A Computationally Efficient Vectorized Implementation of Localizing Gradient Damage Method in MATLAB

In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding interface. As a result, MATLAB is generally preferred for the initial development (prototyping) of computational models by researchers. However, MATLAB-developed codes are seldom used for large-scale simulations (after initial development is complete) due to their computational inefficiency. Hence, a computationally efficient implementation of LGDM using MATLAB vectorization is presented in this work. The choice of LGDM (as the fracture modeling method) is based on its thermodynamically consistent formulation built upon the micromorphic framework. Moreover, the non-linear coupled field formulation of LGDM makes it suitable for testing the computational efficiency of vectorized MATLAB implementation in a non-linear finite element setting. It is shown in this work that the vectorized MATLAB implementation can save significant computational resources and time as compared to non-vectorized implementations (that are parallelized with MATLAB parfor). The vectorized MATLAB implementation is tested by solving numerical problems in 1D, 2D and 3D on a consumer-grade PC, demonstrating the capability of vectorized implementation to run simulations efficiently on systems with limited resources. The sample source codes are provided as supplementary materials that would be helpful to researchers working on similar coupled field models.