Abstract
This article presents an effective computational approach that incorporates a quasi-brittle damage model into the isogeometric analysis of plates made of functionally graded materials. The plate kinematics is represented by a third-order shear deformation theory for higher accuracy. A coupling nonlocal equivalent strain field is introduced on the plate neutral surface to control the softening behavior. The utilization of the neutral surface in functionally graded plates enables the use of a single damage parameter over each plate cross-section. As a consequence, plate stiffness matrices can be calculated analytically, which simplifies the proposed damage model and its computer implementation. The discretization of the problem domain is based on basis functions generated from the non-uniform rational B-splines (NURBS) which are used for both geometric representation and field variable approximations, i.e., displacement and nonlocal equivalent strain. Owing to the high-order continuity of the NURBS basis functions, local features such as fracture damage zones can be resolved accurately. The performance of the proposed approach is demonstrated through several numerical examples under different loading configurations and compared with results from other approaches.
Highlights
Fracture is a typical failure mode in structures made of quasibrittle materials such as rock, limestone, concrete, high-strength steel, and polymers
The discretization of the problem domain is based on basis functions generated from the non-uniform rational B-splines (NURBS) which are used for both geometric representation and field variable approximations, i.e., displacement and nonlocal equivalent strain
Some common numerical approaches including the finite element method (FEM), isogeometric analysis (IGA) [1], the extended finite element method (XFEM) [2,3], the cohesive zone model (CZM) [4,5], and the phase-field method [6,7,8,9], with different underlying continuum descriptions [10,11,12,13], have been extensively developed to study the fracture problems in materials and structures which are of significant challenges in practice
Summary
Fracture is a typical failure mode in structures made of quasibrittle materials such as rock, limestone, concrete, high-strength steel, and polymers. The existing works in this area can be categorized into two major branches consisting of discrete methods based on linearly elastic fracture mechanics (LEFM) and the smear damage approaches The former methods, e.g., XFEM [2,3] and CZM [4,5], represent the discontinuities of the crack geometries by embedding an additional field to the approximated primary variable (i.e., displacement field). As a result, dissipated energy unphysically vanishes when the element size tends to zero In such a case, the numerical solution heavily depends on the mesh size in the damaged area; the local damage models require certain calibrations, e.g., adapting the material softening rate concerning element sizes [15,16], to be utilized in practice.
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