Surgical implants for replacing cartilage are provided with hydrogel polymers affixed to anchors made of "shape-memory" materials, such as nitinol alloys. These implants can be flexed, allowing them to be inserted into joints arthroscopically. After insertion, an implant will return to its manufactured size and shape, and can be anchored to bone or other tissue. The anchoring components can grip and hold hydrogels or other soft polymers by means of an interface of porous fabric. The fabric can support a reinforcing mesh embedded within the soft polymer, and its bottom surface can promote tissue ingrowth, leading to stronger anchoring. Two or more porous layers can enclose a soft polymer, for purposes such as sustained drug release or holding transplanted cells.