics · Physics 2021-08-19 Franz Hirsch , Erik Natkowski , Markus Kästner

This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…

Numerical Analysis · Mathematics 2024-06-19 Martin Rumpf , Stefan Simon , Christoph Smoch

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…

A coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive…

Materials Science · Physics 2014-10-02 Alberto Sapora , Marco Paggi

This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…

Numerical Analysis · Mathematics 2012-09-03 Karin Saavedra , Olivier Allix , Pierre Gosselet

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

Numerical Analysis · Mathematics 2017-12-08 Brendan Keith , Socratis Petrides , Federico Fuentes , Leszek Demkowicz

We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack…

Analysis of PDEs · Mathematics 2017-10-25 Marco Barchiesi

We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional…

Numerical Analysis · Mathematics 2019-05-27 Mark Ainsworth , Christian Glusa

The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic…

Analysis of PDEs · Mathematics 2023-01-18 Eduard Rohan , Jan Heczko

Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Experimental and synthetic material microstructures are often represented by 3D image data. The…

Numerical Analysis · Mathematics 2022-09-07 Sanath Keshav , Felix Fritzen , Matthias Kabel

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…

Numerical Analysis · Mathematics 2025-10-20 Suzanne M. Shontz , Stephen A. Vavasis

This article deals with the prediction of thermomechanical properties of fiber reinforced composites using several micromechanics models. These include strength of material approach, Halpin-Tsai equations, multi-phase mechanics of materials…

Applied Physics · Physics 2017-08-03 S. I. Kundalwal

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…

Numerical Analysis · Mathematics 2022-12-28 Tom Gustafsson , Peter Råback , Juha Videman

In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…

Computational Engineering, Finance, and Science · Computer Science 2022-10-07 R. Pinto Carvalho , A. M. Couto Carneiro , F. M. Andrade Pires , A. Popp

In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size…

Soft Condensed Matter · Physics 2016-03-22 Francesco Mancarella , Robert W. Style , John S. Wettlaufer

With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution.…

Numerical Analysis · Mathematics 2024-06-10 Zhizhuo Zhang , Xiaobing Nie , Mikaël Barboteu , Jinde Cao