An efficient algorithm for biomechanical problems based on a fully implicit nested Newton solver

Finite element methods applied to problems in solid mechanics (74S05) Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) (74C15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids (74-10)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
A poroplastic model of structural reorganisation in porous media of biomechanical interest
Perspectives on biological growth and remodeling
A mortar-based frictional contact formulation for large deformations using Lagrange multipliers
Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
A global strategy for solving reactive transport equations
On the permeability of fibre-reinforced porous materials
Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity
Thermomechanics of viscoplasticity. Fundamentals and applications
Functional analysis, Sobolev spaces and partial differential equations
Geometrical material structure of elastoplasticity
Plasticity. Mathematical theory and numerical analysis
A mortar segment-to-segment contact method for large deformation solid mechanics.
Thermomechanics of volumetric growth in uniform bodies
An Allen-Cahn approach to the remodelling of fibre-reinforced anisotropic materials
An elasto-visco-plastic model of cell aggregates
A massively parallel geometric multigrid solver on hierarchically distributed grids
\textit{UG} 4: a novel flexible software system for simulating PDE based models on high performance computers
Multigrid analysis of spatially resolved hepatitis C virus protein simulations
On the geometrical material structure of anelasticity
On the mechanics of solids with a growing mass.
Stress, strain, growth, and remodeling of living organisms
A global approach to reactive transport: application to the momas benchmark
A global method for coupling transport with chemistry in heterogeneous porous media
Adaptive numerical analysis in primal elastoplasticity with hardening
Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions
An elasto-plastic biphasic model of the compression of multicellular aggregates: the influence of fluid on stress and deformation
A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted finite element method
Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions. Global implicit solver for multiple gas components
A primal--dual active set strategy for nonlinear multibody contact problems
Residual stresses in soft tissue as a consequence of growth and remodeling: Application to an arterial geometry
Mathematical characterization and identification of remodeling, growth, aging and morphogenesis
Modelling the compression and reorganization of cell aggregates
Poroelastic materials reinforced by statistically oriented fibres--numerical implementation and application to articular cartilage
Variationally consistent discretization schemes and numerical algorithms for contact problems
Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems
Remodelling in statistically oriented fibre-reinforced materials and biological tissues
Stress-Modulated Growth
Statistical Analysis of Spherical Data
A continuum‐based finite element formulation for the implicit solution of multibody, large deformation‐frictional contact problems
The variational formulation and solution of problems of finite‐strain elastoplasticity based on the use of a dissipation function
Monotone Multigrid Methods on Nonmatching Grids for Nonlinear Multibody Contact Problems
A generalised algorithm for anelastic processes in elastoplasticity and biomechanics
A Globally Convergent Filter-Trust-Region Method for Large Deformation Contact Problems
ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH
Numerical Methods for Elliptic and Parabolic Partial Differential Equations
On the origins of the idea of the multiplicative decomposition of the deformation gradient
Anelastic reorganisation of fibre-reinforced biological tissues
Mesh generation for thin layered domains and its application to parallel multigrid simulation of groundwater flow