arXiv subjects

Chad M. Landis

Publications and source records attributed to Chad M. Landis.

4 recordsLinked to original sources

arXiv2026

A Monolithic Computational Homogenization Framework for Nearly Incompressible Magnetoelastic Composites

Magneto-active elastomers exhibit large, nonlinear deformations under combined mechanical loading and magnetic fields, and their effective behavior is strongly governed by microstructural heterogeneity. Predictive modeling of these materials is challenging because their response involves strong magneto-mechanical coupling, large deformations, and the nearly incompressible behavior of elastomeric matrices. Existing multiscale approaches often rely on staggered strategies or formulations that do not robustly treat near-incompressibility in strongly coupled settings. This work presents a fully coupled computational homogenization framework for nearly incompressible magnetoelastic composites in which the mechanical deformation and magnetostatic fields are solved monolithically on a representative volume element (RVE). The microscale problem uses a mixed finite-element discretization with Lagrangian displacement degrees of freedom and a N'ed'elec-based magnetic vector potential, enabling a curl-conforming representation of magnetic induction together with periodic boundary constraints for both mechanical and magnetic fields. Near-incompressibility is treated using J-bar stabilization, in which the volumetric response is controlled by the cell-averaged dilatation while the isochoric response is evaluated using a scaled deformation gradient. The constitutive behavior is derived from an additive free-energy decomposition with hyperelastic, vacuum magnetic, and saturation-type magnetization contributions. The resulting formulation enables robust three-dimensional RVE simulations of heterogeneous magneto-elastic composites with complex particle distributions under large deformations and strong coupling. Numerical examples show how particle interactions, microstructural arrangement, and inclusion compressibility influence deformation patterns and the effective magneto-mechanical response.

cs.CE↗

arXiv2020

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$α$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

cs.CE↗

arXiv2019

An isogeometric finite element formulation for phase transitions on deforming surfaces

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 differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation. Both PDEs can be efficiently discretized using $C^1$-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise $C^1$-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-$α$ scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.

math.NA↗

arXiv2017

Nano-actuator concepts based on ferroelectric switching

The concept of a nano-actuator that uses ferroelectric switching to generate enhanced displacements is explored using a phase-field model. The actuator has a ground state in the absence of applied electric field that consists of polarized domains oriented to form a flux closure. When electric field is applied, the polarization reorients through ferroelectric switching and produces strain. The device is mechanically biased by a substrate and returns to the ground state when electric field is removed, giving a repeatable actuation cycle. The mechanical strains which accompany ferroelectric switching are several times greater than the strains attained due to the piezoelectric effect alone. We also demonstrate a second design of actuator in which the displacements are further increased by the bending of a ferroelectric beam. Phase-field modelling is used to track the evolution of domain patterns in the devices during the actuation cycle, and to study the design parameters so as to enhance the achievable actuation strains.

physics.app-ph↗