Some features in the code are oriented toward the investigation of fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, thermal, face loading), interaction integrals for computation of linear-elastic fracture parameters (stress intrensity factors and T-stress), very general element extinction and node release facilities to model crack growth, nonlinear material models including viscoplastic and cyclic, cohesive elements and cohesive constitutive models, hydrogen effects on plasticity, Norton creep, and the Gurson-Tvergaard dilatant plasticity model for void growth. The crystal plasticity material model offers extensive features. Interfaces for Abaqus style UMAT and UEXTERNALDB routines support ready inclusion of user-defined capabilities.

Meshing and Post-Processing

WARP3D uses a text-file based input and output system. Other (graphical) programs are used to generate models and to post-process the results. Cubit, ParaView and Patran, for example, are used extensively by our group for these tasks - WARP3D has built-in features to interface with Patran for model construction and post-processing through standard Patran (2.5-style) neutral files and formatted/binary files of nodal and element results. Simple flat files of the model description and nodal/element results are used to interface with ParaView (these files are designed to be read very efficiently by simple Python programs).

The WARP3D distribution includes a Python program (warp3d2exii) that converts the flat description file for the model (written out by WARP3D) and flat files of node/element results files into an EXODUS II file compatible with ParaView (developed by Kitware, Inc., Sandia National Laboratories, and others). The flat results files are generated directly in WARP3D via output commands (they are text, stream or compressed text files). 

The company Quest Integrity Group offers the commerical software FEACrack that provides fully-integrated mesh generation and post-processing capabilities for complex fatigue and fracture analyses on Windows computers. FEACrack incorporates extensive, direct support for WARP3D to generate complete models containing cracks, to drive the execution of WARP3D for nonlinear analyses and to post-process results including specialized features for fracture parameters. The FEACrack software includes the latest release of the standard WARP3D distribution for Windows. The FEACrack developers collaborate with our group to provide users with fully updated access to WARP3D capabilities and have contributed source code contained in the open-source distribution.

Note: our research group does not have a business relationship with either MSC.Software, Quest Reliability, or Kitware.

Key Modeling Features and Algorithms in WARP3D

  • Incremental-iterative, implicit formulation with full Newton iterations 
  • Time history integration with Newmark's beta method
  • Line search and adaptive load step logic to assist global Newton iterations
  • Large-displacements, large-strains
  • Polar decomposition based, rotation neutralized finite-strain plasticity
  • Elastic-predictor, radial return constitutive updates
  • Consistent tangent moduli for fast convergence of Newton iterations
  • Non-global, absolute coordinate systems at nodes
  • Element block data architectures throughout for vector/threads parallel and MPI-parallel
  • Arbitrary rigid body contact (frictionless)
  • Mesh-tieing with automatic generation of multi-point constraints
  • User-specified multi-point constraints, periodic boundary conditions
  • Node release and element extinction for crack growth (adaptive damage accumulation)
  • Simplified definition of eigenstrains to model residual stresses
  • User-defined initial (residual) stress fields
  • Functionally graded materials (linear-nonlinear) supported by definition of all material properties at structure nodes
  • Integrated procedures to compute J-integrals, stress-intensity factors (KI, KII, KII) and T-stress values using domain-based and interaction integral methods. J-integral methods include crack face tractions, thermal loading, dynamic effects and finite strain plasticity. Residual strains-stresses accommodated via the initial-state framework.
  • UMAT compatible interface to accommodate existing and newly developed user-defined material modeling capability. UEXTERNALDB also supported.
  • Code is written in professional style, modern Fortran with extensive internal documentation 

Equation Solvers

  •  Sparse direct & iterative solver (PARDISO) in the Intel MKL library. Exceptionally fast with excellent parallel execution via threads. PARDISO is included in the pre-built WARP3D executables -- no additional software needed. Available in Windows, Linux and OSX versions of WARP3D. Supports symmetric and asymmetric systems of equations.
  • CPardiso. This is the MPI-based version of Pardiso that provides sparse, direct solutions of symmetric and asymmetric equations intended for execution on compute cluster architectures. CPardiso is included the pre-built WARP3D executable -- no additional software needed. Available only in the Linux version of WARP3D.
  • Hypre Scalable, sparse-iterative, MPI-based, linear solver from Lawrence Livermore National Laboratory. Hypre is included the pre-built WARP3D executable -- no additional software needed. Available only in the Linux version of WARP3D.

