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A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe…
In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning…
We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
This paper presents an analytical framework, based on Floquet modal expansions of the electromagnetic fields and equivalent circuits, to model reconfigurable metasurfaces loaded with generic lumped elements (resistors, capacitors,…
This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite…
An extension to the interface finite element with eMbedded Profile for Joint Roughness (MPJR interface finite element) is herein proposed for solving the frictional contact problem between a rigid indenter of any complex shape and an…
This paper describes a novel homogenization methodology for analyzing the failure of elastoplastic composite materials based on elastic and eigen influence tensors-driven transformation field analysis ($\mathtt{E}^2$-TFA). The proposed…
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…
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid mesh regeneration procedure when solving moving interface…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…
A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large…
The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a…
This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…
Closed-form solutions for the modified exterior Eshelby tensor, strain concentration tensor, and effective moduli of particle-reinforced composites are presented when the interfacial damage is modeled as a linear spring layer of vanishing…