A phase field method of crack nucleation investigation for experimental validation by using the improved degradation functions and strain orthogonal decompositions

•Strain orthogonal condition is applied into PFM to raise the mechanical behaviours.•Improved degradation functions are applied into PFM to reduce the number of elements.•Ensure linear elastic condition of mechanical curve before the first crack appeared.•Accurately predict peak value of mechanical curve when regularization length changed.•Validation between experimental results and simulation results. In recent decades, the phase field method has been widely used in order to model and simulate the damage in various materials and/ or structures. In this simulation method, the regularization length is an important parameter to describe the width of the smeared crack and reflect the crack as a sharp discontinuity. The regularization parameter depends on the material properties thus its value must be small enough. This leads to the element mesh size being small, in other words, the number of elements increases, causing computation costs to much increase. On the other hand, in brittle materials, the positive and negative parts of the strain tensor represent the tension and compression behaviours in the materials. Two parts of the strain tensor must satisfy strain orthogonal decompositions in the context of the elastic stiffness tensor behaving as a metric. Therefore, in this work, the phase field method is incorporated into the improved degradation functions and strain orthogonal condition in order to investigate the crack nucleation and propagation as well as predict the peak load and/ or the critical stress corresponding to the first crack onset appeared in the experimental brittle material such as plaster. A comparison between the obtained results and results of the available experimental tests and/ or relevant simulation methods will demonstrate that the present proposed method makes the mesh size coarser thus the computational cost is significantly reduced without changing the crack path. Moreover, the present simulation method helps to raise the accuracy of the global and local mechanical responses in the material, which is represented by smoother relationship curves.