Hex Elements (8, 9, 12, 15, 20-node isoparametric solids)

  • Finite strains
  • B-bar formulation with hourglass stabilization
  • Lumped mass
  • Body and face loadings, temperature loadings
  • Extensive output options
  • 8, 9, 14 point integration rules for higher-order elements 

Tet Elements (4 and 10-node isoparametric solids)

  • Finite strains
  • Lumped mass
  • Body and face loadings, temperature loadings
  • Extensive output options 

Interface-Cohesive Elements

  • 8 node, quadrilateral elements to connect 8 node hex elements
  • 6 and 12 node, triangular elements to connect 4 and 10-node tet elements
  • Large displacements & rotations

Material Models

  Mises Plasticity

  • Bilinear, power-law, segmental uniaxial response
  • Temperature dependent material properties
  • Power-law viscoplasticity
  • Finite-strain, small-strain options
  • Mixed isotropic-kinematic hardening with full temperature dependence
  • Cyclic plasticity with mixed, nonlinear kinematic-isotropic hardening (Frederick-Armstrong)
  • Generalized  thermo-cyclic plasticity with nonlinear kinematic hardening, non-zero terminal hardening modulus with ability to model Cotterell-Stokes effect)
  • Hydrogen effects on local plastic flow for saturated materials
  • Elastic-predictor radial return stress updating
  • Exact consistent tangents 

 Crystal Plasticity

  • Rate and temperature dependent simulation of microscale plastic flow in metals
  • Multiple hardening schemes from simple Voce, MTS to Ma-Roters-Raabe
  • Options for simple gradient-based geometric hardening to incorporate the effects of necessary dislocations on hardening
  • 12 slip systems for FCC/BCC, 48 slip system BCC, HCP6, HCP18 and 1 slip system model for education

  Deformation Plasticity

  • Nonlinear (J2) elasticity
  • Linear, then power-law uniaxial response (not Ramberg-Osgood)
  • Small-strains, inviscid response 

 Gurson-Tvergaard Dilatant Plasticity

  • Bilinear, linear+power-law, segmental uniaxial matrix response
  • Power-law viscoplasticity
  • Finite-strain, small-strain options
  • Nucleation models (stress, strain controlled)
  • Highly adaptive, local stress-update algorithms based on elastic-predictor radial return
  • Exact consistent tangent


  • Paulino-Park-Roesler model for mixed-mode and uncoupled mode fracture
  • Linear-elastic uncoupled
  • Needleman exponential coupled normal-shear tractions
  • Penalty method to prevent inter-penetration

Domain Integral Computation

  * Domain Integral formulations for J
  * Interaction integrals to compute all 3 stress-intensity factors for linear-elastic models
  * Interaction integrals to compute T-stresses for linear-elastic models
  * Automatic and manual q-function definition
  * Inertia loading of near-front material included
  * Crack-face tractions Included
  * Temperature effects included (supports anisotropic expansion coefficients)
  * Collapsed or blunt crack tip shapes
  * Finite strain effects
  * All domain and interaction integrals support models with FGMs 

Crack Growth Procedures

 Element Extinction

  • Uses critical porosity to trigger extinction, or
  • Critical plastic strain defined by Stress Modified Critical Strain criterion or
  • Interface-cohesive elements with severely degraded tractions
  • Force releases by traction-separation model
  • Force releases by fixed number of steps
  • Adaptive load stepping to control increments of:
  • ..... porosity with GT model and cell extinction
  • ..... plastic strain with SMCS-based cell extinction
  • ..... relative interface separation with cohesive element 

Node Release

  • Use CTOA to trigger node release
  • Any number of initial crack fronts supported
  • Crack fronts may coalesce during solution
  • Initial and growth CTOAs user specified
  • Option to enforce uniform growth over front based on critical node
  • Automatic location/tracking of crack front in 3-D
  • Force releases by traction-separation model
  • Force releases by fixed number of steps
  • Adaptive load stepping to control increments of CTOA 

Program Input

  • English-like, fully free-form commands
  • Interactive and batch execution modes
  • Translator from MSC-Patran neutral file format to WARP3D provided (performs element blocking operations, domain decomposition and automatic definition of transition elements between 8 and 20-node brick elements) 

Program Output

  • Printed by node/element user defined lists
  • Flat text and binary (stream) files for simple processing by warp3d2exii and other Python programs
  • Patran compatbile node/element ASCII and binary files
  • Packet files of requested values in binary format

Large-Scale Analysis Features

  • Fully automated restart from a single file
  • Status message file for jobs running in batch/background mode
  • Stacks of input files 
  • Wall Clock Time Limit - code stops analysis and writes restart file if next step will exceed time limit