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Theoretical Development of an Orthotropic Elasto-Plastic Generalized Composite Material Model

The need for accurate material models to simulate the deformation, damage and failure of polymer
matrix composites is becoming critical as these materials are gaining increased usage in the aerospace and
automotive industries. While there are several composite material models currently available within LS-
DYNA (Livermore Software Technology Corporation), there are several features that have been
identified that could improve the predictive capability of a composite model. To address these needs, a
combined plasticity and damage model suitable for use with both solid and shell elements is being
developed and is being implemented into LS-DYNA as MATi213. A key feature of the improved
material model is the use of tabulated stress—strain data in a variety of coordinate directions to fully define
the stress-strain response of the material. To date, the model development efforts have focused on
creating the plasticity portion of the model. The Tsai-Wu composite failure model has been generalized
and extended to a strain-hardening based orthotropic yield function with a nonassociative flow rule. The
coefficients of the yield function, and the stresses to be used in both the yield function and the flow rule,
are computed based on the input stress-strain curves using the effective plastic strain as the tracking
variable. The coefficients in the flow rule are computed based on the obtained stress—strain data. The
developed material model is suitable for implementation within LS-DYNA for use in analyzing the
nonlinear response of polymer composites.
As composite materials are gaining increasing use in aircraft components where impact resistance
under high energy impact conditions is important (such as the turbine engine fan case), the need for
accurate material models to simulate the deformation, damage and failure response of polymer matrix
composites under impact conditions is becoming more critical. Within LS-DYNA (Ref. 1), several
material models are available for application to the analysis of composites. For example, the Chang—
Chang failure model (Ref. 2) is utilized in MAT_22 and MAT_54. In these models, combinations of
ratios of stresses to failure strengths are utilized to predict fiber or matrix based failure. The response is
assumed be linear elastic, with limited capability to simulate the nonlinear shear response. In MATi22
the failure is assumed to be brittle, while in MATi54 the composite elastic constants are selectively
reduced based on the failure mode, and a gradual unloading is permitted until ultimate element failure is
reached. In MAT_58, a continuum damage model developed by Matzenmiller et a1 (Ref. 3) is employed,
where the initiation and accumulation of damage is assumed to be the primary driver of nonlinearity in
the composite response.