Articular cartilage from a material science point of view is a soft network composite that plays a critical role in load-bearing joints during dynamic loading. Its composite structure, consisting of a collagen fiber network and a hydrated proteoglycan matrix, gives rise to the complex mechanical properties of the tissue including viscoelasticity and stress relaxation. Melt electrospinning writing allows the design and fabrication of medical grade polycaprolactone (mPCL) fibrous networks for the reinforcement of soft hydrogel matrices for cartilage tissue engineering. However, these fiber-reinforced constructs underperformed under dynamic and prolonged loading conditions, suggesting that more targeted design approaches and material selection are required to fully exploit the potential of fibers as reinforcing agents for cartilage tissue engineering. In the present study, we emulated the proteoglycan matrix of articular cartilage by using highly negatively charged star-shaped poly(ethylene glycol)/heparin hydrogel (sPEG/Hep) as the soft matrix. These soft hydrogels combined with mPCL melt electrospun fibrous networks exhibited mechanical anisotropy, nonlinearity, viscoelasticity and morphology analogous to those of their native counterpart, and provided a suitable microenvironment for in vitro human chondrocyte culture and neocartilage formation. In addition, a numerical model using the p-version of the finite element method (p-FEM) was developed in order to gain further insights into the deformation mechanisms of the constructs in silico, as well as to predict compressive moduli. To our knowledge, this is the first study presenting cartilage tissue-engineered constructs that capture the overall transient, equilibrium and dynamic biomechanical properties of human articular cartilage.