Nonlinear hardening material and stretching case implemention

tests/user_examples/extra_src/shared/inelastic_solid_hardening.h

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+/* ------------------------------------------------------------------------- *
+ *                                SPHinXsys                                  *
+ * ------------------------------------------------------------------------- *
+ * SPHinXsys (pronunciation: s'finksis) is an acronym from Smoothed Particle *
+ * Hydrodynamics for industrial compleX systems. It provides C++ APIs for    *
+ * physical accurate simulation and aims to model coupled industrial dynamic *
+ * systems including fluid, solid, multi-body dynamics and beyond with SPH   *
+ * (smoothed particle hydrodynamics), a meshless computational method using  *
+ * particle discretization.                                                  *
+ *                                                                           *
+ * SPHinXsys is partially funded by German Research Foundation               *
+ * (Deutsche Forschungsgemeinschaft) DFG HU1527/6-1, HU1527/10-1,            *
+ *  HU1527/12-1 and HU1527/12-4.                                             *
+ *                                                                           *
+ * Portions copyright (c) 2017-2023 Technical University of Munich and       *
+ * the authors' affiliations.                                                *
+ *                                                                           *
+ * Licensed under the Apache License, Version 2.0 (the "License"); you may   *
+ * not use this file except in compliance with the License. You may obtain a *
+ * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.        *
+ *                                                                           *
+ * ------------------------------------------------------------------------- */
+/**
+ * @file 	inelastic_solid_hardening.h
+ * @brief 	These are classes for define properties of elastic solid materials.
+ *			These classes are based on isotropic linear elastic solid.
+ * 			Several more complex materials, including neo-hookean, FENE noe-hookean
+ *			and anisotropic muscle, are derived from the basic elastic solid class.
+ * @author	Xiangyu Hu and Chi Zhang
+ */
+#pragma once
+
+#include "inelastic_solid.h"
+
+namespace SPH
+{
+
+/**
+ * @class NonlinearHardeningPlasticSolid
+ * @brief Class for plastic solid with nonlinear hardening
+ */
+class NonLinearHardeningPlasticSolid : public HardeningPlasticSolid
+{
+protected:
+	Real saturation_flow_stress_, saturation_exponent_;
+public:
+  /** Constructor */
+  explicit NonLinearHardeningPlasticSolid(Real rho0, Real youngs_modulus, Real poisson_ratio, Real yield_stress,
+    Real hardening_modulus, Real saturation_flow_stress, Real saturation_exponent)
+    : HardeningPlasticSolid(rho0, youngs_modulus, poisson_ratio, yield_stress, hardening_modulus),
+    saturation_flow_stress_(saturation_flow_stress), saturation_exponent_(saturation_exponent)
+  {
+    material_type_name_ = "NonLinearHardeningPlasticSolid";
+
+  };
+  virtual ~NonLinearHardeningPlasticSolid() {};
+
+ Real NonlinearHardening(Real hardening_parameter_pre)
+	{
+	  return  (hardening_modulus_ * hardening_parameter_pre + yield_stress_
+			       + (saturation_flow_stress_ - yield_stress_)* (1 - exp(-saturation_exponent_ * hardening_parameter_pre)));
+	};
+
+	Real NonlinearHardeningDerivative(Real hardening_parameter_pre)
+	{
+		return  (hardening_modulus_+ saturation_exponent_ * (saturation_flow_stress_ - yield_stress_)
+			       * exp(-saturation_exponent_ * hardening_parameter_pre));
+	};
+
+	/** compute the stress through defoemation, and plastic relaxation. */
+	virtual Matd PlasticConstitutiveRelation(const Matd  &F,  size_t index_i, Real dt = 0.0)
+	{
+
+  		Matd normalized_F =  F * pow(F.determinant(), -OneOverDimensions);
+		Matd normalized_be = normalized_F * inverse_plastic_strain_[index_i] * normalized_F.transpose();
+		Real normalized_be_isentropic = normalized_be.trace() * OneOverDimensions;
+		Matd deviatoric_PK = DeviatoricKirchhoff(normalized_be - normalized_be_isentropic * Matd::Identity());
+		Real deviatoric_PK_norm = deviatoric_PK.norm();
+
+		Real relax_increment = 0.0;
+		Real trial_function =  deviatoric_PK_norm - sqrt_2_over_3_ * NonlinearHardening(hardening_parameter_[index_i]);
+		if (trial_function > 0.0)
+		{
+			Real renormalized_shear_modulus = normalized_be_isentropic * G0_;        
+			while (trial_function > 0.0)
+			{		
+				Real function_relax_increment_derivative = -2.0 * renormalized_shear_modulus
+					* (1.0 + NonlinearHardeningDerivative(hardening_parameter_[index_i] + sqrt_2_over_3_ * relax_increment) / 3.0 / renormalized_shear_modulus);
+				relax_increment -=  trial_function / function_relax_increment_derivative;
+
+				trial_function = deviatoric_PK_norm
+					- sqrt_2_over_3_ * NonlinearHardening(hardening_parameter_[index_i] + sqrt_2_over_3_ * relax_increment)
+					- 2.0 * renormalized_shear_modulus * relax_increment;	
+			}      
+			hardening_parameter_[index_i] += sqrt_2_over_3_ * relax_increment;
+			deviatoric_PK -= 2.0 * renormalized_shear_modulus * relax_increment * deviatoric_PK / deviatoric_PK_norm;
+			normalized_be = deviatoric_PK / G0_ + normalized_be_isentropic * Matd::Identity();	
+
+		}
+
+		Matd inverse_normalized_F = normalized_F.inverse();
+		Matd inverse_normalized_F_T = inverse_normalized_F.transpose();;
+		inverse_plastic_strain_[index_i] = inverse_normalized_F * normalized_be * inverse_normalized_F_T;
+
+		return (deviatoric_PK + VolumetricKirchhoff(F.determinant()) * Matd::Identity()) * inverse_normalized_F_T;
+
+	};
+
+	virtual NonLinearHardeningPlasticSolid *ThisObjectPtr() override { return this; };
+};
+
+} // namespace SPH

tests/user_examples/xj_stretching/CMakeLists.txt

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+STRING(REGEX REPLACE ".*/(.*)" "\\1" CURRENT_FOLDER ${CMAKE_CURRENT_SOURCE_DIR})
+PROJECT("${CURRENT_FOLDER}")
+
+SET(LIBRARY_OUTPUT_PATH ${PROJECT_BINARY_DIR}/lib)
+SET(EXECUTABLE_OUTPUT_PATH "${PROJECT_BINARY_DIR}/bin/")
+SET(BUILD_INPUT_PATH "${EXECUTABLE_OUTPUT_PATH}/input")
+SET(BUILD_RELOAD_PATH "${EXECUTABLE_OUTPUT_PATH}/reload")
+
+add_executable(${PROJECT_NAME})
+aux_source_directory(. DIR_SRCS)
+target_sources(${PROJECT_NAME} PRIVATE ${DIR_SRCS})
+target_link_libraries(${PROJECT_NAME} extra_sources_2d)
+set_target_properties(${PROJECT_NAME} PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${EXECUTABLE_OUTPUT_PATH}")
+
+add_test(NAME ${PROJECT_NAME}
+		 COMMAND ${PROJECT_NAME}
+		 WORKING_DIRECTORY ${EXECUTABLE_OUTPUT_PATH})