Related papers: Nonlinear material identification of heterogeneous…
We present a novel isogeometric discretization approach for the Kirchhoff-Love shell formulation based on the Hellinger-Reissner variational principle. For mitigating membrane locking, we discretize the independent strains with spline basis…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of…
Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…
We present a scalable and efficient framework for the inference of spatially-varying parameters of continuum materials from image observations of their deformations. Our goal is the nondestructive identification of arbitrary damage,…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
In a companion article (Part 1), we presented the development of a thick continuum-based (CB) shell finite element (FE) based on Mindlin-Reissner theory. We verified the accuracy, efficiency and locking insensitivity of the element in…
For Kichhoff-Love shell problems a new mixed formulation solely based on standard $H^1$ spaces is presented. This allows for flexibility in the construction of discretization spaces, e.g., standard $C^0$-coupling of multi-patch isogeometric…
This work presents a shear elastoplasticity model for textile fabrics within the theoretical framework of anisotropic Kirchhoff-Love shells with bending of embedded fibers proposed by Duong et al. (2023). The plasticity model aims at…
In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain…
Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of…
We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…