CODES

The codes presented here are used for the paper titled "A Phase-Field Fracture Model for Fatigue using Locking-Free Solid Shell Finite Elements: Analysis for Homogeneous and Layered Composites". These codes are applicable with or without fatigue considerations and are written as UEL and UMAT subroutines for use in Abaqus. We have tested the files for compatibility with Abaqus versions 2020 and 2022. When utilizing the code, remember to update the "allelem" variable with the number of elements in the UEL for each layer. This variable is located within the module Kvisual. Please exercise caution when defining the fatigue model from the input file..

Authors: Pavan Kumar Asur Vijaya Kumar, Aamir Dean, Jose Reinoso, Heinz Pettermann, Marco Paggi 

This document offers a brief summary of the numerical computation of the material tangent within implicit Finite Element Analysis (FEA), with a focus on its implementation within the Abaqus UMAT subroutine. It begins with an introduction emphasizing the importance of the material tangent in FEA simulations and the challenges associated with its analytical derivation. The methodology section delves into the use of finite difference methods, particularly the forward difference first-order scheme, for approximating the Jacobian material tangent. Practical considerations such as numerical effects and floating-point arithmetic are discussed in detail. Subsequently, the document outlines a step-by-step methodology for computing the numerical tangent, integrating insights from the newly added section on Finite Difference Methods. Finally, a Fortran code snippet for the UMAT subroutine is provided, illustrating the practical implementation details of the numerical tangent computation. This document serves as a beginner's guide for understanding and implementing the numerical computation of the material tangent in implicit FEA simulations.

Authors: Aamir Dean