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
CGPACK - our
Cellular Grains PACKage, a cellular automata
microstructure simulation library,
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

Help with usage, modification and further development of this code can provided via CMPLX Engineering Ltd, an engineering consultancy which specialises in Fortran, solid mechanics and supercomputing.

- 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
CGPACK.
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.

- Global optimisation in Fortran 77, 90 and 2003
- Solid mechanics, Abaqus UMAT and VUMAT in Fortran 77, 90 and 2003
- Micromechanics of materials for clusters and supercomputers in Fortran 2008 with coarrays
- Inverse method for residual stress calculation in Fortran 2003 with OpenMP
- Fortran 2008, 2015 coarrays course
- Calculation of mixed mode (I+II) stress intensity factors (SIF) from crack tip displacements
- Validation of Fortran 2008 complex intrinsics and minus zero on branch cuts
- Error functions of complex arguments, erf(z), implemented in modern Fortran