To satisfy the increasing need in today's industry for high performance, more complex chips are being designed. These chips, when integrated in 3D packages, have a high energy density and require new and innovative cooling strategies as many of them are designed as flip-chip assemblies, usually requiring back-side cooling. Classical underfills currently used offer poor thermal conductivity. But cooling through the underfill would enable cost-efficient and low complexity cooling solutions. For this purpose, thermal underfills with percolating fillers and necks are currently under development. They are to provide a significant improvement in thermal conductivity to classical capillary underfills and will find applications in, for example, 3D integrated packages to improve heat dissipation. The idea behind the percolating thermal underfill (PTU) comprises a sequential joint forming process ensuring a high fill fraction. Although flip chip technology has been well described, the addition of the neck based percolating underfill could entail several new thermo-mechanical reliability concerns that need to be studied using a physics of failure approach, since the PTU exhibits vastly different thermo-mechanical behavior, giving rise to possible new failure mechanisms and locations. This paper in particular deals with FE simulations carried out to understand different key aspects of the thermal underfill and to study the effects of the increased underfill stiffness at these locations. The simulations are implemented using detailed elastic, plastic, visco-elastic and visco-plastic material data. In case of larger models a complexity reduction is required and implemented by using effective material data to improve computational time.