The library contains routines for implicit and
explicit integration of elastic, plastic and
ductile damage material models, via Abaqus
user material subroutines. It can be used
together with
CASUP
(Cellular Automata library for SUPercomputers),
to understand and quantify damage and fracture on
the micro-scale.
The
```
cafe.old
```

directory is an implementation of CAFE idea fully within an Abaqus VUMAT subroutine.
ABUMPACK is distributed under 2 clause BSD style license.
See
```
LICENSE
```

file.

With any questions, bug reports, feedback and any other comments please submit a ticket.

26-DEC-2017: release 4. GTN VUMAT routines have been updated. Some disagreement with Abaqus own GTN is observed. This is expected where "finite rotation of a material point is accompanied by finite shear". This is because VUMAT uses the Green-Naghdi stress rate, whereas Abaqus own solver uses the Jaumann stress rate. See the VUMAT manual for full details.

JAN-2017 | NOV-2016 | JUL-2016 | MAR-2016

- 2016: A. Shterenlikht, Integration of Rousselier's continuous ductile damage model, report, 2016, PDF.
- 2012: A. Shterenlikht, N. A. Alexander, Levenberg-Marquardt vs Powell's dogleg method for Gurson-Tvergaard-Needleman plasticity model Computer Methods in Applied Mechanics and Engineering 237-240:1-9, 2012, DOI:10.1016/j.cma.2012.04.018, PDF with final corrections.
- 2012: A. Shterenlikht, Integration of 3D GTN for Abaqus VUMAT and UMAT, PDF.
- 2006: D. W. Beardsmore, M. A. Wilkes, A. Shterenlikht, An implementation of the Gurson-Tvergaard-Needleman plasticity model for Abaqus Standard using a trust region method, In Proc. ASME PVP Conf. ICPVT-11, 23-27 July 2006, Vancouver, BC, Canada, American Society of Mechanical Engineers, p. 615-624, ISBN: 0-79184-757-8, DOI: 10.1115/PVP2006-ICPVT-11-93561, or locally: PDF.
- 2006: S. Das, A. Shterenlikht, I. C. Howard, E. J. Palmiere, A general method for coupling microstructural response with structural performance, Proc. Roy. Soc. A 462:2085-2096, 2006, DOI:10.1098/rspa.2006.1681.
- 2006: A. Shterenlikht, I. C. Howard, The CAFE model of fracture - application to a TMCR steel Fat. Fract. Eng. Mat. and Struct. 29(9-10):770-787, DOI:10.1111/j.1460-2695.2006.01031.x.
- 2005: S. J. Wu, C. L. Davis, A. Shterenlikht, I. C. Howard, Modeling the ductile-brittle transition behavior in Thermomechanically Contolled Rolled Steels, Met. Mat. Trans. A 36:989-997, 2005, DOI:10.1007/s11661-005-0292-z, PDF.
- 2004: A. Shterenlikht, I. C. Howard, Cellular automata finite element (CAFE) modelling of transitional ductile - brittle fracture in steel, Proc. 15th European Conference of Fracture (ECF15), KTH, Stockholm, Sweden, 11-13 August 2004, paper P151, European Structural Integrity Society (ESIS), PDF talk and PDF paper.
- 2003: A. Shterenlikht, 3D CAFE modelling of transitional ductile - brittle fracture in steel, PhD thesis, The University of Sheffield, UK, PDF.

SEM images of ductile fracture surfaces of a thermomechanically controlled rolled (TMCR) steel, at different magnifications.

Below are
the results of linking the single FE shear+tension model
(see below) with
CASUP.
The results show the evolution of
the maximum principal stress, σ_{1}, resolved to 3
crystallographic planes: 100, 110, 111. In all cases, the
preferential plane is chosen of all planes of the same
family.

The two plots are the outcomes of 2 runs, with 2 randomly chosen orientations of some cubic single crystal enclosed in the finite element. These show (a) a complex evolution of the resolved stresses during the deformation, and (b) significant variation in stresses with the orientation of the crystal. This illustrates some of the capabilities of a cellular automata finite element (CAFE) model.

We use Levenberg-Marquardt (LM)
`dnls1.f`

and Powell's dogleg (DL)
`dnsq.f`

solution routines from
Slatec
library.
For GTN model the LM method shows
faster convergence than the DL.
For more details see:
A. Shterenlikht, N. A. Alexander,
Levenberg-Marquardt vs Powell's dogleg method for Gurson-Tvergaard-Needleman plasticity model
Computer Methods in Applied Mechanics and Engineering 237-240:1-9, 2012,
DOI:10.1016/j.cma.2012.04.018,
PDF with final corrections.

This is an 3-point impact bend test of a notched bar. The standard bar dimentions are 50 mm length and 10 mm by 100 mm cross section. The striker geometry is according to British Standard BS EN ISO 148-3:2016. GTN VUMAT - explicit dynamic analysis. Levenberg-Marquardt solver is used. The contour plots show von Mises stress.

Animation, 7MB, avi.

A circular cylinder bar is loaded in shear under displacement control. GTN UMAT material model is used with the Levenberg-Marquardt non-linear solver. The contour plot shows von Mises stress.

Animation, 9M avi.

A 3D model of a circular cylinder under axial tension. Displacement control is used. GTN UMAT material model is used with the Levenberg-Marquardt non-linear solver. The contour plot shows the volumetric void fraction (VVF) variable.

Animation, 11MB avi.

This circular cylinder is loaded under displacement control in shear+tension. This is an elasto-plastic model wit isotropic hardening and VUMAT explicit dynamic GTN implementation. The contour plot shows the volumetric void fraction (VVF) variable.

Animation, 10MB avi.

This is a single FE, 1st order 8-node brick with reduced integration, C3D8R from Abaqus element library. The element is loaded under displacement control in shear+tension. This is an elasto-plastic model with isotropic hardening and no damage, implemented in a UMAT implicit quasi-static user material subroutine. The contour plot shows U2 displacements, along Y. variable.

Animation, 5.2MB avi.

This is a single FE, 1st order 8-node brick with reduced integration, C3D8R from Abaqus element library. The element is loaded under load control in pure shear. This is an elasto-plastic model with isotropic hardening and no damage, implemented in a VUMAT explicit dynamic user material subroutine. The contour plot shows U2 displacements, along Y. variable.

Animation, 10MB avi.

A 3D model of a circular cylindrical rod loaded under displacement control in shear+tension. This is an elasto-plastic model with isotropic hardening and no damage, implemented in a UMAT implicit quasi-static user material subroutine. The contour plot shows PEEQ variable - equivalent plastic strain.

Animation, 9.3MB avi.

- ABUMPACK - Abaqus UMAT and VUMAT for GTN, Rousselier, von Mises plasticity
- CASUP - Cellular Automata library for HPC and supercomputers
- Fortran 2008, 2018 coarrays course
- Validation of Fortran 2008 complex intrinsics and minus zero on branch cuts
- Global optimisation in Fortran 77, 90 and 2003
- Inverse method for residual stress calculation in Fortran 2003 with OpenMP
- Calculation of mixed mode (I+II) stress intensity factors (SIF) from crack tip displacements
- Error functions of complex arguments, erf(z), implemented in modern Fortran