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In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…

Computational Engineering, Finance, and Science · Computer Science 2025-11-19 Abhishek Arora , Caglar Oskay

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

We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…

Numerical Analysis · Mathematics 2024-10-24 Omar Richardson , Omar Lakkis , Adrian Muntean , Chandrasekhar Venkataraman

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…

Materials Science · Physics 2024-10-29 J. Ulloa , M. P. Ariza , J. E. Andrade , M. Ortiz

In this paper, the performance of different structural models based on global approach in evaluating the static response of curvilinear fibre composite laminates is analyzed. A Co shear flexible Quad-8 element developed based on…

Materials Science · Physics 2014-07-29 Anand Venkatachari , Sundararajan Natarajan , K Ramajeyathilagam , M Ganapathi

This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…

Materials Science · Physics 2009-07-09 Martin I. Idiart , Francois Willot , Yves-Patrick Pellegrini , Pedro Ponte Castaneda

We investigate the role of architected thin films in the interfacial failure properties of bi-layer composites. Our results show that, while graded structures can be used to prescribe failure at the interface, they do not offer significant…

Materials Science · Physics 2026-03-10 Christian Greff , Leon Pyka , Michael Zaiser , Paolo Moretti

The use of composite materials for structures subjected to impacts requires a deep understanding about the dynamic behaviour of the material. To this end, a physically-based computational micromechanics simulation tool has been developed to…

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

We introduce a novel computational framework for the multiscale simulation of higher-order continua that allows for the consideration of first-, second- and third- order effects at both micro- and macro-level. In line with classical…

Computational Engineering, Finance, and Science · Computer Science 2022-03-08 Felix Schmidt , Melanie Krüger , Marc-Andre Keip , Christian Hesch

Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…

Graphics · Computer Science 2025-04-15 Bojja Venu , Adam Bosak , Juan Raul Padron-Griffe

The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high…

Materials Science · Physics 2023-05-24 Philip P. Müller , Falk K. Wittel , David S. Kammer

We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…

Numerical Analysis · Mathematics 2021-11-18 Luca Heltai , Alfonso Caiazzo

Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation…

Computational Engineering, Finance, and Science · Computer Science 2024-12-19 Asghar A. Jadoon , Karl A. Kalina , Manuel K. Rausch , Reese Jones , Jan N. Fuhg

A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…

Numerical Analysis · Mathematics 2025-12-24 Wei Xie , Viet Ha Hoang , Yin Yang , Yunqing Huang

The complexity and heterogeneity of bone tissue require a multiscale modelling to understand its mechanical behaviour and its remodelling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based…

Medical Physics · Physics 2014-03-13 Abdelwahed Barkaoui , Abdessalem Chamekh , Merzouki Tarek , Ridha Hambli , Mkaddem Ali

Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…

Numerical Analysis · Mathematics 2025-09-03 Eric T. Chung , Changqing Ye , Xiang Zhong

This paper presents a hybrid continuum discrete macro modelling strategy with a multiscale calibration procedure for realistic simulations of brick masonry bridges. The response of these structures is affected by the intrinsic nonlinearity…

Computational Engineering, Finance, and Science · Computer Science 2022-02-15 Bartolomeo Panto' , Corrado Chisari , Lorenzo Macorini , Bassam A. Izzuddin

In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…

Numerical Analysis · Mathematics 2022-03-23 Yiran Wang , Eric Chung , Shubin Fu

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…

Numerical Analysis · Mathematics 2024-10-18 N. Kovács , M. A. Maia , I. B. C. M. Rocha , C. Furtado , P. P. Camanho , F. P. van der Meer