A process makes electrical connections between electrical wires and flexible conductive elements, such as conductive fabrics. The process makes strong electrical connections that are mechanically flexible and can simultaneously create multiple electrical connections. The process involves creating an assembly that includes at least a TPE layer, an electrical wire, an insulating layer, and a flexible conductive element, and applying heat and pressure to the assembly. For example, a conductive fabric is disposed on an insulating layer, a wire is positioned onto a surface of the insulating layer, and a TPE layer is disposed over the wire and overlaps the conductive fabric element. When applying the heat and pressure, the wire melts through the insulating layer to make electrical contact with the conductive fabric element, and the TPE layer conforms to an exterior of the wire and bonds to the insulating layer.