Interfacial stabilization at finite strains for weak and strong discontinuities in multi-constituent materials

Chen, Pinlei; Truster, Timothy J.; Masud, Arif

doi:10.1016/j.cma.2017.06.020

Cited by 20 publications

(21 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where U h 1 and U h 2 are solutions with mesh sizes h 1 and h 2 , respectively, taken at the comparison points. 3 The main result of this section, the convergence of the non-conforming interface FEM problem, is shown in Fig. 8.…”

Section: Case 1: Flat Interfacementioning

confidence: 95%

“…Higher-order tensors, which are formed by the tensor product of more than two vectors, are denoted with preceding superscript showing the order, e.g. 3 E is a third-order tensor. Standard fourth order identity tensor and its right transpose are denoted as 4 I = e s e k e k e s , 4 I RT = e s e k e s e k , respectively, where e i , i ∈ {1, 2, 3} are basis vectors.…”

Section: Notationmentioning

confidence: 99%

“…Weak form (33) is similar to the weak form of [38,39], however, with different interface stabilisation terms. In [38,39], the stabilised discontinuous Galerkin (DG) method was proposed for large deformations, while in [3], this approach was extended to include models of damage and debonding.…”

Section: Variation Of the Potential Energy And The Weak Formmentioning

confidence: 99%

“…Moreover, similar von Mises stress distribution is observed. 3 Column U h can be formally defined as…”

Section: Case 2: Curved Interfacementioning

confidence: 99%

See 3 more Smart Citations

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

Poluektov

Figiel

2018

Comput Mech

View full text Add to dashboard Cite

In this paper, a novel finite-element based method for finite-strain mechanochemistry with moving reaction fronts, which separate the chemically transformed and the untransformed phases, is proposed. The reaction front cuts through the finite elements and moves independently of the finite-element mesh, thereby removing the necessity for remeshing. The proposed method solves the coupled mechanics-diffusion-reaction problem. In the mechanical part of the problem, the force equilibrium and the displacement continuity conditions at the reaction front are enforced weakly using a Nitsche-like method. The formulation is applicable to the case of large deformations and arbitrary constitutive behaviour, and is also consistent with the minimisation of the total potential energy. Keywords Chemo-mechanical processes • Finite strains • Moving interfaces • Nitsche method • Cut elements • Variational consistency B M. Poluektov

show abstract

Section: Case 1: Flat Interfacementioning

confidence: 95%

Section: Notationmentioning

confidence: 99%

Section: Variation Of the Potential Energy And The Weak Formmentioning

confidence: 99%

“…Moreover, similar von Mises stress distribution is observed. 3 Column U h can be formally defined as…”

Section: Case 2: Curved Interfacementioning

confidence: 99%

See 2 more Smart Citations

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

Poluektov

Figiel

2018

Comput Mech

View full text Add to dashboard Cite

show abstract

“…This formulation can also be viewed as a variational generalization of the standard Nitsche method 24 that enforces the continuity of the velocity field, and possesses the features of the interface operators from the cutFEM approach 28,29 to FSI. In the earlier works of the senior author, the VMDG class of methods was developed for problems involving finite strain interfacial kinematics and interfacial damage in multi-constituent materials, 35 evolving biomaterial interfaces in coupled thermomechanical problems, 36 shear-rate dependent non-Newtonian fluids, 37 and immersed boundary method for incompressible flows. 38 An outline of the article is as follows.…”

Section: Introductionmentioning

confidence: 99%

Variational coupling of non‐matching discretizations across finitely deforming fluid–structure interfaces

Kang

Kwack

Masud

2022

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

This paper presents a stabilized monolithic method for coupling incompressible viscous fluids with finitely deforming elastic solids across non‐matching interfacial meshes. Governing equations for the solid are written in the finite deformation Lagrangian frame using velocity field as the primary unknown, while the governing equations for the fluid are written in an Arbitrary Lagrangian–Eulerian (ALE) frame to accommodate large motions of the fluid–solid interfaces. Interface coupling terms are derived by embedding Discontinuous Galerkin (DG) ideas in the Variational Multiscale (VMS) framework and locally resolving the fine‐scale variational equations from the fluid and the solid subdomains along the common interface. The unique attribute of the proposed Variational Multiscale Discontinuous Galerkin (VMDG) method is a systematic procedure for deriving analytical expression for the traction Lagrange multiplier at the fluid–solid interface. The structure of the interface stabilization tensor emerges naturally and is shown to be a function of the boundary operators that are associated with the domain interior operators from the fluid and the solid subdomains. The derived stabilization tensor possesses the features of area‐averaging and stress‐averaging and evolves spatially and temporally with the evolving nonlinear fields at the interface. An analysis of the mathematical properties of the interface stabilization tensor is presented and subsequently verified numerically. The method is implemented using four‐node tetrahedral elements for the fluid as well as the solid subdomains while employing equal‐order interpolations for the various interacting fields. Benchmark problems are presented for the verification of the method for finitely deforming fluid–structure interfaces.

show abstract

An elastic‐inelastic model and embedded bounce‐back control for layered printing with cementitious materials

Wijaya

Kreiger

Masud

2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

This paper presents a finite‐deformation model for extrusion‐based layered printing with cementitious materials. The evolution of mechanical properties as the printed material cures and stiffens results in nonphysical reduction in the magnitude of elastic strains when standard constitutive models are employed. This elastic recovery of the printing induced deformation contradicts the experimentally observed behavior of the printed cementitious materials that harden at a nearly‐frozen deformed state. A thermodynamically motivated constraint on the evolution of elastic strains is imposed on the constitutive model to remedy the nonphysical bounce‐back effect. An algorithm that is based on a strain‐projection technique for the elastic part of deformation is developed that complements the inelastic response given by the Drucker–Prager model. It is then embedded in a finite strain finite element framework for the modeling and simulation of cure hardening and inelastic response of the early age cementitious materials. A ghost mesh method is proposed for continuous layer‐wise printing of the material without the need for intermittent mesh generation technique or adaptive remeshing methods. The model is validated via comparison with experimental data and representative test cases are presented that investigate the mathematical and computational attributes of the proposed model.

show abstract

Interfacial stabilization at finite strains for weak and strong discontinuities in multi-constituent materials

Cited by 20 publications

References 48 publications

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

Variational coupling of non‐matching discretizations across finitely deforming fluid–structure interfaces

An elastic‐inelastic model and embedded bounce‐back control for layered printing with cementitious materials

Contact Info

Product

Resources

About