The research will examine models of rigidity percolation in random mechanical networks of springs. Networks are studied under pressure. These simple models may lead to insights into the phase diagrams of solids under pressure. It is proposed to examine the controversial question of rotational invariance of free standing solids with strained interiors which has important consequences for critical exponents. The reasons why Cauchy's relations are obeyed in these random systems are explored. The static and low frequency critical behavior will be pursued both numerically and using scaling relations.
