Thermal-mechanical coupling constitutive theory for nonlinear ceramic matrix composite laminates

Temperature-dependent constitutive models under complex stress states are essential for designing and evaluating thermal structures. This study develops an inelastic theoretical framework to characterize the deformation behavior of damageable nonlinear ceramic matrix composites (CMCs) laminates under thermo-mechanical loads, addressing limitations of classical laminate theory (CLT). An anisotropic nonlinear stress-strain model for a single layer is formulated based on post-loading linearization, with damaged compliance and stiffness matrices described via a decoupled damage evolution law. The thermo-mechanical deformation of damaged laminates is expressed using mid-plane strain and curvature, partitioned into elastic and inelastic components. CLT is modified to capture post-damage elastic deformation, leading to a generalized physical equation relating internal forces and moments to mid-plane strain and curvature. For cross-woven CMC laminates, explicit relations are provided. The proposed theory is validated through simulations of on- and off-axis tensile behavior of a 2D-C/SiC composite laminate at elevated temperature.