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On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutitive equations. (English) Zbl 0994.74004
Summary: On the basis of continuum constitutive models (stress vs. strain), the introduction of strong discontinuity kinematics (considering jumps in the displacement fields across a discontinuity interface) induces projected discrete constitutive models (traction-displacement jumps) in a consistent manner. Therefore, this projection provides possible links between classical continuum strain localization analysis and nonlinear (decohesive) fracture mechanics. The strong discontinuity analysis shows that (bandwidth based) regularization of the hardening/softening parameter is the crucial modification to be done on the continuum model to achieve such a projection, and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format. This methodology is illustrated on two classical families of nonlinear constitutive models (scalar continuum damage and elasto-plasticity), for which we derive the corresponding discrete constitutive models and strong discontinuity conditions.

MSC:
74A45Theories of fracture and damage
74A20Theory of constitutive functions
74R20Anelastic fracture and damage