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We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy…

Numerical Analysis · Mathematics 2025-10-20 R. V. N. Melnik , A. J. Roberts

Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…

Numerical Analysis · Mathematics 2020-03-03 Björn Stinner , Andreas Dedner , Adam Nixon

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

Bone adaptation models are often solved in the forward direction, meaning that the response of bone to a given set of loads is determined by running a bone tissue adaptation model. The model is generally solved using a numerical technique…

Tissues and Organs · Quantitative Biology 2012-01-31 Amir A. Zadpoor , Gianni Campoli , Harrie Weinans

We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…

Numerical Analysis · Mathematics 2019-02-05 Erik Burman , Daniel Elfverson , Peter Hansbo , Mats G. Larson , Karl Larsson

This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…

Optimization and Control · Mathematics 2025-07-23 Huangxin Chen , Piaopiao Dong , Dong Wang , Xiao-Ping Wang

Fracture of viscoelastic materials is considered to be a complex phenomenon due to their highly rate sensitive behavior. In this context, we are interested in the quasi-static response of a viscoelastic solid subjected to damage. This paper…

Computational Engineering, Finance, and Science · Computer Science 2023-05-15 Rajasekar Gopalsamy , Nicolas Chevaugeon , Olivier Chupin , Ferhat Hammoum

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…

Analysis of PDEs · Mathematics 2021-06-21 Stefano Almi , Ulisse Stefanelli

Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…

Materials Science · Physics 2023-08-08 Owais Ahmad , Naveen Kumar , Rajdip Mukherjee , Somnath Bhowmick

Long-term bone healing/adaptation after a dental implant treatment starts with diffusion of mesenchymal stem cells to the fracture callus and their subsequent differentiation. The healing phase is followed by the bone-remodeling phase. In…

Tissues and Organs · Quantitative Biology 2020-11-25 Soroush Irandoust , Sinan Muftu

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…

Computer Vision and Pattern Recognition · Computer Science 2015-06-17 Paweł Dłotko , Ruben Specogna

Bone is a stiff and though, hierarchical and continuously evolving material that optimizes its structure to respond to mechanical stimuli, which also govern growth and remodeling processes. However, a full understanding of the underlying…

Applied Physics · Physics 2022-06-30 M. Fraldi , A. Cutolo , A. R. Carotenuto , S. Palumbo , F. Bosia , N. M. Pugno

Bone serves as a remarkable example of nature's architectured material with its unique blend of strength and toughness, all at a lightweight design. Given the hierarchical nature of these materials, it is essential to understand the…

This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…

Numerical Analysis · Mathematics 2021-11-09 Fucheng Tian , Xiaoliang Tang , Tingyu Xu , Liangbin Li

In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…

Optimization and Control · Mathematics 2022-02-03 Wendong Huo , Chang Liu , Zongliang Du , Xudong Jiang , Zhengyu Liu , Xu Guo

While purely data-driven assessment is feasible for the first levels of the Structural Health Monitoring (SHM) process, namely damage detection and arguably damage localization, this does not hold true for more advanced processes. The tasks…

Computational Engineering, Finance, and Science · Computer Science 2021-05-03 Thomas Simpson , Vasilis Dertimanis , Costas Papadimitriou , Eleni Chatzi

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

An algorithm is presented for constructing high-order signed distance fields for two phase materials imaged with computed tomography. The signed distance field is high-order in that it is free of the quantization artifact associated with…

Image and Video Processing · Electrical Eng. & Systems 2021-11-03 Bryce A. Besler , Tannis D. Kemp , Nils D. Forkert , Steven K. Boyd

This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Tshilidzi Marwala

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…

Optimization and Control · Mathematics 2016-12-14 Igor Ostanin , Ivan Tsybulin , Mikhail Litsarev , Ivan Oseledets , Denis Zorin