When modeling low-density foams, it is important to consider potential failure under tensile loading. In LS-DYNA, the most popular constitutive material model is MAT_LOW_DENSITY_FOAM (MAT_057), in which the default treatment of foams under tensile loading is linear with no failure. The Elastic Modulus (Emax) in tension is computed to be the max( max(slope of the stress-strain curve in compression), E). With this treatment, the element does not fail and its stiffness in tension is based on Emax.

One option provided by LS-DYNA is to input a limiting stress in the form of TC (Tensile cut-off stress) which essentially models a elastic-perfectly plastic behavior in tension. Under tensile loading, when the tensile stress reaches the value of TC, the stress is min( tensile_stress, TC) for any further loading.

In addition to TC, we can also specify FAIL = 1, to reset the tensile stress to zero for any tensile loading beyond TC thereby eliminating the element’s capacity to offer any further resistance under further tensile loading. It must be noted that when tensile stress reaches TC with FAIL =1, the element is NOT eroded but simply loses resistance along tensile direction. Upon unloading, the element continues to have zero stress until it reaches a relative volume of 1 (original volume) after which the stress is governed by the compressive behavior.