A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code

DOI10.1016/j.cma.2014.06.034zbMath1423.74953OpenAlexW2070301516MaRDI QIDQ1668400

Harry R. Millwater, John T. Foster, Michael D. Brothers

Publication date: 28 August 2018

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.06.034

zbMATH Keywords

Newton's methodnumerical differentiationautomatic differentiationNewton-Raphsoncomplex-steptangent-stiffness

Mathematics Subject Classification ID

Related Items (12)

Mixed peridynamic formulations for compressible and incompressible finite deformations ⋮ Determination of the tangent stiffness tensor in materials modeling in case of large deformations by calculation of a directed strain perturbation ⋮ Computationally efficient and effective peridynamic model for cracks and fractures in homogeneous and heterogeneous materials ⋮ A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain ⋮ Quasistatic fracture using nonlinear‐nonlocal elastostatics with explicit tangent stiffness matrix ⋮ A novel sampling method for adaptive gradient-enhanced kriging ⋮ An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities ⋮ Peridynamics review ⋮ A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics ⋮ Static solution of crack propagation problems in peridynamics ⋮ Peridynamic Petrov-Galerkin method: a generalization of the peridynamic theory of correspondence materials ⋮ An implicit non-ordinary state-based peridynamics with stabilised correspondence material model for finite deformation analysis

Uses Software

• ADIFOR
• Trilinos
• ABAQUS
• TFad
• Peridigm

Cites Work

• Unnamed Item
• A peridynamic formulation of pressure driven convective fluid transport in porous media
• A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities
• The complex step approximation to the Fréchet derivative of a matrix function
• Extensions of the first and second complex-step derivative approximations
• Studies of dynamic crack propagation and crack branching with peridynamics
• Computational inelasticity
• Numerical differentiation for local and global tangent operators in computational plasticity
• On the generalization of the complex step method
• Reformulation of elasticity theory for discontinuities and long-range forces
• Peridynamic states and constitutive modeling
• An overview of the Trilinos project
• Peridynamics as an Upscaling of Molecular Dynamics
• Unconditionally stable algorithms for quasi-static elasto/visco-plastic finite element analysis
• Consistent linearization in mechanics of solids and structures
• Using Complex Variables to Estimate Derivatives of Real Functions
• Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-Lade model
• Numerical Solution of Partial Differential Equations
• Numerical time integration for dynamic analysis using a new higher order predictor‐corrector method
• Peridynamic State-Based Models and the Embedded-Atom Model
• The complex-step derivative approximation
• Numerical Differentiation of Analytic Functions
• Differentiation Formulas for Analytic Functions

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