Practical implementation of asymptotic expansion homogenisation in thermoelasticity using a commercial simulation software

• A fully integrated thermoelastic homogenisation methodology in a widely used commercial simulation software.
• Pedagogic guide for new researchers and students working in homogenisation methods.
• Pedagogic issues and troubleshooting of frequent problems.
• Specific details of the implementation in the commercial software.
• A set of code blocks in order to demonstrate, help and encourage future implementations.

Asymptotic expansion homogenisation (AEH) is a rigorous homogenisation method that allows to model the thermomechanical behaviour of periodic materials in an efficient manner. The main advantages of this method are the reduction of the problem size and the capability of quantifying the strain and stress levels in the microscale using macroscale results. This method provides explicit equations for its purpose, an advantage not found on typical homogenisation methods.This paper presents a pedagogic implementation and validation of AEH using the commercial simulation software ABAQUS. The scope of this work lies on thermoelasticity applied to heterogeneous materials. In this work, guidelines and troubleshooting for a successful implementation are analysed and discussed. Its purpose is to motivate the use of homogenisation methods, specially the AEH, and to detail every step needed to implement it using a commercial software. Key points, such as boundary conditions, computation of characteristic displacements and effective properties are discussed. Given the complexity of the problem, a series of validation schemes and results are presented and analysed. A user subroutine code is also presented.