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Manual for LS-DYNA Wood Material Model 1431.5 PLASTIC FLOWThe plasticity algorithms limit the stress components once the failure criterion in equations 13 or 14 is satisfied. This is done by returning the stress state back to the yield surface.1 Our traditional approach for modeling plasticity is to partition the stress and strain tensors into elastic and plastic parts. Partitioning is done with return mapping algorithms that enforce the plastic consistency conditions. Such algorithms allow one to control plastic strain generation. In addition, return mapping algorithms with associated flow satisfy the second law of thermodynamics. Associated flow is discussed in appendix D. 1Two simple types of plasticity algorithms are those that reduce the moduli directly and those that scale back the stresses directly. Although simple to implement, such methods do not allow one to control plastic strain generation and do not necessarily satisfy the second law of thermodynamics. 1.5.1 Consistency Parameter UpdatesSeparate plasticity algorithms are modeled for the parallel and perpendicular modes by enforcing separate consistency conditions. Each consistency condition is derived in appendix D. The solution of each consistency condition determines the consistency parameters Dlรบรบ and Dl^. The Dl solutions, in turn, determine the stress updates. Parallel Modes The parallel failure criterion from equation 13 is redefined as f|| (I1, I4) ≥ 0, with:
where I1 and I4 are two of the five invariants of a transversely isotropic material. In this case, the expression Dl|| is:
Dl|| is calculated from specification of the total strain increments and the yield function
Perpendicular Modes The perpendicular failure criterion from equation 14 is redefined as f^ (I3, I4) ≥ 0, with:
where I2 and I3 are two of the five invariants of a transversely isotropic material. In this case, the expression for Dl^ is:
Dl^is calculated from specification of the total strain increments and the yield function
1.5.2 Elastoplastic Stress UpdatesThe stresses are readily updated from the total strain increments and the consistency parameters:
where: Total strain increments are calculated by the finite element code from the dynamic equations of motion and the time step. Each normal stress update depends on the consistency parameters and failure surface functions for both the parallel (Dl = Dl|| and f = f||) and perpendicular (Dl = Dl^ and f = f^) modes. Each shear stress update depends on just one consistency parameter and failure surface function. If neither parallel nor perpendicular yielding occurs For the stress updates in equation 27, the partial derivatives are:
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