A physically based, finite deformation, rate and temperature dependent theory and model have been developed to simulate the deformation and failure of FRP composite materials and structures. Failure modes include: inter alia, fiber crushing and kinking as occurs during extreme compressive loading; fiber fracture as occurs in for example fragmentation; interlaminar shear as occurs at elevated temperatures and that leads to kinking; debonding and delamination including the coupling with laminate kinking; and debonding as occurs in cored FRP panels. The theory/model is capable of describing quasi-static (including creep) as occurs at elevated temperatures, and dynamic deformation and failure as occurs during shock, blast or impact. The model is implemented within LS DYNA and specific example simulations are described that illustrate the theory/model capabilities. In Part I, fragmentation is not covered in detail. Fiber fracture and fragmentation are to be covered to detail with specific examples in Part II.